Predicting tensile properties of sub-sized nuclear materials using data augmentation strategies on imbalanced and sparse datasets

1 Introduction

Modern nuclear reactor technologies are designed for high-efficiency power generation and operate under extreme conditions of elevated temperatures and intense radiation, which present significant engineering challenges that necessitate innovative materials solutions (Li et al., 2016; Kornecki and Wise, 2024; Ramana, 2021; Stacey, 2007; Zhan et al., 2021). Addressing these challenges has driven extensive research in materials science aimed at developing advanced alloys and implementing accelerated testing protocols to ensure reliable performance under harsh environments (Wright and Wright, 2010; Gurovich et al., 2009; Olson and Kuehmann, 2014). In particular, significant efforts have been devoted to understanding deformation mechanisms, fracture behavior, and microstructural evolution under service-relevant conditions, forming the foundation for reliable material qualification.

The certification of nuclear materials requires rigorous evaluation procedures and assessment techniques to support the advancement of nuclear technology (Escobar and Meeker, 2006; Beausoleil et al., 2022). Traditional qualification approaches often rely on large-scale specimens and extensive irradiation campaigns, leading to long testing times and high experimental costs. To address these challenges, the use of specimens with reduced dimensions for mechanical testing provides a practical strategy for expediting the qualification of candidate alloys (Hosemann et al., 2015; Klueh, 1985; Arzt, 1998; Tomaszewski, 2020; Hyde et al., 2007). Miniaturized specimen geometries enable more efficient utilization of limited test reactor space, allowing a greater number of samples to be irradiated simultaneously and thereby significantly increasing the volume of available mechanical property data. In addition, the reduced material volume lowers fabrication and testing costs, facilitates post-irradiation examination, and minimizes the handling hazards associated with radioactive materials (Gussev et al., 2017; Prasitthipayong et al., 2018). These advantages make small-specimen testing particularly attractive for screening new alloys and evaluating irradiation-induced degradation in environments where material availability and experimental resources are constrained.

Nevertheless, small-scale mechanical testing places stringent demands on experimental rigor and control, as the measured responses are highly sensitive to boundary conditions and specimen quality. Even minor variations in loading alignment, strain measurement, machining tolerances, or surface roughness can result in significant scatter or bias in the inferred mechanical properties (Greer et al., 2012; Suzuki et al., 2010; Hurst and Matocha, 2015). Moreover, the mechanical, thermal, and electrical behaviors of sub-sized and miniature specimens can differ markedly from those of bulk materials. These deviations stem from geometric constraints, increased surface-to-volume ratios, and consequent changes in microstructural mechanisms, including grain boundary activity, precipitation kinetics, and dislocation dynamics (Cicero et al., 2020; Camin and Gille, 2021). As specimen dimensions approach characteristic microstructural length scales, such as grain size, precipitate spacing, or dislocation mean free path, the underlying deformation mechanisms may transition from bulk-dominated processes to size-affected or surface-mediated behavior. This includes enhanced grain boundary sliding, altered precipitation and coarsening kinetics, and modified dislocation nucleation and mobility (Corwin and Hougland, 1986; Dieter and Bacon, 1988; Kohno et al., 2000). Consequently, conventional models of deformation and fracture mechanics often lose validity when specimen dimensions fall below critical thresholds (Wallin et al., 2016; Konopík et al., 2017; Dohi et al., 2002). The size-dependent phenomena, commonly referred to as size effects, complicate the interpretation of small-scale mechanical behavior, while simultaneously providing important opportunities to engineer material properties for advanced applications and emerging technologies.

The investigation of size effects on tensile properties of nuclear structural materials remains an active area of research (Kumar et al., 2014; Li et al., 2025a; Zheng et al., 2020; Bergonzi et al., 2020; Zhang et al., 2023; LaVan and Sharpe, 1999). Recent advances in Machine Learning (ML) offer promising avenues to address current challenges, given their ability to model complex interactions across material scales (Agrawal and Choudhary, 2016; Schwab, 2015; Biswas et al., 2020; Boehnlein et al., 2022; Li et al., 2024). A range of conventional and advanced ML models and techniques, including transformer neural networks, Extreme Gradient Boosting (XGBoost), decision trees, random forests, neural networks, Gaussian Process Regressors, Support Vector Machines (SVMs), k-Nearest Neighbors (k-NN), and Physics-Informed Neural Networks (PINNs) (Karniadakis et al., 2021; Zhang et al., 2021; Yang et al., 2021), have been utilized to solve size effects correlations (Li et al., 2025a; Hu et al., 2023; Wan et al., 2019; Pan et al., 2023; Luo et al., 2021). Despite these advances, prior studies largely rely on limited experimental datasets, and their performance is often constrained by insufficient data diversity and representativeness.

Progress in this domain, however, is constrained by the limited, sparse, and often imbalanced nature of available datasets (Li et al., 2025b; Lee et al., 2025), as experimental acquisition of tensile data under representative nuclear conditions is costly and technically challenging. These limitations yield datasets that are of small size, unevenly distributed, and sometimes incomplete, which hinders the development of robust predictive models. Dataset imbalance can further introduce bias, particularly affecting minority regions of interest that are critical in size-effect investigations.

To mitigate the challenges, data augmentation techniques such as Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) and Synthetic Minority Over-sampling Technique for Regression with Gaussian Noise (SMOGN) (Branco et al., 2017) have been employed. GANs utilize adversarially trained generator and discriminator networks to produce synthetic data that closely resembles real data, effectively generating realistic samples for minority classes. SMOGN, an extension of SMOTE for regression tasks (Torgo et al., 2013), generates synthetic data points by perturbing existing samples with Gaussian noise, thereby enhancing dataset balance and improving model generalization. While these methods have shown promise in improving statistical performance, their application to size-dependent tensile behavior remains relatively underexplored, particