Toward predictable hydrochar properties at scale: a critical review of design of experiments-guided machine learning in hydrothermal carbonization

1 Introduction

1.1 Context and importance of hydrothermal carbonization for biomass valorization

Hydrothermal carbonization (HTC) is more than a technological refinement. It represents a shift in how biogenic residues can be managed and valorized (Yang et al., 2026; Mikusińska et al., 2023; Mkilima, 2025; González-Arias et al., 2022; Ţurcanu et al., 2022; Zhou, 2026; Singh, 2024a). As Funke and Ziegler (2010) point out in their literature review, HTC operates under controlled temperature and autogenous pressure to convert wet biomass efficiently into value-added products. In contrast to more energy-intensive routes such as pyrolysis, HTC avoids the need for energy-demanding pretreatments, particularly drying (Funke and Ziegler, 2010). This approach aligns well with circular-economy strategies and provides a practical pathway for supporting the ecological transition.

The benefits of HTC are particularly evident in the energy domain. Heilmann and others have highlighted hydrochar production as a solid fuel with properties comparable to those of fossil coal but with a markedly lower environmental footprint. This product combines high energy density with low moisture content, making it a promising candidate for displacing fossil fuels (Reza, 2014). This energy-oriented pathway is also associated with a substantial potential to mitigate greenhouse gas emissions. Hydrochar also offers compelling opportunities for the development of advanced materials (Aveling et al., 2025). Hydrochar is an attractive precursor for the production of activated carbon. These materials, widely applied in gas purification and wastewater treatment, often outperform conventional counterparts while exhibiting a lower environmental footprint (Sevilla et al., 2011; Gallifuoco et al., 2017).

In environmental applications, HTC plays an important role by contributing to water treatment. In their synthesis, Kambo, Minaret, and Dutta (2018) showed that hydrochar can be particularly effective for removing contaminants such as heavy metals and persistent organic compounds. These findings underscore the versatility of HTC within modern treatment systems (Kambo, Minaret, and Dutta, 2018). Nevertheless, despite its advantages, HTC still faces major industrial challenges. As noted by Xiao et al. (2012), a key limitation is the difficulty of accurately predicting final product properties. Variability in reaction conditions, including temperature and feedstock chemical composition, complicates the development of reliable predictive models (Xiao et al., 2012).

At the industrial scale, energy-related challenges also remain. Liu and Balasubramanian (2012) emphasized that the liquid by-products generated during HTC require dedicated management to avoid secondary environmental impacts. Integrated strategies, including coupling with energy-recovery systems, are being explored to improve the overall process efficiency (Liu and Balasubramanian, 2012). To fully realize HTC’s potential, expanding the industrial applications of its derived products is essential. As noted by Shen (2019), hydrochar could be deployed in high-value fields such as supercapacitor electrodes and advanced catalysts, thereby creating new avenues for technological development and economic opportunity.

Ultimately, HTC goes beyond waste valorization technology. A growing body of studies indicates that it can simultaneously address environmental and industrial challenges by enabling more sustainable pathways to convert wet biogenic residues into value-added products. As research continues to refine process understanding, scale-up strategies (Dang, 2024), and application-specific tailoring of hydrochar and liquid fractions (Ighalo et al., 2025), HTC could become an important component of broader decarbonization and circular-economy frameworks.

1.2 Roles and challenges of modeling and optimization in the HTC industry

In the HTC industry, modeling and optimization are not merely technical tools. They act as essential drivers for improving how biomass resources are processed and valorized. Key operating variables, including temperature, residence time, and the solid-to-liquid ratio, function as strategic levers for achieving robust process performance (Singh, 2024b). As emphasized across the literature, rigorous control and rational tuning of these parameters are critical for maximizing both energy and material yields while minimizing environmental impacts (Yin et al., 2023; Lucian and Fiori, 2017; Heidari et al., 2019; Ischia and Fiori, 2021).

Optimization can substantially extend current industrial capabilities by enabling systematic improvements in both process performance and product quality. Carefully selected operating adjustments can increase hydrochar energy density while also enhancing adsorption-related properties relevant to water and gas purification. When supported by sophisticated algorithms, these targeted strategies can improve efficiency and deliver meaningful economic benefits (Gallifuoco, 2019; Román, 2018; Maniscalco et al., 2020). Modeling plays an equally central role by providing a structured basis for navigating complex industrial process spaces. It enables the prediction of outcomes under varied conditions, thereby reducing reliance on costly trial-and-error experimentation. As illustrated by Kambo and Dutta (2015), robust predictive models can be used to evaluate multiple scenarios and identify operating configurations that are best suited to a given industrial context.

Beyond the purely technical dimension, the integration of modeling and optimization reflects an ambitious vision for the future of the HTC industry (Ubene et al., 2022). These tools do more than improve efficiency. They also create the conditions for disruptive innovation. One can envisage biomass conversion being steered with high precision to deliver application-specific products or intelligent systems adjusting operating parameters in real time to accommodate unexpected changes in feedstock supply and quality. This transformative potential positions HTC not only as a conversion technology but also as a platform for scientific and industrial exploration that continually pushes the boundaries of what is achievable.

1.3 Limitations of traditional approaches and the rise of new prediction and optimization methods

Traditional process-optimization approaches, largely based on empirical models such as linear regression and response surface methodology, have long been regarded as foundational tools in industry. They provide straightforward and cost-effective solutions for systems of moderate complexity (Rao, 2011). However, as industrial processes increasingly exhibit interconnected and strongly nonlinear behavior, the limitations of these approaches have become more apparent (Luthfi et al., 2024a).

Empirical models, particularly linear regression, remain attractive because they are simple to implement and can deliver rapid, first-pass predictions. However, they are poorly suited to capturing the subtleties of complex interactions and nonlinear phenomena, as encountered in HTC, where reaction pathways are intrinsically nonlinear and multivariate (Zabiri et al., 2018). In such settings, traditional linear models typically fail to represent higher-order interactions and cross-effects among variables, which can lead to oversimplified or inaccurate predictions (Zabiri et al., 2018). More fundamentally, the assumption of linear relationships between operating variables is often unrealistic in complex industrial environments. In reactors, for example, heat and mass transfer commonly exhibit strongly nonlinear dependencies that shape the system response. Under these conditions, classical linear formulations do not reproduce the true process dynamics, which motivates the use of more advanced nonlinear models to describe coupled interactions and transport mechanisms with greater fidelity (Ip and Wan, 2012).

To address the shortcomings of purely empirical approaches, the design of experiments (DoE) provides a structured framework that improves data acquisition and enables a more rigorous analysis of interactions among process variables. By reducing the number of experiments required, DoE strategies lower experimental cost and effort while maximizing the information content of the resulting dataset. In a study on gas purification processes, the application of DoE was reported to increase exergy efficiency by more than 6% while reducing prediction errors to below 4% (Shi, 2020). Response surface methods, which constitute a core component of DoE, also enable the identification of non-trivial relationships, including quadratic and cubic effects that are often overlooked by traditional empirical approaches. Such models are particularly useful for describing coupled interactions in advanced chemical processes (Parsafard, 2024).

In contrast, the adoption of machine learning models for process optimization represents a fundamental shift (Wolday and Ramteke, 2023). These tools can handle large and complex datasets and can uncover latent relationships that are often missed by classical approaches. For instance, artificial neural networks and Gaussian process regression have been used to predict the outcomes of highly nonlinear processes with high accuracy while explicitly accounting for uncertainty (Gunnell et al., 2022; Akbari, 2023). Hybrid strategies that combine machine learning algorithms with design of experiments-based modeling further illustrate this potential. The integration of neural networks with genetic algorithms, for example, has been shown to substantially reduce the need for exhaustive experimentation while enabling the optimization of critical operating parameters in complex process systems (Kumar and Chhabra, 2024). The limitations of traditional empirical approaches, therefore, highlight the need for more advanced methodologies. Design of experiments and machine learning models offer complementary routes to address the challenges of optimizing complex systems such as the HTC process.

This review provides an in-depth examination of recent work on innovative strategies that combine design of experiments and machine learning (ML) for hydrothermal carbonization. We adopt a clear and structured organization to provide a comprehensive understanding of how these two methodological frameworks interact within the context of the HTC process. We first introduce the methodological foundations of DoE and ML, covering key principles, the specific strengths of each approach, and the tools most frequently applied in HTC studies. We then emphasize their complementarity in streamlining experimentation and strengthening predictive capabilities. We next analyze major contributions from the scientific literature, grouping studies according to their primary objectives, including optimization of reaction parameters, prediction of hydrochar properties, reduction of experimental effort, and the development of HTC-derived materials.

This organization highlights how the DoE–ML coupling can address the multifactorial nature of HTC and unlock underexplored opportunities. We then provide a critical assessment of current approaches. Although DoE is effective for structuring experimentation, it can be constrained by initial requirements in time and resources. In parallel, ML models, despite their ability to capture complex relationships, raise persistent challenges related to data quality and the interpretability of predictions. We also discuss practical constraints and costs associated with industrial implementation of combined DoE–ML strategies. A central contribution of this review is to delineate the synergies between DoE and ML. We examine how DoE can generate structured datasets that strengthen ML training, improving predictive accuracy while limiting computational burden. Practical case studies illustrate these dynamics and show how combined toolchains can enhance process efficiency and economic performance. Finally, we adopt a forward-looking perspective and propose strategies for the more effective integration of DoE and ML into industrial value chains. We underscore the importance of interdisciplinary collaboration to address technical and industrial challenges and to support the transition toward a sustainable circular economy. In addition, this review contributes to a clearer understanding of DoE methodology in the HTC context and clarifies common misconceptions regarding its applications and limitations. Overall, our objective is not only to clarify the contributions and challenges of DoE and ML but also to stimulate future research and inform their deployment in industrial settings.

2 Scope and literature-search approach of the critical review

2.1 Search strategy, eligibility criteria, and critical synthesis

This review used a structured literature search and critical synthesis approach to identify peer-reviewed studies addressing the application of design of experiments, response surface methodology (RSM), machine learning, and integrated DoE–ML workflows in hydrothermal carbonization.

Literature searches were conducted in March 2025 and updated in December 2025 using ScienceDirect and SpringerLink. These publisher platforms were used to identify relevant literature in chemical engineering, biomass conversion, environmental applications, and data-driven modeling. Searches were restricted to English-language peer-reviewed journal articles and review papers published between 2010 and 2025.

Two complementary search streams were applied. The first focused on experimental-design approaches in hydrothermal carbonization using the following terms: (“hydrothermal carbonization” OR “hydrochar”) AND (“design of experiments” OR “DoE” OR “response surface methodology” OR “RSM” OR “Box-Behnken” OR “central composite”). The second focused on machine-learning applications using the following terms: (“hydrothermal carbonization” OR “hydrochar” OR “hydrothermal pretreatment” OR “hydrothermal treatment”) AND (“machine learning” OR “artificial intelligence” OR “neural network” OR “random forest” OR “support vector” OR “XGBoost” OR “Gaussian process”).

Studies were considered in the core critical synthesis when they explicitly addressed hydrothermal carbonization and reported the use of DoE, RSM, machine learning, or related modeling approaches for process optimization, prediction of hydrochar properties, or assessment of critical process variables. Studies outside the HTC field, studies without a clear optimization or modeling component, and sources lacking sufficient methodological information for critical appraisal were not included in the main comparative analysis.

This review does not claim to provide an exhaustive systematic evidence synthesis or a quantitative meta-analysis. Its purpose is to critically evaluate the methodological positioning, validation practices, limitations, and transferability of reported DoE- and ML-based approaches. The review is, therefore, limited by the coverage and indexing of the selected search platforms, as well as by the substantial heterogeneity of feedstocks, reactor configurations, operating conditions, target properties, and validation protocols reported across the literature.

2.2 Descriptive distribution of records retrieved from the selected platforms

To contextualize the scope of the literature identified through the selected platforms, the retrieved records were examined by publication year, search stream, and source platform. This descriptive analysis distinguished DoE- and ML-related records retrieved from ScienceDirect and SpringerLink.

As shown in Figure 1, the annual distribution of retrieved records varied across the two selected platforms and between the two methodological search streams. Within the applied search strategy, the number of retrieved records increased during the later years of the search period, particularly for the ML-related stream. This pattern is presented only to contextualize the body of literature identified through the selected search approach.

These results should nevertheless be interpreted with caution. They reflect platform-specific retrieval outputs and may be influenced by the coverage and indexing practices of each platform, the exact search syntax, and the inclusion of studies addressing related hydrothermal processes. Accordingly, they should not be interpreted as an exhaustive bibliometric representation of the entire hydrothermal carbonization literature. Rather, the descriptive distribution shown in Figure 1 supports the relevance of both DoE and ML approaches within the selected body of the literature. The subsequent sections critically examine how these approaches have been applied, their respective methodological limitations, and the extent to which genuinely integrated DoE-guided ML workflows have been demonstrated in the HTC field.

Overall, this platform-specific distribution confirms that both DoE- and ML-related studies are represented in the selected literature. However, retrieval counts alone do not establish the extent or effectiveness of genuinely integrated DoE–ML workflows in HTC. The following sections, therefore, focus on the methodological nature, validation practices, and limitations of the reported approaches rather than on publication counts.

3 Hydrothermal carbonization process: key variables and challenges

3.1 HTC fundamental principles

Before discussing the fundamental principles of hydrothermal carbonization, it is important to clarify how it differs from other hydrothermal conversion routes. These processes, including hydrothermal liquefaction (HTL) and hydrothermal gasification, primarily differ in the temperature and pressure domains in which they operate, which directly determines their products and target applications (Teoh et al., 2024). Hydrothermal carbonization operates in a relatively moderate regime, typically between 180 °C and 250 °C, with autogenous pressures of approximately 20 bar. In contrast, hydrothermal gasification, which is used to generate gases such as hydrogen, requires temperatures above 374 °C and extreme pressures exceeding 220 bar, corresponding to the supercritical region of water (Pecchi et al., 2022). Hydrothermal liquefaction, often applied to produce liquid biofuels such as biocrude, operates at intermediate temperatures, typically 250 °C–350 °C, and at higher pressures than HTC, commonly in the range of 50–200 bar (Yang, 2020).

These distinctions are clearly captured in the water phase diagram (cf. Figure 2), where each process occupies a specific operating domain. HTC lies in the subcritical region, which favors the formation of solid products such as hydrochar through reaction pathways dominated by dehydration and decarboxylation (Ro et al., 2020). This operating window makes HTC particularly energy-efficient for processing wet biomass compared with other hydrothermal techniques that require substantially higher energy inputs (Güleç et al., 2022).

In addition, hydrothermal gasification and HTL require more complex technological investments to handle high-pressure and high-temperature conditions, which increase both capital and operating costs (Cao et al., 2021). Comparative analyses have shown that HTC is often preferred for the valorization of agricultural and municipal wastes because of its energy efficiency and operational simplicity (Lachos-Perez et al., 2022). Nonetheless, the products obtained from each route address distinct end-use needs, which makes these methods complementary rather than directly competitive (Hussin et al., 2023).

Hydrothermal carbonization is, therefore, well positioned for converting wet biomass into solid products such as hydrochar while maintaining relatively high energy efficiency due to its mild operating conditions. HTC is rooted in an improved understanding of the natural mechanisms underlying coal formation. The process is often described as a controlled acceleration of geological transformations that would otherwise occur over millions of years, and it has been refined to provide a more sustainable pathway for wet biomass valorization (Marinovic et al., 2015). As reported by Romano et al. (2023), early twentieth-century investigations into the behavior of materials under high pressure helped establish the scientific foundations of the process (Romano et al., 2023). Since then, HTC has gained momentum through modern applications within circular-economy frameworks.

The core principle of hydrothermal carbonization relies on the thermal decomposition of biomass in an aqueous medium at temperatures typically ranging from 180 °C to 250 °C, under autogenous pressures that can reach approximately 20 bar. These conditions create a closed reactive environment that promotes a cascade of coupled chemical pathways, including hydrolysis, decarboxylation, dehydration, and recondensation reactions (Pauline and Joseph, 2020). Unlike processes such as pyrolysis, which require dry feedstocks, HTC is well suited to wet raw materials and therefore avoids energy-intensive pretreatment steps. For example, Wang et al. (2019) reported that using high-moisture biomass can markedly reduce the energy costs associated with prior drying (Wang et al., 2019).

The products generated by HTC are diverse. Hydrochar, the solid phase produced during HTC, is a versatile carbonaceous material with tunable properties and represents the primary target product. It was initially considered mainly a solid biofuel, with a heating value comparable to lignite, typically 15–25 MJ kg^-1 (Kapetanakis, 2021). However, hydrochar has attracted substantial interest for higher-value applications. After physical or chemical activation, it can be converted into high-performance adsorbents for water remediation. For instance, a biomass-derived hydrochar functionalized with carboxylate groups reached an exceptional adsorption capacity of 1,155 mg g^-1 for methylene blue in solution​ (Li et al., 2019), exceeding that of conventional activated carbons. More broadly, the literature indicates that activated hydrochars often exhibit enhanced porosity and increased surface functionality, which are favorable for pollutant capture (Zhou, 2022; El Ouadrhiri et al., 2021; El Ouadrhiri et al., 2023; Ercegović et al., 2024; Hu et al., 2024; Ding, 2024; Gautam, 2024; Puccini et al., 2018; Kimbi Yaah et al., 2021; Han et al., 2017; Xiao et al., 2020; Tran et al., 2020). As discussed by Shen (2019), these properties also make hydrochar a competitive candidate for replacing fossil-derived carbons in several industrial sectors (Shen, 2019). Other studies exploit the electrical conductivity and structural features of hydrochar to develop advanced electrode materials for energy storage. In particular, hydrochars doped with nitrogen, phosphorus, or metal species can display high electrochemical performance and are therefore considered promising candidates for supercapacitors and battery systems​ (Prieto et al., 2024). In addition, the liquid phase produced during HTC, which is rich in organic acids such as furfural and acetic acid and contains leached nutrients, can be further valorized rather than treated as waste. It has been investigated for nutrient recovery, including nitrogen and phosphorus, for fertilization purposes, and for biological processing routes such as coupled anaerobic digestion for biogas production (Maniscalco et al., 2020). This simultaneous valorization of the solid and liquid fractions reinforces the role of HTC within circular-economy strategies for organic waste management.

Owing to these advantages, HTC has attracted increasing industrial interest over the past few years. According to Romano et al. (2023), more than 200 companies and organizations worldwide are reported to be involved in the development of this technology​. Pilot and full-scale facilities have emerged, particularly for the treatment of municipal sludge and organic wastes. As early as 2010, Ingelia commissioned the first continuous HTC plant in Spain, designed to process up to 14,000 tons of green and municipal waste per year, producing biocoal with a higher heating value (HHV) of 24 MJ kg^-1 and fertilizer concentrates (Romano et al., 2023). The largest HTC facility reported to date, operated by AVA-CO₂ in Germany, processes approximately 8,400 tons of biomass per year, marking a clear step toward industrial-scale deployment (Ho et al., 2024). In China, an HTC unit treating municipal sludge from a catchment serving population equivalent of 500,000 has been operating in Jining since 2016, producing approximately 7,000 tons of vaporizable hydrochar per year. Collectively, these initiatives illustrate the increasing technical maturity of HTC and its progressive adoption for the sustainable management of wet waste. Nevertheless, despite these successes, key challenges remain. The intrinsic variability of biomass feedstocks in terms of composition and moisture content, together with the multiplicity of operating parameters, makes the prediction and standardization of process performance difficult. Optimizing hydrochar yield or tailoring its properties, including heating value, energy density, and contaminant content, requires a more detailed understanding of how each operating variable, such as temperature, residence time, pH, solids loading, and catalysts, influences process outcomes and how these variables interact (Luthfi et al., 2024a). In addition, the long-term environmental and economic impacts must be evaluated rigorously, including energy balance, greenhouse gas emissions, and effluent ecotoxicity, to ensure that the benefits of HTC outweigh the potential costs or negative externalities. These optimization and sustainability requirements motivate advanced experimental and modeling approaches, prominently including the design of experiments and machine learning methods discussed throughout this review.

3.2 Hydrothermal carbonization process parameters

Hydrochar performance and composition arise from a delicate balance among several operating parameters, with temperature, residence time, the solid-to-liquid ratio (S/L), pressure, and reaction-medium pH playing central roles. Each of these factors controls both process yield and the physicochemical properties of the final solid, thereby shaping its energy potential and structural stability.

3.2.1 Temperature

Temperature is generally considered the most influential parameter in HTC (Petrović et al., 2024; Canencio et al., 2024). Increasing temperature accelerates carbonization and typically yields a more carbon-rich, energy-dense hydrochar but at the expense of mass yield (Petrović et al., 2024). For a given organic residue, for example, increasing the temperature from 180 °C to 260 °C can reduce hydrochar yield from approximately 57% to 38% while increasing the heating value from approximately 15 to 17 MJ kg^-1. Similar trends have been reported for sludges and manures, where yield decreases from roughly 59% to 50% as temperature increases from 200 °C to 280 °C, accompanied by an increase in HHV from 12.4 to 16.0 MJ kg^-1 (Petrović et al., 2024). Lower temperatures, at or below 200 °C, tend to favor hydrochars enriched in oxygen-containing functional groups, which can be advantageous for pollutant adsorption, whereas higher temperatures, at or above 240 °C, produce more aromatic and hydrophobic hydrochars with improved properties for use as solid fuels (Masoumi et al., 2021).

In general, increasing the reaction temperature from 180 °C to 300 °C promotes dehydration and decarboxylation reactions, thereby lowering oxygen content and increasing the relative carbon fraction in the final solid. Higher temperatures have been shown to enhance hydrochar thermal stability and heating value, although these gains are typically achieved at the expense of overall yield (Sui et al., 2023). In the case of livestock wastes, increasing HTC temperature has also been associated with improved carbon retention and higher thermal stability, which strengthens the suitability of the resulting hydrochar as a biofuel (Li et al., 2022).

Temperature can further influence the conversion of animal residues by altering elemental partitioning and the chemical composition of the process liquid phase (Devnath et al., 2024). A recent study similarly reported that higher temperatures improve thermal stability and reduce H/C and O/C ratios in hydrochars derived from agricultural residues, thereby increasing their potential as solid fuels (Sui et al., 2023). In practice, temperature is commonly optimized according to the targeted outcome, with approximately 180 °C–200 °C used to maximize yield or preserve surface functionalities and approximately 240 °C–260 °C selected to maximize energy densification (ED) and the extent of carbonization (Ahmed, 2024; Köchermann et al., 2018; Xie et al., 2024; Czerwińska, Śliz, and Wilk, 2022).

3.2.2 Residence time

Residence time influences the chemical structuring of hydrochar by modulating polymerization and aromatization reactions. Longer residence times generally allow carbonization to proceed further, through continued hydrolysis, polycondensation, and aromatization, which tends to reduce solid yield while increasing the degree of carbonization of the hydrochar (Kozyatnyk et al., 2023). Overall, this effect is typically less pronounced than that of temperature. Reaction time can, nonetheless, affect conversion efficiency, chemical composition, and the physical properties of the resulting hydrochar. Several studies indicate that most biomass conversion occurs during the first hours of reaction, with hydrochar properties continuing to evolve as residence time increases. For example, work on agricultural residues showed that increasing residence time from 30 min to 6 h led to a progressive increase in energy density, although beyond a certain threshold further improvements became marginal (Zhang et al., 2015). For sewage sludge, extended residence time has been reported to enhance the hydrophobicity of hydrochars, which can facilitate storage and handling (Czerwińska et al., 2024). Other authors reported that varying residence times of 0.5, 1, and 2 h did not markedly change hydrochar physicochemical properties, which remained broadly similar across these conditions. However, a longer residence time of 2 h produced a more hydrophobic hydrochar, thereby improving dewatering performance.

3.2.3 Pressure

In HTC reactors, pressure is typically autogenous and generated by water at the reaction temperature, commonly on the order of 2–4 MPa for 200 °C–250 °C. It is, therefore, closely coupled to temperature. Although pressure is sometimes treated as an operating variable, its direct effect is often reported to be less pronounced than that of temperature or residence time (Canencio et al., 2024). The primary role of pressure is to maintain water in the liquid phase. In practice, pressures generally exceed 2 MPa, which keeps water liquid between approximately 180 °C and 250 °C and provides the hydrothermal environment required to promote key reactions such as hydrolysis, dehydration, and decarboxylation (Wilk and Magdziarz, 2016). Several studies indicate that pressure can nonetheless influence reaction kinetics by facilitating the breakdown of complex lignocellulosic structures and steering hydrochar formation toward specific characteristics, including carbon content, aromaticity, and thermal stability (Pauline and Joseph, 2020). Pressure also affects product distribution among solid, liquid, and gas phases by controlling the solubility and retention of organic by-products in the aqueous phase. In this respect, insufficient pressure may promote excessive formation of volatile compounds, reducing both hydrochar yield and quality, whereas adequate pressure can favor the condensation of reactive intermediates into a carbonaceous solid (Shen, 2019). Recent work further suggests that the combined temperature-pressure regime can be tuned to adjust final hydrochar properties, including porosity, hydrophobicity, and energy density, thereby enabling alignment with targeted energy or environmental applications (Kladisios and Sagia, 2018).

At an industrial scale, pressure management is critical for reactor safety and mechanical integrity. Modular multi-reactor designs, such as those adopted in the Ingelia and AVA-CO₂ processes, have been used to distribute pressure demands and increase throughput without disproportionately increasing the pressure rating of individual units​ (Ho et al., 2024). Overall, pressure is typically maintained at a level sufficient to ensure hydrothermal conditions, while optimization efforts focus more strongly on temperature, residence time, and reaction proportions to tune process outcomes.

3.2.4 Solid-to-liquid ratio

The solid-to-liquid ratio, often expressed as the biomass-to-water ratio, is a key parameter that influences both hydrothermal carbonization reactions and the quality of the resulting hydrochar (De Francesco et al., 2024). This ratio governs not only the concentration of reactants but also the intensity of biomass-water interactions and the transport of reaction intermediates within the reactive medium. Several studies have reported that increasing the solid-to-liquid ratio, which corresponds to reducing the amount of water, tends to improve the energy-related properties of hydrochar, notably carbon content and heating value. It can also promote the formation of secondary char through the recombination of soluble intermediates (Aliyu et al., 2022). In contrast, overly low S/L ratios, with excess water, dilute reactive intermediates and can limit the formation of condensed carbon networks, thereby decreasing the energy density of the final product (Ghaziaskar, 2018). In addition, higher S/L ratios reduce the volume of post-process liquids, which can facilitate management of effluents enriched in soluble organic compounds (Wilk et al., 2020). However, reducing water content may increase slurry viscosity and limit heat and mass transfer, potentially slowing key reactions such as hydrolysis (Guo et al., 2016). Recent studies, particularly on wet wastes such as sludge and manure, have suggested that S/L ratios close to 1:1 can maximize both energy yield and material valorization while limiting dilution requirements (Aliyu et al., 2022). Overall, the solid-to-liquid ratio represents a critical optimization lever in HTC, shaping hydrochar quality, overall energy efficiency, and the environmental management burden associated with the process.

3.2.5 Catalysts and additives

The addition of catalysts can markedly influence reaction pathways during HTC. Acidic, basic, metallic, and carbon-based catalysts can substantially alter biomass degradation routes by promoting or inhibiting key reactions (Rasaq et al., 2024). As a result, catalysts can accelerate reaction kinetics and, in many cases, improve both hydrochar yield and energy-related quality, for example, by increasing fixed carbon content or reducing volatile matter. Several studies report that catalysts such as zinc chloride, often applied to cellulosic wastes, promote the formation of highly porous hydrochars enriched in oxygen-containing functional groups, thereby enhancing their potential for pollutant adsorption applications (Rosly et al., 2023). In parallel, basic or metallic catalysts can steer conversion toward a higher production of vaporizable liquid compounds, including oils rich in phenolic species (Rasaq et al., 2024). Catalyst selection must, therefore, be carefully matched to the biomass type and the targeted outputs, whether hydrochar, liquid products, or gases, because certain catalysts may also promote excessive fragmentation and reduce solid yield.

Organic or inorganic additives, including dopants such as nitrogen and phosphorus, can further impart specific functionalities to hydrochars, which is particularly relevant for advanced applications such as heterogeneous catalysis or CO₂ capture (Tumkot, 2018). Heterogeneous catalysts, including metals and metal oxides, have also been explored. For example, adding 2%–4% Fe(NO₃)₃ during the HTC of wood increased the degree of carbonization and raised the hydrochar higher heating value from approximately 26.8–30.1 MJ kg^-1, while leaving the mass yield nearly unchanged at approximately 55%​ (Petrović et al., 2024). In this case, iron catalyzes dehydration and aromatization pathways, producing a more energy-dense hydrochar. Similarly, nickel-based catalysts supported on hydrochar have been reported to enhance the energetic valorization of biomass by intensifying decomposition reactions and increasing carbon enrichment in the solid products. Recent work indicates that Ni catalysts supported on hydrochar can substantially improve conversion of lignocellulosic residues, although the achieved HHV values depend on the specific biomass and operating conditions (Khandelwal and Dalai, 2024). Catalysts can also modify hydrochar texture, including surface area and pore volume. Certain metal oxides or salts, such as zinc chloride, can act as porosity templates or promote controlled partial gasification, inducing the formation of porous networks and carbon microspheres (Susanti et al., 2024). Overall, the literature suggests that homogeneous catalysts, including acids and bases, accelerate key steps such as hydrolysis and decarboxylation and can shift the solid-liquid partitioning (El Ouadrhiri et al., 2021). In contrast, heterogeneous catalysts, including supported metals, molecular sieves, and doped activated biochars, can be used to tailor hydrochar structure and functionality, including specific surface area and heteroatom doping (Rasaq et al., 2024). Accordingly, controlling the use of catalysts and additives in HTC emerges as a key strategy for tuning hydrochar structure, composition, and functional properties to meet the requirements of targeted energy and environmental applications.

As a synthesis, the complex interplay among these operating parameters and their sometimes opposing effects on process outcomes is summarized in the figure below (cf. Figure 3). The figure highlights the unavoidable trade-off between mass yield, which is favored under milder conditions, and hydrochar energy quality, which is typically enhanced under more severe conditions.

3.3 Hydrochar properties

Hydrochar is typically the dominant product of HTC, often accounting for approximately 50%–80% of the initial biomass mass, depending on operating conditions and the nature of the feedstock (Supee and Zaini, 2024; Gallant et al., 2022; Wang, 2018). The final properties of hydrochar largely determine its potential applications. Key target attributes include yield and energy content, porous structure and specific surface area, elemental composition and surface functionality, along with performance in application-specific contexts such as pollutant adsorption, energy storage, or agricultural amendment. Figure 4 provides an overview of the HTC formation pathway (dehydration, decarboxylation, and condensation/polymerization) and summarizes the main property domains typically used to characterize hydrochar, including morphology (SEM), surface chemistry (FT-IR/functional groups), elemental evolution (Van Krevelen), and energetic upgrading (HHV). In this section, we examine how these properties can be tuned either through the choice of HTC operating conditions or through post-treatments in order to tailor hydrochar to a given end use.

3.3.1 Yield and energy densification

These two metrics are often antagonistic in HTC. Mass yield, defined as the fraction of the initial biomass converted into solid hydrochar, is generally higher under milder reaction conditions, such as lower temperatures and shorter residence times, which preserve a larger share of the solid matter (Supee and Zaini, 2024). However, hydrochars produced at low severity typically retain substantial oxygen and hydrogen contents, reflected in higher O/C and H/C ratios, which limits their higher heating value. Conversely, increasing process severity, through higher temperatures, longer residence times, or the use of acidic catalysts, promotes carbon enrichment in the solid by driving the removal of light species, including H₂O, CO₂, and CH₄, into the liquid and gas phases. This increases hydrochar HHV but usually at the expense of mass yield.

HTC conditions are, therefore, optimized according to the targeted end use. When the priority is maximizing yield, for example, for soil amendment where quantity can be decisive, temperatures around 180 °C–200 °C and short reaction times are typically favored to retain a large fraction of carbon in the solid (Wilk et al., 2022). In contrast, producing a solid biofuel with coal-like quality generally requires higher temperatures, at or above 240 °C, and in some cases catalysts to obtain hydrochars with high fixed carbon content and elevated heating values, typically 20–30 MJ kg^-1 (Luthfi et al., 2024a). For instance, industrial hydrochars produced from green waste using the Ingelia process exhibit a lower heating value of approximately 24 MJ kg^-1 and a carbon content of approximately 58%, approaching lignite-like characteristics, but with a mass yield limited to roughly 64% (Gallant et al., 2022). Depending on the study, the energy recovery, defined as the fraction of the initial energy retained in the hydrochar, can exceed 60%–70% when conditions are appropriately optimized (Dang et al., 2024). A central trade-off therefore lies in the degree of carbonization. Highly carbonized hydrochars are generally more hydrophobic and stable, which supports combustion and carbon sequestration applications, whereas less transformed hydrochars retain a higher density of oxygenated functional groups, which can be beneficial for adsorption or soil amendment (Roslan, 2023). Increasingly, multi-objective optimization strategies, using optimization algorithms or DoE-based approaches, have been proposed to reconcile yield and energy quality by simultaneously targeting high HHV while limiting mass loss. Finally, recycling the liquid phase, which is rich in dissolved organic compounds, has also been considered a route to increase overall process yield by promoting the precipitation of carbonaceous species over additional cycles (Lilian et al., 2024).

3.3.2 Fixed carbon content

Fixed carbon content is a central parameter that strongly determines hydrochar energy density and, by extension, its competitiveness relative to fossil fuels. This non-volatile carbon fraction, measured after the release of volatile compounds, is highly dependent on operating conditions, such as temperature, residence time, and the possible use of catalysts or additives. In general, increasing reaction temperature promotes fixed-carbon enrichment by driving off volatile elements, mainly hydrogen and oxygen, in the form of H₂O, CO₂, and other light gases. For example, a study on HTC of rice husk reported a progressive increase in fixed carbon with temperature, alongside a decrease in volatile matter, consistent with enhanced aromatic condensation and the development of a more structured carbon matrix. The addition of additives such as CaO can further modulate these transformations by inhibiting or promoting specific carbonization steps (Liu et al., 2022). In the valorization of animal manures, hydrochars containing up to 40% carbon have been obtained at 260 °C, supporting the direct role of temperature in carbon densification of the solid product (Devnath et al., 2024). This increase in fixed carbon content is typically accompanied by a decrease in the atomic O/C and H/C ratios, indicating a more advanced degree of carbonization and higher aromaticity (Song et al., 2022). Overall, controlling HTC conditions offers a practical means of tuning hydrochar composition according to the intended application, whether as a solid fuel, an adsorbent material, or a medium for carbon sequestration.

3.3.3 Carbon retention ratio

In addition, the carbon retention ratio (CRR), defined as the fraction of the carbon initially present in the biomass that remains in the hydrochar, is typically reported in the range of approximately 60%–85%, depending on the study (Saqib, Baroutian, and Sarmah, 2018; El Ouadrhiri et al., 2021; El Ouadrhiri et al., 2023; Wang et al., 2020; Castro, 2021; Khoo et al., 2020; Li et al., 2022). CRR is a key indicator for assessing the effectiveness of carbon valorization. It is strongly influenced by operating conditions, particularly temperature, residence time, and feedstock type (Lau Abdullah and Hamid, 2021; Luthfi et al., 2024a). One study on forest residues, for example, reported carbon retention values up to approximately 80% when the reaction was conducted at moderate temperatures of 200 °C–220 °C for 6 h (Mendoza Martinez et al., 2021). Such high retention levels are generally attributed to dehydration and carbon recondensation mechanisms that limit carbon losses to the liquid and gas phases. Overall, CRR emerges as a critical parameter to optimize depending on the targeted objective, whether environmental, such as carbon sequestration, or energy-oriented, such as producing a solid biofuel.

3.3.4 Porosity and specific surface area

Hydrochar morphology and pore structure are central to many industrial and environmental applications, particularly those related to filtration and purification (Qureshi et al., 2020). In general, hydrochars produced by HTC alone, without additional activation, exhibit only moderate specific surface areas, often below 100 m² g^-1, and limited porosity, which can constrain performance in advanced applications (Supee and Zaini, 2024). Operating conditions can influence these features. Higher HTC temperatures tend to promote the formation of more rigid, aromatic carbon frameworks that better preserve macropores inherited from the parent biomass (Canencio et al., 2024). In contrast, more moderate temperatures may produce chars richer in hydrophilic functional groups, which can facilitate micropore development after subsequent activation (Petrović et al., 2024).

To obtain highly porous materials, post-treatments are commonly applied, including chemical activation using KOH, ZnCl₂, or H₃PO₄, and thermal activation under CO₂ or steam. For example, the use of FeCl₃ during the carbonization of bamboo residues enabled the formation of hierarchical porous carbons with an exceptionally high specific surface area, reaching 3,688 m² g^-1, and a total pore volume of 1.989 cm³ g^-1, which translated into strong electrochemical performance (Qiu, 2022). Similarly, hydrochars derived from marine biomass, such as Sargassum sp., and activated with ZnCl₂ and CaCl₂, exhibited mesoporous structures with pore sizes of approximately 3.9–5.2 nm and an optimized specific surface area up to 55 m² g^-1, illustrating the direct effect of these activating agents on internal structuring (Rustamaji et al., 2022). More recent work on “superactivated” hydrochars, combining HTC with chemical activation, reported specific surface areas in the range of 1,462–1,703 m² g^-1 together with controlled development of micro- and mesoporosity, which is critical for applications such as CO₂ capture and hydrogen storage (Sultana et al., 2022). Overall, controlling HTC operating conditions and the targeted use of catalysts, additives, and activation strategies are decisive for optimizing hydrochar porosity and surface area and for tailoring these materials to application-specific requirements.

3.3.5 Chemical composition and functional groups

During HTC, the molecular structure of biomass evolves through dehydration, decarboxylation, and aromatic condensation reactions, which reshapes the distribution of key elements such as carbon, oxygen, hydrogen, and nitrogen (Luthfi et al., 2024b). As reported across multiple studies, the elemental composition of hydrochar, including C, H, O, N, S, and ash, is determined by both the initial feedstock and the synthesis conditions, and it directly influences potential applications in adsorption, catalysis, and energy valorization (Sun et al., 2023; Pauline and Joseph, 2020; Wang et al., 2023; Dang et al., 2023). In general, increasing HTC temperature decreases the O/C and H/C ratios, reflecting the progressive loss of oxygen and hydrogen and the formation of a more carbon-rich and aromatic solid (Roslan, 2023).

From a functional-group perspective, hydrochars produced at relatively low temperatures typically retain oxygen-containing moieties such as phenolic, carboxylic, and carbonyl groups. These functionalities confer surface polarity and chemical reactivity that can favor pollutant uptake through mechanisms such as chemisorption and ion exchange (Petrović et al., 2024). At higher temperatures, many of these groups are removed through decarboxylation and decarbonylation, and the surface becomes more hydrophobic and more aromatic, which can be advantageous for energy-related applications, including improved conductivity after partial graphitization. Hydrochar composition can also be tuned through targeted functionalization treatments. For example, phosphorylation, achieved by adding phosphoric acid during or after HTC, can introduce phosphate groups onto the hydrochar surface and enhance its ability to complex heavy metals (Zhao et al., 2021; Khanzada, 2024). FT-IR analyses further show that hydrochar surfaces commonly retain residual oxygenated groups, including hydroxyl, carbonyl, carboxyl, and ether functionalities, although their abundance decreases with increasing process severity (Wang R et al., 2022). This residual oxygen functionality contributes to the high chemical reactivity of hydrochars, supporting applications in pollutant adsorption and heterogeneous catalysis.

Illustratively, a sewage-sludge-derived hydrochar produced at 250 °C exhibited enhanced energy-related properties together with a decrease in O/C from 0.51 to 0.18 and H/C from 2.67 to 1.42, indicating a shift toward a more graphitic and energetically stable structure (Roslan, 2023). Recent studies have also highlighted the role of metallic catalysts, such as FeCl₃ and ZnCl₂, in modifying hydrochar functional chemistry. These additives can facilitate the formation of polyaromatic structures while altering the distribution of oxygen-containing active sites, which is particularly relevant for adsorption applications (Zhang W et al., 2023). More broadly, tailoring hydrochar chemical composition can be achieved by selecting appropriate feedstocks, for example, nitrogen-rich algae to obtain N-doped chars, by adding dopants or additives such as phosphoric acid, urea, or metal salts to promote heteroatom doping or catalytic nanoparticle incorporation, or by applying post-treatments such as acid oxidation to introduce carboxyl groups (Wang et al., 2023; Ayiania et al., 2022; Wutthipattarathorn et al., 023). In this context, AI-based predictive models can support process planning by estimating elemental composition as a function of operating conditions, for example, predicting nitrogen and phosphorus contents to assess agronomic value (Ischia et al., 2024).

Overall, these characteristics underscore the modularity of hydrochar as a functional material. Variations in production temperature, reaction time, and feedstock type directly influence pore structure, specific surface area, and surface chemistry, enabling tailoring to application-specific requirements. Table 1 summarizes the influence of selected HTC parameters on key hydrochar characteristics and highlights general trends. In practice, each feedstock can respond differently, which reinforces the need for modeling and predictive optimization, including AI-enabled approaches, to adjust HTC conditions on a case-by-case basis.

TABLE 1. Summary table of the influence of HTC parameters on hydrochar characteristics.

3.4 Optimization challenges and modeling needs

Improving energy efficiency, maximizing valorization of all product streams, including hydrochar, the liquid phase, and gases, and reducing the environmental footprint are central drivers for HTC development. Process optimization remains a fundamental challenge because of the complex interplay among operating variables (Gao et al., 2019; Czerwińska, Śliz, and Wilk, 2022; Shafizadeh, 2023). HTC is a multifactorial process governed by coupled thermochemical reactions, including hydrolysis, dehydration, decarboxylation, and polymerization, which requires a rigorous approach to identify operating windows that are optimal for a given feedstock and a defined set of end-use objectives (Dang, 2024). Among the most influential variables, temperature, residence time, the solid-to-liquid ratio, and the possible use of catalysts are consistently identified as dominant levers. Recent studies using optimization methodologies such as response surface methodology and multi-objective analysis have shown that appropriate operating conditions can substantially improve both hydrochar yield and heating value. Several HTC studies have shown that multi-objective optimization can identify operating windows that balance hydrochar yield and energy-related properties (Min et al., 2026; Dang, 2024). More broadly, each parameter, including temperature, reaction time, and biomass chemical composition, shapes not only hydrochar properties but also the energy and environmental sustainability of the overall process (Sharma et al., 2022).

To reduce reliance on trial-and-error experimentation and address parameter optimization challenges, AI-based predictive models are increasingly being adopted. A hybrid model combining artificial neural networks with a Kriging approach was developed to improve prediction accuracy for carbon recovery and inorganic phosphorus recovery during HTC (Ismail, 2019). The model indicated that temperature is the dominant factor governing carbon recovery, whereas reaction time becomes more critical at lower temperatures. These advances support both improved process understanding and enhanced predictive capability across varying conditions. In a related direction, Li et al. (2021) used deep neural networks to optimize hydrochar properties and showed that feedstock elemental composition and higher temperatures are key levers for tuning attributes such as heating value and carbon storage potential.

Bayesian approaches, including Bayesian optimization, complement these tools by explicitly quantifying predictive uncertainty (Arróyave, 2022). In the HTC context, Bayesian methods can be used to optimize operating variables such as temperature, pressure, and reaction time to achieve targeted product outcomes (Vallejo et al., 2022). For example, Bayesian optimization has been applied to tune HTC conditions for woody biomass and delivered promising results (Vallejo, 2024). However, these approaches face challenges associated with high dimensionality, which can make efficient exploration of the parameter space difficult (Valleti et al., 2022). Interdependent and nonlinear constraints can further lead to non-compact feasible regions, complicating optimization and limiting applicability in certain scenarios (Hickman et al., 2022). In addition, achieving consistently high predictive accuracy under the complexity of HTC remains a major challenge for Bayesian-based modeling frameworks (Paulson and Tsay, 2024). Nonetheless, uncertainty-aware optimization is valuable for establishing operating safety margins while refining process set points, which is particularly important for complex conversion systems such as HTC.

A further major challenge is the development of predictive models for HTC itself, which remains an active area of research. Current modeling strategies include empirical formulations, thermodynamic simulations, and machine learning techniques (Ubene, Heidari, and Dutta, 2022). A key difficulty lies in representing heat transfer, reaction kinetics, and interactions among biomass components with sufficient fidelity. The complexity of reaction mechanisms makes accurate predictive modeling challenging, particularly because biomass compositions are heterogeneous and strongly influence yields and product properties. Existing models are often limited by insufficient data on reaction dynamics and scale effects, which complicates extrapolation from laboratory studies to industrial operation (Ho, Nadeem, and Choe, 2024).

When advanced models are combined with design of experiments, parameter optimization can be conducted more systematically and efficiently. In their review, Heidari et al. (2021) reported that this coupling can substantially reduce experimental requirements while improving predictive quality. The analysis of complex interactions can also reveal non-obvious synergies, such as the combined influence of solid-to-liquid ratio and temperature on hydrochar energy density. Other studies have similarly emphasized that integrating predictive modeling with DoE can improve product quality while reducing energy costs, providing practical solutions to industrial constraints (Li et al., 2021).

AI and machine learning approaches are now increasingly applied to HTC modeling (Moussaoui, 2024; El Ouadrhiri, 2024; Zhang W et al., 2023; Zhang, 2024; Leng, 2024). Recent studies indicate that algorithms such as random forests, support vector machines, and extreme gradient boosting can predict key hydrochar properties, including yield, HHV, and fixed carbon content, as a function of operating variables (Liu et al., 2024). Reported predictive performance is often high, with coefficients of determination reaching up to 0.985, indicating strong agreement between model predictions and experimental outputs. However, broader deployment of these methods still requires larger and more diverse datasets that include multiple biomass types and wide operating ranges.

Finally, industrialization and scale-up of HTC represent critical challenges that demand further advances in modeling and optimization. The transition from laboratory systems to industrial installations raises issues related to reactor design, management of liquid and gaseous effluents, and process energy integration (Ho et al., 2024). In particular, handling the post-HTC aqueous phase, which is rich in dissolved organic compounds, remains a major bottleneck and requires dedicated treatment strategies to avoid secondary pollution and improve the overall environmental balance (Liu et al., 2024). In this review, we focus primarily on the contribution of DoE and AI-based predictive modeling to strengthen HTC process understanding and optimize hydrochar properties in a more efficient and cost-effective manner.

4 Classical DoE and RSM for HTC process optimization

4.1 DoE approaches overview

Building on the challenges outlined in the previous section, design of experiments emerges as a practical and increasingly indispensable route for handling the complexity of HTC. The inherently multifactorial nature of the process, combined with often nonlinear interactions among operating variables, calls for a rigorous methodological framework. DoE not only helps identify critical variables but also clarifies how they act in synergy or in opposition under specific operating windows. When implemented properly, this strategy can substantially reduce experimental workload while improving the reliability of predictions. This section expands on DoE concepts as applied to HTC, highlighting their role in modern process optimization, while discussing representative applications, strategic advantages, and the main limitations that remain to be addressed. Also, the studies discussed in this section are classified as DoE-only HTC optimization studies. They use factorial designs, response surface methodology, central composite designs, Box-Behnken designs (BBDs), or related experimental-design approaches to quantify factor effects and define local operating optima. Unless an ML model is subsequently trained on the resulting experimental dataset, these studies should not be interpreted as DoE-guided ML workflows.

DoE clearly outperforms traditional experimental approaches such as the one-factor-at-a-time (OFAT) method. The OFAT technique, which varies a single factor while holding others constant, is straightforward to implement but becomes inefficient for complex systems such as HTC. In particular, it cannot detect interaction effects among factors, which limits its ability to optimize process parameters (Gilman et al., 2021). In contrast, DoE enables the simultaneous evaluation of multiple variables while explicitly accounting for interactions. This approach improves the quality of inference and often reduces the number of experiments required. For example, one DoE application in HTC reported that jointly optimizing temperature, reaction time, and solid-to-liquid ratio increased fixed carbon content by approximately 25% compared with optimizing each factor independently (Shen, 2019). In this regard, DoE provides an effective response to the multifactorial challenges of HTC while helping constrain experimental costs.

Successful experimental design requires a disciplined workflow built around clearly defined steps. The strength of DoE lies in its ability to systematically explore the experimental space, detect significant effects and interactions, and optimize one or multiple objectives simultaneously (Shen, 2019). The first step is to formulate the study objectives with precision, for instance, maximizing yield, improving a functional property, or identifying the most influential variables. This step is essential for selecting an appropriate design and avoiding unnecessary or overly costly experiments (Jindal and Goswami, 2020). The next step is to define relevant factors as independent variables and their levels as tested values. This selection can be informed by the literature, empirical knowledge, or preliminary trials. In parallel, response variables must be defined in direct alignment with the objectives (Yahya Alashwal et al., 2021).

The choice of experimental design follows from these definitions. Full or fractional factorial designs are commonly used for screening, response surface methodology for optimization, and central composite designs for modeling curved response surfaces. Each design represents a trade-off between statistical resolution and experimental burden (Lee et al., 2022). Once the design is selected, adequate randomization and replication are required to minimize systematic bias, matrix effects, and experimental noise. These practices strengthen robustness and are particularly important in industrial and environmental contexts (Zacks, 2020). Finally, the collected data are analyzed using appropriate statistical tools, including ANOVA, regression models, and response surfaces. This step enables identification of main effects and interactions and supports the prediction of optimal conditions with quantified confidence (Hecht, Oberg, and Muddiman, 2016). The overall DoE workflow is summarized in Figure 5, which links objective definition, factor and response selection, experimental design choice, and the subsequent stages of statistical analysis and optimization.

It is important to note that the OFAT approach, which is still used in some studies, is largely inadequate for complex systems because it cannot resolve interactions among factors, thereby limiting the scope and reliability of experimental conclusions (Gorbounov et al., 2022). This conceptual distinction between OFAT and DoE is summarized in Figure 6, which contrasts the restricted, one-dimensional exploration of the experimental space achieved with OFAT (Panel A) with the multidimensional exploration enabled by DoE designs (Panel B) for multifactorial processes such as HTC.

4.2 Existing applications of DoE for optimizing HTC operating parameters

Among the most widely used DoE strategies are full and fractional factorial designs, Box-Behnken designs, and central composite designs used within response surface methodology to approximate responses with a quadratic polynomial (Amenyeku et al., 2024; Nguyen et al., 2024; Sarker, Nanda, and Dalai, 2023; Chowdhury et al., 2016; Shakiba et al., 2023; Malhotra and Garg, 2023; Rasaq, 2024; Luo et al., 2025; Yıldız Uzun, 2024).

4.2.1 Full and fractional factorial designs

Among the foundational DoE approaches, full factorial designs and fractional factorial designs occupy a central role during the screening stage for experimental parameters that influence hydrochar yield, heating value, or elemental composition (Kay et al., 2023; Figueroa, 2023; Tomas-Morer et al., 2013; Patil and Chalikwar, 2024). Their value lies in their ability to evaluate main effects systematically and capture selected first-order interactions, thereby providing a structured overview of the studied system (Montgomery, 2020).

Full factorial designs test all possible combinations of factor levels, which makes them particularly powerful when the number of variables is limited. However, their experimental cost increases rapidly as the number of factors grows. In such cases, fractional factorial designs provide a more economical alternative by reducing the number of experiments while retaining the ability to identify the most influential effects. The work of Cazetta et al. (2021) provides a useful methodological perspective. The authors emphasize that factorial designs are well suited to the early stages of optimization strategies, notably for isolating significant variables before moving to more complex approaches such as response surface designs. They also highlight their relevance for carbon-based materials systems, where multiple variables can concurrently shape structure, porosity, and yields (Cazetta et al., 2021).

In the HTC context, several studies have applied these methodologies to optimize operating conditions. Aurnob et al. (2022) used a fractional factorial design to investigate the conversion of biogenic municipal wastes into hydrochar. Their study examined three key factors, temperature, residence time, and the water-to-solid ratio, and multivariate analysis revealed not only individual effects but also critical interactions, in particular between residence time and moisture level. This illustrates the high information density that factorial designs can provide in complex HTC settings (Aurnob et al., 2022).

Complementarily, Gomes et al. (2010) investigated the synthesis of biomass-derived quantum dots via HTC using a two-factor full factorial design. They showed that interaction effects, notably between temperature and the chitosan-to-chitin ratio, could significantly modulate the optical performance of the resulting carbon-based products. This experimental strategy enabled a clearer understanding of subtle cross-effects in a process combining HTC with optoelectronic functionalization (Gomes et al., 2019). Nonetheless, increasing process complexity can render factorial designs insufficient. As noted by Ribeiro et al., in an agronomic case involving 14 factors, full factorial designs become impractical, requiring up to 2¹⁶ experiments, which pushes researchers toward hybrid solutions that combine fractional designs with more advanced screening strategies such as definitive screening designs (Ribeiro et al., 2019).

Generally, although factorial designs are not designed to model quadratic or more strongly nonlinear effects, they remain an essential starting point for rigorous optimization workflows. By identifying first-order interactions and rationally narrowing the experimental space, they lay the groundwork for second-order designs that are better suited for fine-tuning operating conditions in HTC.

4.2.2 Response surface designs

Response surface methodology represents a powerful extension of DoE that aims to model, in a predictive manner, the relationship between multiple independent variables and one or more target responses. It enables the construction of quadratic models that are useful for locating experimental optima and probing nonlinear interactions among operating parameters. The two most widely used designs in the literature are the central composite design and the BBD.

The central composite design is particularly valued for its flexibility. It combines a two-level factorial core with axial and center points, making it possible to capture curvature in the response surface. This design is well suited to complex processes such as hydrothermal carbonization, especially when quadratic effects and interaction terms are expected. For example, in a study on date-derived hydrochar, a CCD coupled with RSM was used to examine the influence of temperature, reaction time, and catalyst dosage on mass yield and carbon recovery (El Ouadrhiri et al., 2021). The optimal conditions were identified as 200 °C, 120 min, and 20 mg of catalyst, resulting in a mass yield of 59.71% and a carbon recovery of 75.84%.

RSM provides an explicit mathematical model that predicts the response as a function of input variables. In one study on sawdust HTC, RSM was used to model the effects of temperature, reaction time, and catalyst loading on hydrochar yield and properties (Lilian et al., 2024). The model predicted optimal conditions at 162.23 °C, 2.51 h, and 7.99 wt% catalyst loading, yielding a hydrochar output of 84.23 wt%.

The Box-Behnken design is developed to minimize experimental runs while retaining a strong ability to detect quadratic effects. It avoids extreme factor-level combinations, which can be advantageous when certain operating conditions may trigger undesirable or hazardous reactions. Murillo et al. (2022) used a BBD framework to valorize oat husk, achieving optimized yield and heating value while minimizing the number of trials required. Similarly, Blach and Engelhart (2021) employed a three-factor BBD (temperature, duration, and pH) to study HTC of sewage sludge ​. Their RSM model indicated a dominant effect of temperature on liquid-phase quality, including a reduction in dissolved organic carbon from approximately 9,400 to 7,400 mg L^-1 as temperature increased from 190 °C to 250 °C, and it also influenced ammoniacal nitrogen release. Together, these examples illustrate how DoE approaches can identify optimal operating conditions while quantifying the contribution of each process variable.

In some cases, variants such as face-centered composite designs or hybrid approaches combining CCD with numerical methods have been adopted, particularly when a large number of factors are investigated or when multiple responses must be optimized simultaneously. Overall, RSM, and especially CCD and BBD designs, has become an essential tool for the fine optimization of HTC operating conditions and the targeted improvement of hydrochar properties.

4.2.3 Optimal experimental designs

Optimal designs are an advanced category of DoE that aim to maximize statistical information from a limited number of experiments. Unlike factorial or response surface designs, these designs are generated using mathematical optimality criteria, such as D-optimal, I-optimal, or A-optimal criteria, which target specific properties of the design matrix, for example, minimizing estimator variance or maximizing predictive precision (Atkinson, 2015).

D-optimal designs are the most widely used. They rely on maximizing the determinant of the information matrix, thereby improving parameter identifiability and strengthening the robustness of effect estimates (Sadab et al., 2023). This class of design is particularly valuable when certain experimental combinations are forbidden or technically infeasible, a common situation in the HTC of complex biomass feedstocks.

Although still relatively scarce in the HTC literature, optimal designs are increasingly being adopted in contexts where experimental resources are constrained or where many variables must be considered simultaneously. For instance, some authors have combined a D-optimal design with machine learning to generate efficient experimental conditions while reducing the number of trials required. This hybrid strategy enabled the identification of operating combinations that maximize hydrochar quality from wet organic wastes (Liu et al., 2024). Other optimality criteria, such as I-optimal designs, focus on minimizing the mean squared prediction error across the experimental domain. This is particularly relevant when the primary objective is predictive accuracy, especially in nonlinear systems with multiple responses, such as yield, heating value, or material stability considered simultaneously (Egorova, Gilmour, and Mylona, 2012). In summary, optimal designs offer a flexible and statistically efficient route for HTC optimization under complex or constrained conditions, supporting reliable modeling while limiting experimental cost and workload.

4.3 Limitations of DoE designs applied to HTC

As discussed in the previous sections, HTC is a promising route for valorizing wet biomass into carbon-rich hydrochar with physicochemical features that support a broad range of applications. Over the last decade, from 2010 to 2025, many studies have applied classical DoE tools, including full factorial designs, response surface methodology with CCD and Box-Behnken designs, and Taguchi orthogonal arrays, to optimize HTC operating conditions and achieve targeted hydrochar yields and properties. These approaches reduce experimental burden while enabling identification of main effects and interaction patterns. Nevertheless, a critical reading of the literature highlights several important limitations associated with applying DoE in the specific context of HTC. In this section, we synthesize five major limitations and describe the strategies that researchers have used to mitigate them.

4.3.1 Nonlinearity and complex mechanisms beyond classical DoE models

HTC involves a network of coupled and time-evolving reactions, including hydration, dehydration, decarboxylation, polymerization, and recondensation, whose kinetics and dominant pathways can shift as conversion proceeds (Román, 2018). Classical RSM is typically built on the assumption that the response surface can be approximated by a relatively simple functional form, most often a second-order polynomial. This assumption can be restrictive for HTC, where strongly nonlinear behavior, threshold effects, and mechanistic transitions may occur. A recurring limitation emphasized in the literature is that polynomial DoE models do not always capture such behavior, particularly when inflection points or higher-order interactions are influential but not represented in the model structure.

This limitation is illustrated by factorial and RSM studies that rely on linear or quadratic models within a restricted experimental domain. Heilmann (2010), working on microalgae-derived biomass, used a full-factorial framework with center points and fitted a linear model to link carbon yield to residence time, temperature, and solids content. While such a formulation can be adequate within a narrow operating window, purely linear or quadratic models may distort the underlying HTC kinetics when the true response exhibits strong curvature, multiple regimes, or higher-order interactions that are not included in the regression. Several authors have stressed that HTC reaction networks are mechanistically complex and cannot be fully described by simple empirical equations (Lu and Berge, 2014; Heidari et al., 2019). Heidari et al. (2019) noted that HTC outcomes “vary substantially” with operating conditions and feedstock characteristics, and that no generic, simple empirical model can reliably represent the full range of regimes encountered in practice.

A direct consequence of this mismatch appears in predictive performance. Machine learning approaches have frequently outperformed conventional RSM models in predicting HTC product outcomes, highlighting the challenge of nonlinearity. Moussaoui (2024) compared a CCD-based RSM model with ML approaches, such as artificial neural networks and support vector machines, for the co-HTC of almond shells and olive pomace. They reported that, while RSM is effective for experimental planning, ANN is better suited for modeling and predicting hydrochar yield and carbon retention, achieving higher predictive accuracy. In their words, “RSM remains more effective in terms of planning and optimization. However, ANN is more suitable for modeling and predicting mass yields and carbon retention rates.” ANN can capture complex nonlinear relationships without requiring the analyst to impose a predefined polynomial form, whereas RSM, typically formulated as a second-order polynomial, can struggle to represent the full range of effects. Similar conclusions have been reached using hybrid strategies. For example, an ANN-Kriging model reported in 2024 delivered improved predictions of HTC product properties compared with RSM, highlighting that the generalized quadratic form of standard response surfaces can miss subtle features of HTC reaction behavior (Gao and Ma, 2024; Mu’Azu, 2022). These observations align with the practical reality that HTC can exhibit nonlinearities beyond the representational capacity of classical DoE models, especially when multiple reactions proceed simultaneously or when threshold effects emerge, such as the onset of strongly exothermic polymerization and recondensation. When the true response surface is highly curved or contains local maxima, a standard RSM may show a meaningful lack of fit, indicating that the model does not adequately represent the data. In practice, this issue is assessed using the lack-of-fit test within ANOVA, where a non-significant lack of fit (p > 0.05) is generally desirable (El Ouadrhiri, 2024), while a significant result indicates model inadequacy. Many published HTC optimization studies report acceptable fits, partly because experimental campaigns often avoid operating regions that trigger irregular or unstable behavior.

A further, and often underestimated, constraint is the validity domain. Polynomial DoE models are usually local approximations, and extrapolation beyond the experimental range, or even a moderate change in feedstock type, can rapidly degrade predictive performance because unmodeled nonlinearities become dominant (Heidari et al., 2019; Lu and Berge, 2014). These limitations are summarized in Figure 7, which contrasts the quadratic approximation implied by classical response surface models with the more complex nonlinear behavior of HTC, highlighting the roles of higher-order interactions, local validity, and limited extrapolation capability.

To mitigate these limitations, some researchers have incorporated mechanistic insight or adopted sequential experimentation strategies. For example, severity-factor-based models have been combined with RSM to better embed reaction kinetics into the empirical framework (Heidari, 2020; Jeder, 2018; Basso et al., 2018; El Ouadrhiri et al., 2023; Vallejo et al., 2020; Xie et al., 2024; Hoekman et al., 2017; Luthfi et al., 2024b), Others have relied on more flexible regression techniques to relax the constraints of low-order polynomial forms. Despite these efforts, capturing the full complexity of HTC using a low-order DoE model remains a fundamental challenge.

4.3.2 Scale-up and generalization from laboratory to pilot scale

A second critical limitation is the limited transferability of DoE-derived optima and models when moving from small-batch laboratory reactors to pilot or industrial systems. Many DoE studies are conducted in bench-scale vessels, often sealed autoclaves in the 50–500 mL range. These tightly controlled conditions can differ markedly from those in larger batch units and continuous or semi-continuous operations in terms of heat transfer, mass transfer, mixing, and reaction equilibrium, which can lead to systematic deviations in outcomes. Laboratory “optimal” conditions therefore do not necessarily translate to the pilot scale, as highlighted by recent comparative studies (Dang, 2024).

Volpe et al. (2022) explicitly examined HTC scale-up and identified multiple pitfalls (Dang, 2024). They showed that scale changes can shift the rate-limiting phenomena. Effects that are negligible in a well-mixed laboratory reactor, such as heating time or transport limitations, can become limiting in larger systems. Even core metrics, such as carbon yield and energy efficiency, can change. Ho et al. (2024) reported that a pilot-scale HTC reactor delivered a lower mass yield than laboratory experiments, partly due to a higher fraction of uncollected char and additional mass losses, whereas the energy content of the pilot hydrochar, expressed as higher heating value, was slightly higher. More specifically, pilot-scale fuel recovery showed a larger deviation relative to laboratory performance, yet approximately 15% of the HTC process energy demand could be offset by combusting part of the produced hydrochar, and the HHV of the pilot hydrochar marginally exceeded that of the laboratory hydrochar (Areeprasert et al., 2014). This observation suggests that scale can effectively alter carbonization severity, potentially through longer effective reaction histories, different thermal profiles, or pressure retention, yielding a more carbon-dense hydrochar at pilot scale.

Key scale-up drivers include heat-transfer limitations that can create temperature gradients in larger reactors, differences in mixing and mass transport, especially in semi-continuous and continuous HTC where feed introduction and product withdrawal fundamentally differ from sealed-batch operation, and equipment constraints such as slower heating and cooling rates that reshape the effective time-temperature trajectory. Laboratory feasibility studies are typically optimized under near-ideal conditions, including rapid heating, near-uniform temperature fields, and finely prepared feedstocks. At pilot scale, reproducing these conditions is often difficult.

In practice, some groups mitigate this limitation by performing intermediate-scale experiments to bridge laboratory and pilot regimes (Ho et al., 2024). More generally, DoE models built at laboratory scale can exhibit reduced predictive performance at larger scales, which resembles an extrapolation error driven by scale-dependent factors that were not included in the model. This is not a limitation of DoE itself but a consequence of unmodeled scale effects. It implies that a laboratory optimum, for example, 1 h at 200 °C to maximize hydrochar energy yield, may no longer be optimal, or may even be infeasible, at pilot scale. For this reason, laboratory optimization is often treated as a first stage, followed by validation and, where necessary, re-optimization at pilot scale.

The literature increasingly suggests integrating scale considerations early. Practical recommendations include designing experiments using dimensional analysis and relevant dimensionless groups to improve transferability and including scale-relevant factors, such as agitation intensity or heating rate, in the experimental design when these variables are expected to influence outcomes. Volpe et al. (2022) also emphasized the need for extended pilot trials and subsequent model recalibration, highlighting that bringing HTC from laboratory studies to industrial deployment requires more than a direct application of laboratory-optimized “recipes.”

Industrial relevance, therefore, requires a broader definition of optimization than maximizing hydrochar yield or HHV under laboratory conditions. Pilot- and continuous-reactor studies indicate that mass recovery, fuel properties, and energy performance may change when heating and cooling histories, mixing, residence-time distribution, solid separation, and process-water handling differ from bench-scale operation. A model-selected operating window should therefore be evaluated jointly against the thermal and hydraulic constraints of the reactor, the management or recirculation of the aqueous phase, the net energy demand of the process, and the quality requirements of the targeted hydrochar application.

Product standardization remains an additional challenge because the relevant quality criteria depend on the intended end use. For fuel applications, moisture, ash content, elemental composition, heating value, stability, and contaminant concentrations should be considered together. For adsorbent, soil amendment, or advanced material applications, additional requirements may include surface properties, leachable compounds, nutrient content, or adsorption performance. Consequently, LCA and techno-economic analysis should be used alongside process optimization to determine whether an operating point selected from laboratory-scale data remains environmentally and economically favorable after scale-up. Under these conditions, DoE-ML should be regarded as a decision-support tool that requires pilot-scale confirmation rather than as a substitute for reactor design, effluent management, energy integration, or product qualification.

4.3.3 Interaction effects and design constraints in experimental planning

DoE strategies differ substantially in their ability to detect and model interaction effects among factors. HTC outcomes are often shaped by interactions. For instance, the impact of temperature on yield may depend on residence time, and the apparent contribution of a catalyst may depend on feedstock moisture or solids loading. Full factorial designs can capture two-factor interactions and, depending on the structure, selected higher-order interactions because they test all factor-level combinations. However, they become impractical as the number of factors increases. This is why many HTC studies rely on reduced designs, including fractional factorial designs, Box-Behnken designs, or Taguchi orthogonal arrays, to decrease the experimental burden at the cost of not exploring all combinations.

A well-known limitation is that Taguchi methods do not explicitly resolve interactions unless the design is specifically constructed to do so. In the Taguchi framework, factors are varied according to an orthogonal array that assumes additive main effects, and interactions are commonly confounded with other terms or implicitly neglected. Fakudze et al. (2021) noted that Taguchi is often criticized for its inability to account for factor interactions, largely because orthogonal arrays do not test all combinations of variables (Fakudze et al., 2021). If temperature and time interact to influence hydrochar properties, a Taguchi L9 array, for example, can miss that interaction and lead to suboptimal or misleading conclusions regarding individual factor effects. Despite this, Taguchi designs have been used in HTC, including in studies on oil palm trunk feedstocks, because of their simplicity and efficiency (Qureshi, 2021). When interpreting Taguchi results, authors sometimes assume interactions are negligible, or they conduct confirmation experiments using additional factorial combinations to verify that no strong interaction was overlooked (Fakudze et al., 2021; Rasam et al., 2021; Xu et al., 2013; Aurnob et al., 2022).

In contrast, RSM designs such as central composite designs and Box-Behnken designs include factorial points that allow estimation of two-factor interactions, along with quadratic terms. A CCD includes a factorial core, typically 2^k, together with center points and axial points. Accordingly, CCD-based studies, such as work on the HTC of tomato peels, can evaluate interaction terms such as temperature × time in relation to yield or product properties (Álvarez-Murillo et al., 2015; Sabio et al., 2016). Many RSM studies in HTC report interaction terms in ANOVA, with some interactions proving significant, while others are not, depending on the feedstock and operating window.

Limitations arise when higher-order interactions involving three factors or non-factorizable combinations are influential because most reduced designs do not provide sufficient degrees of freedom to estimate them. Many HTC optimization studies assume that two-factor interactions and quadratic curvature are adequate. Yet, if the process exhibits more complex coupling, such as a catalyst that jointly modulates the temperature-time effect, a standard RSM model may show meaningful lack of fit or leave substantial variance unexplained. Researchers address this issue either by extending the model when the data support it, for example, adding interaction terms, or by simplifying the problem, for example, fixing a factor at a constant level to reduce dimensionality.

A related constraint concerns restricted experimental domains in HTC. Safety considerations and equipment limits often constrain factor ranges, for example, limiting temperature to avoid excessive pressure or imposing minimum residence times due to heating-rate constraints. If the true optimum lies outside the tested domain, DoE optimization can converge to a boundary solution, which is inherently less reliable (Xu et al., 2013). Several RSM studies in HTC report optima located at the edge of the experimental space, such as an “optimal” temperature equal to the highest temperature tested. This pattern suggests that the objective function, such as energy yield, was still increasing at the boundary and that a higher temperature might have improved performance further, but the required data were not collected (Shokri et al., 2024). In such cases, the fitted quadratic model may underestimate gains beyond the tested interval, and extrapolation is not defensible. To mitigate this, some researchers use iterative DoE strategies. An initial design defines a working region and then a subsequent design shifts or expands the domain. Practical constraints remain, however, because certain regions may be inaccessible due to risks such as excessive pressure or undesirable over-carbonization. As a result, DoE studies in HTC often explore only a constrained subspace, and the resulting models remain valid only within that defined domain (Yousefifar, 2019; Keiller et al., 2021; Basso, 2016; Lucian and Fiori, 2017; da Silva Carvalho et al., 2025).

The lack-of-fit test is an important diagnostic linked to these issues. A significant lack of fit indicates that structure present in the data is not captured by the terms included in the model. Many published works report non-significant lack of fit, which supports model adequacy within the studied domain (El Ouadrhiri, 2024). At the same time, cases where lack of fit is significant may lead researchers to revise the modeling strategy, for example, by applying transformations or introducing higher-order terms, or such studies may be less likely to appear in the published record.

The central implication is that interaction effects and model-form constraints can compromise DoE-based optimization in HTC. If relevant interactions or system curvature are not captured, the experimental design can yield misleading optima. Using sufficiently informative designs, such as CCDs with center and axial points (Román, 2018), and combining DoE with mechanistic understanding to prioritize plausible interactions are practical ways to reduce this limitation. Several studies also complement DoE with confirmation experiments at intermediate conditions to ensure that strong, unmodeled interactions have not been missed.

4.3.4 Multi-objective optimization challenges for hydrochar quality

HTC studies rarely target a single performance metric. Depending on the intended application, hydrochar optimization may involve maximizing solid yield, maximizing energy density expressed as HHV, increasing specific surface area or porosity for adsorption-oriented uses, and, in some cases, tuning nutrient content for soil amendment applications. These objectives are frequently antagonistic. A classic example is the trade-off between hydrochar yield and energy densification. More severe HTC conditions, such as higher temperature and longer residence time, tend to produce a more carbon-rich solid with higher HHV, often closer to coal-like properties, but they also intensify devolatilization and solubilization, which reduces mass yield. Conversely, milder conditions preserve mass yield but typically result in a lower HHV. This inverse relationship is consistently reported, where improvement in one objective is accompanied by deterioration in the other (Nakano et al., 2025; Guo et al., 2022). For instance, increasing temperature from 180 °C to 240 °C has been associated with a decrease in hydrochar mass yield from roughly 70% to 50%, alongside a marked increase in HHV (Chen et al., 2021; Ischia et al., 2024). Under such constraints, a DoE workflow that optimizes a single response can be structurally limiting. Optimizing yield alone or HHV alone may fail to meet application needs when both targets matter.

Traditional RSM frameworks can handle multi-response optimization through composite desirability functions or weighted aggregation of responses into a single objective. Yet, the selection of weights and desirability criteria remains partly subjective and may not reflect a process-engineering optimal compromise. Guo et al. (2022) addressed this issue by performing a multi-response optimization of sewage-sludge HTC to simultaneously maximize hydrochar yield and HHV. They used RSM to identify operating conditions delivering a balanced outcome and subsequently assessed hydrochar performance in CO₂ gasification. Such studies typically reveal that the optimal individual responses occur at different operating conditions, which makes a compromise solution necessary. Multi-objective work therefore often reports either a compromise point or a set of Pareto-optimal solutions.

More recently, ML-supported multi-objective optimization has been used to overcome limitations associated with weighted-sum formulations. Zhang (2024) applied a machine-learning-driven multi-objective optimization strategy to simultaneously maximize hydrochar carbon content and yield (Li et al., 2021). Using a trained predictive model, they identified a Pareto set of operating conditions that improved both objectives beyond what is commonly achievable with a simple weighted aggregation. This illustrates a structural limitation of conventional DoE approaches for multi-objective problems. Response surface modeling is naturally formulated around a single response, or a composite response created by forcing multiple criteria into one scalar objective.

A representative strategy for handling these conflicts within an RSM framework is the construction of composite indices. Fan et al. (2018), aiming to optimize hydrochar as a solid fuel, combined multiple targets, including yield, carbon content, and energy efficiency, into a single energy-retention factor or performance index, then used RSM to maximize that index. This approach enabled the simultaneous incorporation of yield and HHV in the optimization of grape-pomace-derived hydrochar. The limitation is that the weighting structure effectively encodes a preference, such as prioritizing energy densification over mass yield, and changing the target application can require the redefinition of the index and re-optimization.

A second challenge in multi-objective optimization is interpretability and visualization of trade-offs. Some studies overlay response surfaces or contour maps for multiple responses to identify feasible operating windows, for example, regions where yield exceeds a defined threshold and HHV remains above a target value. Others have adopted Pareto-front analysis using evolutionary multi-objective algorithms rather than relying solely on classical RSM. Recent work increasingly integrates multi-objective evolutionary optimization or advanced surrogate modeling to move beyond RSM limitations in this area (Zhang, 2024; Li et al., 2021). These approaches represent trade-offs explicitly by generating sets of non-dominated solutions rather than a single weighted compromise.

In summary, multi-objective optimization of HTC using traditional DoE tools is challenging because of intrinsic trade-offs and the need to combine multiple criteria into a single objective. Studies addressing this typically use composite indices (Fan et al., 2018) or conduct separate RSM optimizations for each objective and then select a compromise condition. Both approaches can miss more nuanced trade-offs. This has driven growing adoption of complementary methodologies, including ML-based surrogates and Pareto optimization, to augment classical experimental designs. When RSM remains the primary framework, it is essential to state clearly which objectives are prioritized, how trade-offs are weighted, and to acknowledge that the selected optimum may not represent the best solution across all criteria.

4.3.5 Biomass heterogeneity and design robustness

HTC feedstocks span a wide spectrum, ranging from pure model compounds such as cellulose to highly variable real wastes including sewage sludge, food waste, and agricultural residues. Biomass heterogeneity is therefore a major obstacle to the generalization of DoE-derived conclusions and to the robustness of optimized conditions. Most DoE studies are performed on a single feedstock, or on a well-homogenized mixture with a stable composition across runs. Consequently, the fitted model and the identified optimum are intrinsically tied to that feedstock’s characteristics, such as its lignocellulosic composition, ash content, and inorganic speciation. When the feedstock changes, even within the broader class of lignocellulosic materials, HTC behavior can shift substantially, altering yields, product chemistry, and kinetics (Wang Y et al., 2022; Mendoza Martinez et al., 2021). Heidari et al. (2019) explicitly noted that HTC outcomes differ markedly across biomass types because of compositional differences among materials.

Composition-driven effects are well established. Lignin-rich biomasses often produce more solid residue and can require longer treatment to reach a comparable degree of carbonization relative to cellulose-rich feedstocks (Lu and Berge, 2014). Ash constituents, including alkali and alkaline-earth metals, may catalyze or inhibit key steps, changing both conversion pathways and product distributions. As a result, a response surface built for one substrate, such as corn residue, will not necessarily predict outcomes for pine wood or food waste under nominally similar conditions. This lack of cross-feedstock robustness becomes a structural limitation when DoE results are presented as broadly generalizable.

To address this issue, composition-based modeling efforts emerged during the 2010s. Instead of treating biomass type as a categorical variable, which would require separate experimental programs for each feedstock, some studies characterize feedstocks using quantitative descriptors, such as cellulose, hemicellulose, and lignin fractions, together with ash and proximate properties. Heidari (2020) developed mathematical models that integrate compositional fractions alongside HTC operating conditions to predict product yields across different biomasses. The goal was to move toward a more generic predictive framework by recognizing that biomass can be described in terms of dominant reactive fractions, commonly grouped into cellulose, hemicellulose, and lignin (Heidari et al., 2019). Such models help rationalize why woody feedstocks behave differently from herbaceous residues or algae. Nevertheless, their predictive scope remains constrained when dealing with real wastes that contain proteins, lipids, plastics, and diverse inorganic phases, which complicate mechanistic interpretation and model transfer.

From an experimental design perspective, biomass variability can be treated as a noise factor. Taguchi methods are conceptually suited to robustness-oriented design by explicitly probing performance under controlled variations. In practice, relatively few HTC studies have implemented robust Taguchi-style designs that introduce, for example, different feedstock types or moisture levels as noise factors to quantify sensitivity of the “optimal” operating point. Some work has addressed heterogeneity more implicitly by studying mixed feedstocks. For example, co-HTC of blended wastes can be used to identify operating conditions that perform acceptably across a composite feedstock distribution, rather than being tuned to a single pure material (Moussaoui, 2024).

Despite these emerging directions, most DoE optimizations still assume a uniform feedstock. For that reason, transferring optimized conditions from one study to another feedstock is expected to introduce systematic deviations. A temperature-time window that maximizes hydrochar energy yield for crop residues may not be appropriate for wood chips, which can be more resistant to hydrolysis and depolymerization. Chacón-Parra and van Eyk (2022), together with Paksung et al. (2020), reported that feedstock structure, such as crystalline versus amorphous cellulose, can significantly affect HTC kinetics, with crystalline cellulose requiring higher activation energy. This implies that kinetic models and optimized operating conditions must be adapted to the structural properties of the feedstock to remain predictive (Chacón-Parra and van Eyk, 2022; Paksung et al., 2020; Reza, 2013; Putra et al., 2021). Without such adaptation, model mismatch and lack of fit become more likely when attempting cross-feedstock prediction.

To strengthen robustness, several studies have expanded their experimental scope to include broader feedstock variability. Varbanov et al. (2019) and Guo et al. (2016), designed experimental campaigns spanning materials with high and low lignin content to generate models with improved generality for hydrochar performance. Others employ severity factors, which compress time and temperature into a single descriptor, to compare outcomes across feedstocks (Heidari, 2020). Severity-based descriptors can facilitate cross-study comparisons, yet they do not explicitly encode biomass composition and therefore cannot resolve composition-driven shifts in reaction pathways.

State-of-the-art evidence suggests that future HTC-focused DoE programs will need to incorporate feedstock properties directly into the experimental design or rely on adaptive models that can be recalibrated with a small number of experiments when new materials are introduced (Ischia and Fiori, 2021; Dang, 2024; Ubene et al., 2022). Until such frameworks become standard, optimization outcomes should be interpreted explicitly within the context of the tested feedstock. The heterogeneity of real wastes, which can vary from batch to batch, also implies that apparent precision in optimization can be fragile. Small changes in composition can shift the optimum or reduce achievable performance. This supports the case for robust optimization strategies that identify operating regions with limited sensitivity to feedstock fluctuations, rather than a single sharp optimum.

Taken together, DoE methodologies remain highly valuable for structuring experimentation and mapping the influence of key operating variables in HTC, yet they exhibit well-defined constraints in this domain. The literature from 2010 to 2025 shows that factorial and response-surface designs can efficiently quantify main effects and selected interactions, but they may struggle with the nonlinear reaction chemistry of HTC when restricted to second-order polynomials. Scale-up introduces additional variables and uncertainties not represented in laboratory-built models. Certain reduced designs, such as Taguchi arrays, can overlook interaction effects unless specifically constructed to resolve them. Restricted experimental domains can produce boundary optima with limited reliability. Multi-criteria targets for hydrochar quality add further complexity because improving one property can degrade another, which motivates the use of composite indices or modern optimization approaches to navigate trade-offs. Finally, feedstock heterogeneity makes universal solutions uncommon, requiring either feedstock-specific optimization or flexible models that incorporate compositional descriptors.

In response, researchers increasingly deploy hybrid modeling that combines DoE with machine learning or mechanistic insight to capture nonlinearities, sequential and adaptive experimentation to refine models and expand domains, and scale-aware methods, including dimensional analysis and CFD-informed design rules, to improve transferability. For multi-objective problems, desirability functions, Pareto-front analysis, and weighted indices are used to define balanced operating regions. For feedstock variability, generalized models based on feedstock properties and multi-biomass experimental programs represent promising directions. As HTC continues to move toward broader industrial deployment, these combined approaches, coupled with transparent reporting of diagnostics such as lack-of-fit tests and validation on new conditions, are expected to improve the reliability and applicability of HTC optimization studies.

In summary, classical DoE approaches remain powerful tools for HTC optimization, but their assumptions and validity domain must be clearly understood. When interpreting RSM- or Taguchi-based results in HTC, it is essential to account for unmodeled nonlinear behavior, the scale at which the study was performed, and the specific feedstock investigated. The 2010–2025 period has been particularly informative in clarifying these limitations. By leveraging the weaknesses identified, including nonlinearity, scale-up effects, interaction structure, multi-objective complexity, and feedstock heterogeneity, researchers can design more robust experiments and build more reliable models. Future work is likely to further integrate advanced modeling techniques into DoE workflows, preserving the efficiency of structured experimental designs while overcoming their current constraints. This hybrid direction, coupled with more transparent reporting of model limitations, such as lack-of-fit diagnostics and validation under new operating conditions, should strengthen the reliability and practical relevance of HTC optimization studies as the technology moves closer to industrial implementation.

5 Standalone machine-learning models for HTC process prediction and optimization

Machine learning encompasses a family of algorithms that infer relationships directly from data without requiring an explicit physical model. In process engineering, ML can build high-capacity predictive models linking operating conditions to process performance while avoiding the formal assumptions that constrain classical empirical approaches, including assumptions of linearity and additivity. Over the past few years, advances in data science and the rapid growth in computing power have enabled the successful testing of ML models to simulate and optimize complex biomass-conversion routes such as HTC. In this section, we review the state of the art from 2010 to 2025 on the use of ML for hydrothermal carbonization, with emphasis on predicting hydrochar properties, including yield, higher heating value, carbon content, and surface characteristics, as well as additional applications such as process control, biomass classification, and operating-condition optimization. We examine the ML algorithms reported in the literature, highlight case studies across diverse feedstocks, compare ML with traditional modeling strategies, and discuss the key challenges associated with deploying ML in HTC research. Most studies reviewed in this section are classified as ML-only approaches. Their models are trained on experimental datasets or literature-derived datasets to predict hydrochar properties or optimize HTC conditions, but the underlying data are not necessarily generated through statistically designed experimental campaigns. Accordingly, ML-only prediction should be distinguished from sequential DoE-to-ML workflows.

5.1 Machine learning algorithms used in HTC process

A broad range of ML algorithms has been applied to HTC, from conventional regression methods to more advanced ensemble and hybrid models. In this section, we summarize the main ML approaches used in the literature to predict hydrochar properties. For each model family, we outline the underlying mathematical principles, clarify its role in representing complex process behavior in HTC, and illustrate its use through representative case studies. Five model families are considered here: artificial neural networks, random forests, support vector machines, gene expression programming, and the XGBoost algorithm.

5.1.1 Artificial neural networks

Artificial neural networks (ANNs) emulate brain-like information processing by connecting layers of computational “neurons.” In a multilayer perceptron with feed-forward propagation (MLP), an input layer passes features through one or more hidden layers, where weighted connections and nonlinear activation functions transform the signal, and an output layer produces the final prediction. The network “learns” by iteratively adjusting the weights during training to minimize a loss function that quantifies prediction error, most commonly the mean squared error (MSE). In a feed-forward architecture, a neuron performs a computation of the following form.

y = f ∑ i = 1 n w i x i + b ,

where x i denotes the input variables, such as temperature, residence time, or carbon content, w i represents the learnable weights, b is the bias term, and f · is the activation function.

This architecture enables ANNs to capture nonlinear relationships between HTC process inputs, for example, feedstock composition, temperature, and time, and output variables describing hydrochar properties. In supervised learning settings, the objective is to approximate complex nonlinear mappings and extract patterns from experimental data, even when cross-interactions and measurement noise are present. Kapetanakis (2021) developed several ANN models, as shown in Figure 8, using experimental and literature-derived data collected over 2014–2021 to predict the HHV and elemental composition (C, H, O) of hydrochar produced from sewage sludge. Their best-performing model achieved R 2 = 0.974 for HHV prediction, highlighting the ability of ANNs to represent complex HTC behavior (Kapetanakis, 2021). These results indicate that, when properly trained, ANNs can outperform polynomial models in predicting hydrochar quality across broader operating domains. Complementarily, Vardiambasis (2020) applied ANN modeling to hydrochars derived from food waste and sludge and showed that carbon content alone can be sufficient to predict HHV with R 2 > 0.89. Other authors trained a multi-input single-output ANN on literature data to predict hydrochar mass yield, energy yield, and HHV. Their optimized ANN architecture achieved very high predictive performance, with R 2 = 0.976 for yield and R 2 = 0.996 for HHV, clearly outperforming multiple linear regression. In that study, simple linear models failed to capture nonlinear effects, whereas the neural network reproduced the complex relationships with high fidelity (Abdulsalam et al., 2020).

Neural networks have also been coupled with optimization algorithms to improve training robustness and predictive accuracy. In one study, the authors proposed a particle swarm optimization-enhanced neural network (PSO-NN) to predict the fuel-related properties of hydrochar using 296 data points (Mu et al., 2022). The PSO-NN approach improved model stability and accuracy, achieving R 2 > 0.85 across all targets while reducing training convergence time by approximately 27% relative to a baseline ANN (Mu et al., 2022). In a second hybrid strategy, Ismail et al. (2019) combined ANN with Kriging interpolation to increase the prediction accuracy of carbon and phosphorus recovery during the hydrothermal carbonization of poultry litter. The ANN-Kriging framework improved predictive performance by 16%–19% compared with the ANN alone (Vardiambasis, 2020). In addition, Li et al. (2021) developed a deep neural network (DNN) model to simultaneously predict multiple hydrochar properties, including HHV, carbon stability, and the H/C ratio, from high-moisture municipal wastes. Their model achieved a mean R 2 of 0.91 and average prediction errors below 10%, and the authors provided a graphical user interface to facilitate laboratory deployment. More recently, Li et al. (2021) introduced a graph neural network (GNN) approach to represent complex biomass mixtures in agricultural HTC. Their bidirectional system not only predicts hydrochar properties from operating conditions but also infers optimal process conditions from a targeted product specification through inverse prediction, which opens new opportunities for AI-assisted process design (Lin et al., 2024).

In summary, artificial neural networks have emerged as powerful prediction and optimization tools for HTC, capable of representing nonlinear mappings between operating variables and hydrochar properties. Hybrid approaches that couple ANN with optimization methods, such as PSO, interpolation strategies, such as Kriging, and more advanced learning paradigms, including DNNs and GNNs, deliver measurable gains in accuracy and robustness. These tools are expected to play a central role in the development of intelligent, sustainable, and economically viable HTC processes.

5.1.2 Decision trees and random forests

Decision trees (DT) and random forests (RF) are widely used supervised learning algorithms for predictive modeling. Regression-tree models partition the feature space into increasingly homogeneous regions through hierarchical if-else rules, which often makes them comparatively interpretable. Random forests aggregate a large number of decision trees trained on bootstrap samples and random feature subsets, which improves predictive robustness and typically reduces variance relative to a single tree (Bulagang et al., 2020; Shaikhina et al., 2019). In the HTC context, DT and RF models can be used to identify key process drivers, such as temperature, moisture content, and feedstock composition, and to predict product properties including hydrochar yield, higher heating value, and carbon content. Compared with neural networks, DT and RF models often provide stronger interpretability through variable-importance analyses while maintaining high predictive accuracy, particularly when datasets are heterogeneous or noisy. Random forests are specifically designed to enhance stability and accuracy while limiting overfitting. Mathematically, the RF predictor can be expressed as follows:

y ^ = 1 N ∑ i = 1 N T i x ,

where T i x denotes the prediction of a single, unpruned decision tree i for the input x. N is the number of trees in the forest (a hyperparameter, typically hundreds or thousands).

RF models have been applied to hydrochar property prediction and are frequently benchmarked against alternative ML approaches. In a recent HTC study on co-processing sewage sludge with biomass, an RF model achieved R 2 values of 0.90–0.95 for predicting carbon content and energy yield (Djandja, 2023a). Liu (2024) reported that RF reached R 2 = 0.942 when predicting HHV and bio-oil yield for lipid-rich biomasses. Across multiple studies, RF performance has been compared with neural networks, polynomial regression, and SVM, often showing competitive accuracy with improved robustness under noisy conditions (El Ouadrhiri, 2024; Padma et al., 2024; Liu et al., 2024; Leng, 2024). Padma et al. (2024) evaluated several regression models, including linear regression, polynomial regression, DT, and RF, to predict hydrochar thermal degradation. The RF model delivered strong performance, although it was slightly inferior to polynomial regression for mass-loss prediction, with an RMSE of 0.017. In another contribution, the authors built an RF model using literature-derived data to estimate recoverable energy via hydrochar as a function of feedstock properties and HTC conditions (Li et al., 2020). Their analysis indicated that the initial carbon content of the substrate is the dominant determinant of recovered energy and that neither extending residence time beyond approximately 150 min nor increasing the initial solids concentration above 20% provides a significant energy gain, trends that were also consistent with experimental observations. Beyond prediction, random forests provide variable-importance metrics that help identify the key drivers, here carbon content and temperature, to guide process optimization.

5.1.3 Support vector machines

SVMs are supervised learning models that are well suited to moderate-sized datasets. They seek an optimal separation in a high-dimensional feature space, typically induced by a kernel mapping, to predict a target variable (Ruiz et al., 2024; Fernández-Delgado et al., 2014; Cervantes et al., 2020; Noble, 2006). SVMs can be applied to classification or regression by identifying an optimal hyperplane that maximizes the margin between data points from different classes, or that yields a smooth regression function. In SVM classification, only a subset of training points located closest to the decision boundary, termed support vectors, determines the hyperplane position (Li et al., 2020). The objective is to identify the decision hyperplane (solid line) that separates two classes with the maximum margin. The margin hyperplanes (dashed lines) are defined by the closest points from each class, which correspond to the support vectors (highlighted points). This large-margin principle underpins the strong generalization performance often observed for SVMs. In support vector regression (SVR), the predictive function is expressed as follows:

f x = ∑ i = 1 n α i − α i * K x i , x + b

where K x i , x is a kernel function (for example, radial basis function or polynomial kernels) and α i and α i * are Lagrange multipliers.

For instance, one study compared SVM, ANN, RF, and k-NN and concluded that SVM achieved strong accuracy for predicting biomass conversion from compositional descriptors (Aghaaminiha et al., 2023). In the broader carbonization context, several studies have highlighted the effectiveness of SVR for modeling and predicting carbon-related behaviors and emissions. Hwang et al. (2021), for example, showed that supervised learning can accurately predict the degree of carbonization of lignin-derived hydrochar using spectroscopic data. Such results support the use of SVR-type models to link operating conditions to the properties of the resulting carbon. Similarly, the coupling of near-infrared spectroscopy with advanced regression methods such as SVR has been validated for non-destructive, real-time prediction of O/C and H/C ratios in hydrochars (Hwang et al., 2021).

A representative example of the application of SVR to HTC modeling is provided by Li et al. (2020) developed SVR models to predict hydrochar yield, HHV, ER, and ED from HTC operating conditions (Li et al., 2020). As illustrated in Figure 9, the parity plots show a strong agreement between predicted and experimental values for both training and testing datasets, with high coefficients of determination (R² generally above 0.88) and low RMSE values. The limited dispersion around the 1:1 line and the overlap between training and testing distributions indicate good generalization performance and limited overfitting. This study clearly demonstrates the capability of SVR to capture the nonlinear relationships governing hydrochar formation and energy-related properties in HTC systems, even when the available experimental dataset remains moderate in size.

Despite these promising results, SVM and SVR remain relatively underused for HTC process modeling compared with ANN or ensemble methods, yet they are particularly attractive when only small datasets are available. For example, an SVR model was trained to predict hydrochar yield and elemental composition in a multi-output HTC study (Shafizadeh, 2023). When benchmarked against a decision-tree model, SVR delivered reasonable accuracy but was slightly less precise than the tree-based ensemble. More broadly, SVM-based approaches have also been tested to predict biomass conversion into hydrochar or oil under HTC conditions, with satisfactory performance even if they are less frequently reported than ANN or random forests in this specific domain (Aghaaminiha et al., 2023). A key strength of SVM/SVR is their ability to mitigate overfitting through regularization, although they are generally less intuitive to interpret than tree-based models.

5.1.4 XGBoost algorithm

XGBoost (eXtreme Gradient Boosting) is a high-performance ensemble learning algorithm built on gradient-boosted decision trees (Gradient Boosting, 2026). It constructs trees sequentially, with each new tree trained to correct the residual errors generated by the preceding ensemble, thereby refining predictive accuracy at each iteration (Chen and Guestrin, 2016; Yao et al., 2022). Owing to its ability to capture complex non-linear relationships, handle feature interactions, and incorporate regularization to limit overfitting, XGBoost has emerged as one of the most effective algorithms for predicting HTC performance metrics (Velusamy, 2023; Xie, 2025; Ge, 2025; Mazibuko and Akindeji, 2025; Liu et al., 2025; Elgart, 2021). The final prediction can be expressed as follows:

y ^ i t = y ^ i t − 1 + η · f t x i ,

where η is the learning rate and f t x i is the prediction of the tth model.

Figure 10 provides a concise schematic of how XGBoost can be applied to modeling and optimizing the HTC process. Unlike ensemble approaches that rely on independent aggregation of trees, XGBoost is built on sequential gradient boosting. Each new tree is trained to fit the residual errors left by the previous trees, so model performance is refined iteratively rather than averaged in a single step. This boosting strategy typically improves predictive accuracy in strongly non-linear and multivariate systems, which is consistent with the reaction network and coupled transport phenomena encountered in HTC, including simultaneous dehydration, decarboxylation, polymerization, and recondensation reactions.

A central advantage of XGBoost is that it incorporates explicit regularization and shrinkage, which helps limit overfitting while preserving high expressiveness (Deng et al., 2021; Boldini et al., 2023; Kolluri et al., 2020; Li et al., 2021). In practical HTC datasets that mix different feedstocks, operating windows, and measurement protocols, this balance between flexibility and regularized learning is often critical. Figure 11 also highlights a second feature that is valuable for process engineering workflows, namely, the extraction of variable-importance indicators. These outputs provide a ranked view of which process descriptors most strongly drive predicted outcomes, enabling rapid identification of dominant levers such as temperature, residence time, solid-to-liquid ratio, pH, or catalyst loading, depending on the target metric. In turn, these insights can inform DoE refinement, targeted experimentation, and multi-objective optimization strategies. Taken together, the combination of strong predictive performance, robustness to heterogeneous datasets, and partial interpretability via feature-importance diagnostics explains the growing interest in XGBoost for advanced HTC analytics and process steering.

In HTC studies, key operating and physico-chemical descriptors such as temperature, residence time, solid-to-liquid ratio, and feedstock type are commonly used as model inputs to predict multiple hydrochar properties in parallel. Target outputs typically include solid yield, higher heating value, carbon content, and recoverable energy, which together provide an integrated view of process performance. Kardani et al. (2022) reported that XGBoost outperformed ANN and SVM in predicting lignocellulosic biomass conversion, achieving R 2 = 0.999 on the training set and R 2 = 0.964 on the validation set (Aghaaminiha et al., 2023). Similarly, Djandja (2023b) applied XGBoost to multi-output prediction in co-HTC systems, simultaneously estimating HHV, carbon content, hydrochar yield, and recovered energy with R 2 values up to 0.95. Wang W et al. (2025) further demonstrated the effectiveness of XGBoost for multi-task prediction using digestate-derived datasets, where it outperformed Random Forest in most evaluated scenarios. Beyond multi-target regression, XGBoost has also been used to predict fuel-related properties while emphasizing the optimization of influential variables such as ash content in the feedstock, reaction temperature, and solid-to-liquid ratio. In that context, the model delivered strong predictive performance with R 2 ranging from 0.825 to 0.985 and RMSE values between 1.119 and 5.426, supporting its robustness for parameter optimization workflows (Liu et al., 2024). While these results highlight XGBoost as a high-performing tool for hydrochar property prediction and process tuning, its added value is best appreciated when linked to downstream application requirements. Hydrochar is deployed across energy storage, soil amendment, and pollution control, and ML-enabled process models can strengthen these application pathways by enabling tighter control over production conditions and more reliable tailoring of resulting material properties (Islam, 2022; Zhang et al., 2018; Maniscalco, Volpe, and Messineo, 2020).

5.1.5 Advanced multivariate regression models

Beyond classical linear regression, regularized regression approaches such as Lasso and partial least squares, as well as non-linear regressions such as higher-order polynomials and splines, can be employed. For example, Vallejo et al. (2020) proposed a robust multivariate linear regression model combined with decision trees to predict, at the same time, the hydrochar mass yield and its HHV. By incorporating global indicators of reaction severity, including a severity factor and a polarity index computed from the biomass C/H/O/N/S composition, their model achieved R² values above 0.9 on a large and diverse dataset (Kapetanakis, 2021). This type of hybrid statistical model, which is more transparent than ANN-based approaches, can provide relatively simple equations that are useful for practitioners, at the cost of additional upfront analytical work to characterize the biomass in sufficient detail.

Several ML applications connected to HTC have emerged in recent years, including the prediction of hydrochar yield and elemental composition as a function of operating conditions to optimize product energy content [41], the joint prediction of solid and liquid yields to close the mass balance (Kapetanakis, 2021), simultaneous prediction of solid and liquid yields to close the mass balance (Blach and Engelhart, 2021), and the estimation of the liquid effluent composition as a function of process conditions, such as total organic carbon and ammoniacal nitrogen, to anticipate post-treatment needs. ML has also been used as a decision-support layer for valorization pathways, for instance, to classify whether a given hydrochar is more suitable for fuel applications or for soil amendment based on measured properties. In addition, ML has been applied in neighboring processes that are methodologically close to HTC, including hydrothermal liquefaction and co-processing schemes. For example, Djandja et al. (2023b) developed XGBoost and random forest models to predict the fuel properties and mass and energy yields of hydrochar produced by the co-hydrothermal carbonization of sewage sludge and lignocellulosic biomass, illustrating how machine learning can support the optimization of mixed-waste treatment conditions. (Djandja, 2023a). Similar modeling practices in digestate management or composting, where neural networks are used to anticipate product quality from input characteristics, can also inform HTC-oriented workflows.

5.2 Validation, uncertainty, and generalizability of ML models

Despite these advances, deploying ML in HTC still faces substantial challenges. A central limitation is the availability of sufficiently large, high-quality datasets for model training, since each HTC experiment yields a relatively expensive data point. Aggregating data from the literature is a practical strategy, as reported by Vallejo et al. (2020), but it can introduce heterogeneity linked to protocol differences and measurement uncertainties, and it rarely spans the full design space. ML models can become biased when training data are concentrated in narrow regions, for example, many experiments near 200 °C with few beyond 250 °C. In such cases, the model may extrapolate poorly outside the best-represented domain (Seifrid, 2022). Interpretability is another important barrier for industrial adoption, since decision-makers often need to understand why a model recommends a given set of conditions. Sensitivity analyses and Shapley-value methods can help convert complex models into actionable insights, for example, highlighting that overly low biomass moisture may be associated with a lower hydrochar HHV (Tasca et al., 2019). Finally, practical integration into process operation is not straightforward. It requires interfaces, sensor systems capable of supplying real-time inputs, and robust strategies to manage model drift when conditions change, such as when a new biomass feedstock differs from those seen during training. These issues are addressed later when discussing DoE-ML coupling strategies.

The validity of an ML model for HTC should not be inferred from a high R² value alone. Reported performance must be interpreted together with the evaluation design, the composition of the dataset, the range of feedstocks and operating conditions represented, and the independence of the data used for testing. As summarized in Table 2, several studies report strong predictive metrics, but the details of train-test partitioning, cross-validation, hyperparameter optimization, or independent external validation are not always fully described. The absence of reported information should not be interpreted as evidence of an inadequate procedure; however, it limits the ability to assess the robustness and reproducibility of the reported performance.

TABLE 2. Comparative performance of major ML algorithms in hydrothermal carbonization.

NR, not reported explicitly in the study/abstract. Test metrics refer to held-out tests or cross-validation when reported by the authors.

Random train-test splitting can be useful as an initial evaluation strategy, but it may overestimate model performance when closely related observations, replicate experiments, or records from the same literature source are distributed across both training and test subsets. This risk is particularly relevant for compiled HTC datasets, in which experimental protocols, reactor configurations, and analytical methods may vary between studies. Data preprocessing, including scaling, outlier treatment, imputation, feature selection, and hyperparameter tuning, should therefore be performed using the training data only and repeated within cross-validation folds when applicable, in order to avoid information leakage.

More robust evaluation strategies should be selected according to the intended use of the model. For small experimental datasets, repeated or nested cross-validation can provide a more stable estimate of model performance than a single train-test split. For multi-feedstock or literature-derived datasets, validation using an unseen feedstock, an independent experimental study, or a separate reactor campaign is more informative because it directly evaluates transferability beyond the original data domain. External experimental confirmation of model-recommended conditions remains particularly important when the objective is process optimization rather than retrospective prediction.

A comparative synthesis of ML models used in HTC, including ANN, decision trees and random forests, SVM, XGBoost, and multivariate regression approaches, is provided in Table 2. For each study, the table reports the biomass, input variables, target outputs, performance metrics such as R² and RMSE, as well as the reported validation approach and the main limitation affecting model robustness or transferability.

The comparison highlights that model generalizability remains a central unresolved issue in HTC. A model trained within a narrow temperature range, on a single feedstock, or using incomplete feedstock descriptors should not be assumed to remain reliable for new biomass types, reactor configurations, or operating conditions outside the original training domain. Models should therefore define their applicability domain and report prediction errors not only globally but also across feedstock classes and relevant operating ranges. In addition to R² and RMSE, the reporting of MAE, residual bias, uncertainty intervals, and the coverage of prediction intervals would provide a more complete assessment of predictive reliability. Ensemble, Bayesian, or other uncertainty-aware approaches are particularly relevant because they can indicate when a model is making predictions in poorly represented regions of the HTC design space. Together, these practices would reduce the risk of overconfident optimization recommendations and improve the credibility of ML-assisted process design.

6 Comparative and integrated DoE-ML workflows in the HTC process

Given the complexity of the HTC process, combining DoE with ML models appears to be a promising strategy to leverage the strengths of both approaches (Mu et al., 2022; El Ouadrhiri et al., 2023). DoE-ML coupling can take multiple forms, ranging from a sequential workflow (DoE to generate training data for ML models, followed by ML to refine optimization) to tighter integrations within adaptive schemes in which ML actively guides the next experiments to be performed (Li et al., 2021; Shafizadeh, 2023). Although relatively few studies have explicitly implemented this coupling in HTC to date, a substantial body of work in other fields has demonstrated its added value, thereby establishing transferable methodological foundations (Dang, 2024; Shafizadeh, 2023).

The literature reviewed in this article can be organized into five distinct methodological categories. The first category comprises DoE-only HTC optimization studies, which use factorial or response-surface designs to identify factor effects and local operating windows. The second comprises ML-only prediction studies, in which algorithms are trained on experimental or literature-derived datasets without a preceding DoE campaign. The third category includes RSM-versus-ML comparisons, where conventional polynomial models and ML algorithms are evaluated on the same dataset. These benchmarking studies are informative, but they do not by themselves constitute an integrated DoE-ML workflow. It is, therefore, important to recognize that, although these approaches may share similar datasets, their objectives and methodological implications differ significantly.

The fourth category corresponds to sequential DoE-to-ML workflows, in which a statistically designed experimental campaign generates a structured dataset that is subsequently used to train and refine an ML model. This category is the most directly aligned with the concept of DoE-guided machine learning. In such cases, the quality and structure of the experimental design play a critical role in determining the robustness and generalizability of the resulting ML models. Finally, active-learning, Bayesian-optimization, and self-driving-laboratory approaches represent more advanced closed-loop frameworks in which the model selects the next informative experiment and is iteratively updated with new measurements. These approaches extend beyond static datasets and introduce adaptive experimentation strategies that can significantly improve efficiency and knowledge discovery. The following discussion explicitly distinguishes these categories. This distinction is essential because conventional DoE optimization, standalone ML prediction, and RSM-ML comparisons address different methodological questions and provide different levels of evidence for predictive, transferable, and adaptive HTC optimization. Clarifying these differences also helps to avoid potential misinterpretations in the literature, particularly when comparing studies that rely on fundamentally different experimental and modeling paradigms.

6.1 RSM-versus-ML comparisons

A widely used but conceptually distinct practice consists of comparing RSM and ML models after data collection to evaluate their relative predictive performance. In the context of biomass pyrolysis, Angin and Tiryaki (2016) were among the early contributors to apply an ANN to predict bio-oil and biochar yields in parallel with a conventional RSM model. Their comparison indicated a slightly higher predictive capability for ANN (R² = 0.939 vs. 0.934), suggesting that ANN could capture effects not represented by the quadratic polynomial, and could therefore substitute RSM for this process in certain cases. Similar RSM-versus-ML comparisons have since been reported in related areas (gasification (Bhange et al., 2019), flue-gas desulfurization (Makomere et al., 2023), and hydrochar-based water remediation (Funke and Ziegler, 2010)). In most cases, ML models—particularly neural networks—match or slightly outperform RSM in predictive accuracy, at the cost of reduced interpretability. A limited number of studies have attempted to combine both approaches, for instance by using DoE outcomes to train a more global ML model (Kapetanakis, 2021).

Beyond these examples, DoE-ML integration has been explored across diverse sectors. In pharmaceutical engineering, mixture designs coupled with neural networks have improved the prediction of drug stability during formulation optimization (Fine, 2022; Dangeti et al., 2023). In materials science, researchers combine high-performance computing with fractional DoE strategies and regression models to explore vast compositional spaces in alloys and ceramics (Angulo et al., 2022; Ishizuki et al., 2023). Comparable concepts have also been adopted in the agri-food sector to optimize fermentation processes through adaptive strategies. Across these domains, the unifying principle is to make experimentation and learning interact synergistically, rather than treating them as competing paradigms (Baskar et al., 2024; Chai et al., 2024).

6.2 Sequential DoE-to-ML workflows in HTC process

For HTC itself, the literature indicates that relatively few studies have fully leveraged this coupling. Most published works either follow a classical DoE workflow (optimizing HTC of a given biomass via RSM) (Chai et al., 2024; Baskar et al., 2024), or apply ML to aggregated literature datasets to extract broader trends (Kapetanakis, 2021). This highlights a gap regarding the fine-grained integration of these tools in HTC research. Nevertheless, the emerging methodologies discussed above suggest concrete pathways forward. One could envision a closed-loop control framework for a laboratory HTC reactor in which an algorithm (ANN or another model) predicts hydrochar yield and proposes the next operating conditions to test; the operator executes the suggested experiment, and the resulting data are then used to update the model (e.g., via sequential Bayesian learning).

Another promising direction to improve robustness in HTC predictive modeling is the development of hybrid models that combine phenomenological knowledge with ML algorithms. This concept relies on incorporating physically meaningful intermediate variables derived from thermochemistry—such as theoretical dehydration extent or atomic H/C and O/C ratios—directly into the ML input space or model structure. For example, Xu et al. (2013) introduced a fixed carbon index (FCI), derived from HTC severity, to model the relationship between hydrochar combustion performance and chemical structure, reporting an exponential correlation between FCI and decarbonylation/dehydration phenomena (Kapetanakis, 2021). Such chemistry-informed variables could effectively guide neural networks toward more transferable predictions across diverse biomasses. More recently, Zhang (2024) developed an intelligent multi-objective prediction framework for hydrochar properties (yield, HHV, and elemental composition), integrating not only operating conditions (temperature and duration) but also biochemical and elemental descriptors of the biomass feedstock, including ash, proteins, lipids, and carbohydrates. Their analysis indicated that intrinsic biomass properties exerted a stronger influence on outcomes than process parameters alone. Collectively, these results suggest that embedding prior knowledge (from chemistry or lignocellulosic structure) into ML models can reduce dependence on large datasets and enhance transferability to new feedstocks. In summary, while DoE–ML coupling remains at an early stage for HTC, the state of the art in other disciplines provides a solid and adaptable methodological framework that could help bridge this gap in the near future.

6.3 Active-learning, Bayesian optimization, and self-driving-laboratory concepts

These approaches should be regarded as emerging and largely prospective for HTC. The examples discussed below originate mainly from organic synthesis, materials science, and catalysis, where closed-loop experimentation has been more extensively developed.

In organic chemistry, for instance, reaction optimization poses challenges comparable to those of HTC, with many adjustable parameters that must be tuned to maximize yield or selectivity. Recent approaches increasingly rely on adaptive experimentation supported by embedded ML models. Li et al. reviewed ML-driven optimization of reaction conditions and emphasized the benefit of combining global models (trained on large datasets) with local models (trained on a limited number of targeted experiments) to steer experimental campaigns (Chen and Li, 2024). In particular, Bayesian optimization has become a widely used framework. A surrogate model (often a Gaussian process) is trained on the experimental outcomes already collected, and an acquisition function is then used to select the next experiment to maximize the expected information gain or performance improvement. This iterative loop—representing a formal implementation of adaptive DoE coupled with ML—has enabled notable progress in organic synthesis, identifying near-optimal conditions within only a few dozen experiments, whereas hundreds of random trials would otherwise be required (Seifrid, 2022). A similar strategy could be envisioned for HTC: an ML model (e.g., a nonlinear multi-parameter regressor) could propose temperature, residence time, and related operating conditions to improve hydrochar yield, energy densification, or a multi-criteria objective function (e.g., maximizing HHV while minimizing oxygen content). Emerging work in materials science and catalysis further underscores the potential of such coupling. For example, automated “self-driving labs” already integrate orchestration platforms (e.g., ChemOS-like software) that combine ML with robotic execution of experiments to accelerate materials discovery (Seifrid, 2022). While these systems have primarily been deployed for catalyst screening or polymer formulation, the underlying philosophy is directly relevant to HTC: automate data acquisition.

7 Critical analysis of DoE-ML coupling: benefits, limitations, and key challenges

The combined use of DoE and ML for optimizing HTC offers substantial potential advantages while also raising challenges that must be assessed critically.

7.1 Expected advantages and benefits of coupling

Coupling DoE with ML creates notable synergies in the context of HTC for hydrochar production. First, it enables a more efficient exploration of the experimental space. A rigorous statistical design ensures that parameter combinations are covered effectively while limiting redundant trials (Baskar et al., 2024; Mu’Azu, 2022). The resulting datasets can then be used to train ML models capable of predicting and optimizing hydrochar properties across the full investigated domain (Mu et al., 2022). For example, Zhang (2024) developed accurate multi-objective ML models (R² ≈ 0.93) to simultaneously estimate hydrochar yield and elemental composition, thereby mitigating the time- and resource-intensive nature of conventional experimental optimization.

The principles and expected benefits of coupling DoE and ML in the HTC context are summarized in Figure 11. This figure presents the methodological framework of integrating DoE with ML algorithms applied to HTC. It shows how a statistically driven exploration of the experimental space can generate a compact yet informative dataset, which is subsequently exploited by models such as random forests, neural networks, or XGBoost to capture nonlinear relationships and complex process interactions. This integrated approach enables multi-objective prediction of hydrochar properties and identification of optimal operating conditions while reducing the number of experimental runs and facilitating translation of findings toward industrial-scale implementation.

This coupling is typically associated with a reduction in the number of experiments required to meet a given objective: a factorial or response surface DoE yields a minimal yet informative dataset, which ML can then exploit to interpolate or extrapolate outcomes between the tested points (Liu et al., 2024). Another major advantage is improved predictive accuracy. Machine-learning algorithms (e.g., random forests, artificial neural networks, and XGBoost) capture non-linear relationships and complex factor interactions more effectively than classical polynomial DoE models. Several comparative studies report that ML models often outperform RSM regression in terms of predictive reliability (Kardani et al., 2022).

In the case of HTC applied to agricultural amendments, an ANN proved more effective than RSM for predicting hydrochar yield from operating conditions (Rasam et al., 2021; El Ouadrhiri, 2024). Moreover, ML models can be used to identify optimal conditions and thus guide experimental work. For instance, the combined use of DoE and ML on biowastes enabled the identification of an optimal compromise between pH, temperature, and residence time to maximize carbon stability and phosphorus availability in the resulting hydrochar—information that would otherwise require extensive trial-and-error experimentation (Shafizadeh, 2023; Li et al., 2021; Xie, 2025). Collectively, these benefits improve laboratory efficiency and facilitate scale-up, supported by predictive models capable of simulating a range of industrial operating scenarios (Wang X et al., 2025).

7.2 Limitations and challenges of DoE–ML coupling

Despite its advantages, DoE–ML coupling entails methodological complexity and several limitations that warrant emphasis. First, effective implementation requires strong multidisciplinary expertise. One must design an appropriate experimental plan (selection of factors, experimental domain, and design type), then select, train, and validate a suitable learning algorithm—each step demanding distinct technical competencies. Consequently, initial costs can be substantial, particularly in terms of data generation and the tooling required. A sufficiently large volume of high-quality data is essential to train robust ML models. In HTC, acquiring such data may require numerous preliminary experiments or the time-consuming compilation of results from the literature. For example, Zhang (2024) compiled data from 87 experimental studies to build a training set rich enough to predict the HTC performance of diverse biomasses. This data requirement can be prohibitive for teams with limited resources. In addition, handling heterogeneous datasets often requires rigorous normalization of protocols and measurement units prior to modeling—an onerous step that also reflects the current lack of unified standards in the field. The associated investment in software infrastructure (computing platforms and potential licenses) and staff training is also non-negligible, which may slow adoption of DoE–ML approaches in certain laboratories and industrial settings.

A second major challenge concerns industrial transfer. Models developed on laboratory data under controlled conditions can lose reliability when scaled up. Scale-dependent phenomena not represented in the original training domain (heat and mass transfer limitations, fouling, and variability in feedstock quality) may emerge and reduce model validity outside the initial operating window. Moreover, the industrial deployment of HTC itself involves significant engineering constraints (high-pressure reactor design, management of aqueous effluents, and energy costs), which further complicate implementation (Ischia et al., 2024). DoE–ML coupling does not inherently resolve these issues and may even exacerbate them if the model recommends “optimal” conditions that are difficult to realize in practice. Organizational complexity should also not be underestimated. Coordinating experimentalists and data scientists, maintaining long-term data governance, and convincing industrial decision-makers of the value of these approaches constitute challenges in their own right. In practice, the promised reduction in experimentation is realized only after a substantial upfront investment and added complexity, while translation from bench to plant still requires additional validation and sustained engineering effort.

In summary, DoE–ML coupling is a powerful lever for improving HTC optimization, but successful implementation requires addressing methodological and organizational constraints. A critical and measured approach is, therefore, necessary: identifying the contexts in which coupling delivers clear added value, and ensuring sufficient mastery of the tools so that it does not become an unnecessary source of complexity. The next section outlines future perspectives to support the effective integration of these methods into HTC optimization. To operationalize this approach, we adopt the workflow presented in Figure 12. Structured across three levels (DoE and experiments → Data and ML → Optimization and transfer), this framework formalizes our methodology into ten steps: (1) definition of objectives/KPIs, (2) selection of factors, (3) DoE design, (4) HTC experiments with QA/QC, (5) data preparation, (6) ML modeling (RF, ANN, SVM, XGBoost, and MLR), (7) validation and interpretability (CV/test and SHAP), (8) multi-objective optimization (constrained Pareto front), (9) robustness and sensitivity analyses (Sobol/Monte Carlo), and (10) pilot/industrial transfer and decision-making. Particular emphasis is placed on the feedback loop (validation → DoE redesign), which enables iterative improvement of the model and alignment with process and industrial constraints.

7.3 Challenges of coupling DoE–ML for HTC

Several specific challenges still need to be overcome in order to fully leverage DoE–ML coupling for HTC in the coming years.

• Integrating domain knowledge into ML models. Most current approaches remain predominantly data-driven, relying on statistical correlations without explicitly embedding the physico-chemical laws governing the process. A key direction will be the development of hybrid models that combine process expertise (known kinetics, thermodynamic constraints, etc.) with the predictive power of ML. Incorporating prior knowledge could reduce data requirements and enhance robustness by preventing non-physical solutions. For instance, constraining ML models with chemistry-based bounds (e.g., mass balances and stoichiometric ratios) would ensure that the operating conditions proposed as “optimal” remain realistic with respect to reactor behavior. Addressing this challenge requires close collaboration between domain specialists (chemists and process engineers) and data scientists to deliver physically interpretable models.
• Explainability of predictive models. ML algorithms commonly used in this area (e.g., deep neural networks or tree ensembles) are often perceived as “black boxes,” which can hinder acceptance in industrial contexts where operating decisions must be understandable and defensible. Developing and systematically applying explainable AI (XAI) methods to HTC is, therefore, essential. Practically, this means extracting information about variable importance and the cause–effect relationships learned by the model. Recent work has demonstrated the feasibility of such approaches: analysis of a multi-target ML model identified key drivers of hydrochar properties (ash content, reaction temperature, initial C and N contents, etc.), with insights consistent with established process chemistry (Zhang, 2024). Generalizing interpretability analyses of this type will improve operator confidence and facilitate model-informed decision-making (e.g., clarifying why a given temperature window maximizes hydrochar HHV). A key requirement will be integrating XAI tools from the earliest stages of model design.
• Minimum reporting schema for HTC DoE-ML datasets. The transferability of DoE–ML models in hydrothermal carbonization depends not only on the number of available observations, but also on the completeness and comparability of the associated experimental metadata. To support reproducible dataset construction and meaningful cross-study comparison, we propose a minimum reporting schema for future HTC studies intended for modeling, optimization, or data sharing. This proposal is not intended as a formal reporting standard but as a practical framework to improve the quality and reusability of experimental data.

As summarized in Table 3, the proposed schema identifies the key categories of information that should be systematically reported to ensure dataset consistency and facilitate downstream modelling efforts.

TABLE 3. Proposed minimum reporting schema for HTC datasets intended for DoE and machine-learning applications.

Adoption of this minimum information would facilitate the development of more coherent multi-study datasets and would reduce ambiguity when comparing reported model performance. In particular, explicit reporting of feedstock descriptors, reactor conditions, response definitions, replication, and validation procedures would help distinguish genuine process-related effects from differences caused by experimental conventions or incomplete metadata.

• Uncertainty quantification and management. A cross-cutting challenge is the explicit consideration and quantification of uncertainty at every stage of the workflow. On the experimental side, DoE studies should incorporate replication and rigorous statistical analysis (ANOVA; confidence intervals) to quantify variability in measured responses. On the modeling side, ML systems should provide not only point predictions but also an estimate of predictive reliability. Bayesian learning approaches and ensemble-based models (bagging and boosting) can yield prediction intervals or confidence scores. For example, a random forest can associate each prediction with a dispersion linked to inter-tree variance, reflecting model uncertainty. Integrating these practices enables decision-makers to evaluate confidence levels in the recommended optimal (e.g., predicting a 60% ± 5% yield with a confidence interval rather than a single value). Moreover, uncertainty-aware optimization naturally promotes robustness: rather than optimizing for a single potentially uncertain point, one seeks an operating region that remains optimal under plausible parameter variability. Meeting this challenge will improve the credibility of DoE–ML coupling and accelerate industrial adoption because users can explicitly assess risk and adjust safety margins accordingly.

In summary, DoE–ML coupling for HTC already delivers tangible gains in experimental efficiency and predictive performance. However, its optimal deployment will require addressing several scientific and technical bottlenecks—from enriching models with process knowledge to establishing shared standards and ensuring transparency and reliability of predictions. Continued progress on these fronts, supported by a growing body of indexed research output, is expected to position DoE–ML as a standard framework for optimizing innovative processes such as biomass hydrothermalization. Recent and ongoing studies suggest that these challenges will progressively be resolved, consolidating the complementarity of DoE and ML in support of an efficient, controlled, and industrially transferable HTC process (Ischia et al., 2024).

8 Outlook for strengthening DoE–ML integration in HTC optimization

In light of the preceding analysis, several future directions emerge to enhance and broaden the combined use of DoE and ML in HTC. These perspectives involve not only scientific and technological advances but also shifts in how research is conducted.

• Automation and intelligent laboratories. Automation, real-time optimization, and self-driving laboratory concepts should currently be regarded as longer-term research directions for HTC rather than as established industrial practices. Although closed-loop experimentation has been demonstrated in adjacent fields such as catalysis, materials science, and organic synthesis (Seifrid, 2022), comparable implementations remain limited in hydrothermal carbonization. In HTC, the transition from laboratory optimization to automated control is constrained by the need for reliable monitoring of temperature, pressure, slurry characteristics, feedstock variability, and relevant liquid-phase indicators, together with robust safety interlocks and uncertainty-aware models.

A more realistic intermediate step is the development of instrumented pilot-scale HTC campaigns in which DoE-ML models are used to support operating decisions while respecting reactor, energy, and effluent-management constraints. Such systems could progressively integrate online measurements and adaptive model updating, but industrial closed-loop control should only be considered after reproducible performance has been demonstrated across feedstocks, operating campaigns, and scale-relevant process conditions.

• Hybridization of mechanistic and ML models (model-data fusion). A promising trend is the development of hybrid models that combine fundamental process knowledge with statistical learning. For instance, physico-chemical constraints (carbon balances and stoichiometric relationships for dehydration/decarboxylation pathways) could be embedded into neural networks to guide learning and prevent physically implausible predictions. Physics-informed approaches (e.g., physics-informed neural networks) are increasingly used in other complex domains (fluid dynamics and chemical reactors) and could be adapted to HTC. Similarly, introducing interpretable latent variables—such as severity factors commonly used in biomass hydrolysis, or proxy indicators of lignin conversion—as inputs or intermediate outputs may improve generalization across substrates (Kapetanakis, 2021). These hybrid models could be trained on both experimental datasets and simulated data generated from simplified kinetic representations, combining complementary sources of information. The longer-term objective is the development of high-fidelity digital twins of HTC that remain consistent with physical laws and can be queried virtually to screen new scenarios prior to experimental validation.
• Broadening the optimization scope. To date, DoE–ML studies in HTC have mainly targeted intrinsic process performance, whereas the routine integration of life-cycle assessment and techno-economic analysis into optimization loops remains limited. Future work should integrate additional criteria that reflect environmental and economic dimensions. For example, multi-objective optimization could aim to maximize hydrochar yield while minimizing process carbon footprint or aqueous-phase toxicity. This will require ML approaches that can handle multi-output targets (multi-task networks) or multi-objective optimization frameworks (e.g., evolutionary algorithms coupled with predictive surrogate models). A further step would be to incorporate life-cycle assessment (LCA) and techno-economic analysis directly into the optimization loop: ML models could be trained not only to predict product quality but also to estimate operating costs or greenhouse-gas impacts under given HTC conditions (via meta-models trained on LCA simulations, as illustrated by recent HTC LCA efforts) (Ogunleye, Flora, and Berge, 2024; Singh, 2024a). In this way, DoE–ML could guide HTC toward globally optimal operating regimes rather than optima defined solely at the unit-operation level, aligning with sustainability imperatives and more holistic process decision-making.
• Cross-domain transfer and data sharing. Another strategic perspective is to transfer knowledge learned through DoE–ML across related thermochemical and hydrothermal processes. For example, insights derived from DoE–ML coupling for the HTC of sewage sludge could inform optimization of hydrothermal liquefaction or fast pyrolysis of other wet wastes, and vice-versa. Transfer learning methods can be explored: a neural network trained on HTC datasets for agricultural residues could provide an effective initialization for models targeting algal HTC, accelerating convergence and reducing data requirements. More broadly, open and shared HTC experimental databases would facilitate training of more general and robust ML models. One can envision academic-industrial consortia aggregating HTC data globally, where each new publication contributes structured data to a centralized repository. Given the strong emphasis on 2015–2025 studies in this review, the field appears to be in a knowledge-accumulation phase; as datasets mature, fully data-driven modeling at scale becomes increasingly feasible, and DoE-ML coupling will be a key mechanism for extracting actionable value from that information.
• Training and accessibility. Beyond technical innovation, broad adoption will depend on skills development and usability. Training the next generation of process engineers in data science and ML-enabled experimentation—through dedicated curricula and applied case studies in chemical engineering—will be essential. In parallel, accessible software environments that integrate DoE and ML natively (either as modules in established DoE tools or as extensions within Python/R ecosystems) will lower adoption barriers. A practical vision is a user-facing platform in which the practitioner specifies HTC factors, receives an optimized experimental design, inputs measured responses, and obtains not only RSM outputs but also automated ML model training, quantified prediction gains, interpretability diagnostics, and recommendations for the next most informative experiments. Making such tools user-friendly and transparent is critical for deployment beyond academic settings.

In summary, future directions for DoE–ML coupling in HTC optimization are diverse and mutually reinforcing. They converge toward a vision of intelligent, data-driven process development, where statistically efficient experimentation and advanced ML enable unprecedented levels of optimization and operational flexibility. Achieving this vision will require coordinated investment in R&D, infrastructure, and training—but the anticipated benefits in efficiency, robustness, and sustainability provide a strong rationale for continued development.

9 Conclusion

Hydrothermal carbonization is increasingly viewed as a materials-manufacturing platform rather than only a biomass upgrading route because it can generate carbonaceous solids whose composition, surface chemistry, and microstructure are adjustable under comparatively mild hydrothermal conditions. At the same time, the process remains intrinsically difficult to control in a predictive manner, precisely because hydrochar formation is governed by tightly coupled and simultaneous dehydration, decarboxylation, polymerization, and recondensation reactions in subcritical water. These concurrent pathways evolve in a strongly nonlinear fashion with temperature, residence time, solid-to-liquid ratio, pressure, and catalysis, and their net outcome is further modulated by feedstock heterogeneity and matrix effects. The consequence is a persistent gap between empirical process tuning and application-driven, property-targeted hydrochar design.

The literature surveyed in this review shows that conventional empirical approaches have been essential for establishing broad operating trends, yet they frequently fall short when the goal is to map multivariate interactions to specific materials descriptors such as fixed carbon enrichment, functional-group retention, pore development, and the balance between aromaticity and surface polarity. In this context, design of experiments provides a rigorous statistical scaffold for exploring multifactorial spaces efficiently, isolating dominant factors, and quantifying interaction effects with manageable experimental effort. DoE strategies are particularly valuable when the objective is to generate structured datasets that preserve interpretability and enable reproducible comparisons, which is critical for translating laboratory observations into transferable design rules for hydrochar properties.

Machine learning extends these capabilities by leveraging algorithms that can learn high-order nonlinear relationships from multidimensional datasets and predict material-relevant outputs more effectively than classical response-surface models in many HTC settings. Algorithms such as artificial neural networks, ensemble methods, boosting, and Bayesian approaches have been used to predict key performance indicators including mass yield, heating value, fixed carbon content, carbon retention, and attributes linked to porosity and surface functionality. However, the utility of these models remains tightly coupled to data quality, representativeness, and harmonization, and interpretability remains a central requirement if predictions are to be trusted for materials design rather than used as black-box regressors.

One of the most consequential messages emerging from this review is that the coupling of DoE and machine learning offers a practical route to bridge mechanistic complexity and design-oriented predictability. We show that DoE can be used not only to reduce experimental burden but also to produce information-rich datasets that are particularly well suited for training and validating machine learning models. In turn, machine learning can capture nonlinearities that reflect the underlying reaction-network behavior and support multi-objective optimization when materials targets compete, for example, when energy densification must be balanced against preservation of oxygenated surface functionalities or when pore development must be reconciled with mass yield constraints. This combined framework is therefore well positioned to accelerate rational hydrochar engineering for use as solid fuels, adsorbents for water and gas treatment, or precursors for advanced carbon materials.

Despite clear progress, several bottlenecks continue to constrain generalization and industrial robustness. These include variability in biomass composition and preprocessing, inconsistent reporting and comparability of experimental descriptors, limited availability of harmonized datasets spanning diverse feedstocks and operating windows, and the need for more interpretable models that can be linked back to physicochemical understanding of HTC transformations. We argue that addressing these challenges will require coordinated efforts in experimental standardization, curated data practices, and hybrid modeling strategies that connect algorithmic prediction to physically meaningful descriptors of hydrochar structure and chemistry.

Overall, we conclude that a materials-driven HTC paradigm becomes substantially more defensible when design of experiments and machine learning algorithms are integrated as complementary tools, enabling structured data generation, improved predictive performance, and more coherent design rules for structure–property relationships. By strengthening the linkage between hydrothermal reaction pathways and measurable materials attributes, these approaches advance hydrothermal carbonization toward a more predictive and application-oriented route for producing functional carbonaceous materials from wet biomass.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Xu Zeng, Huaqiao university, China

Reviewed by: Zeai Huang, Southwest Petroleum University, China

Eslam Gomaa Al-Sakkari, Polytechnique Montréal, Canada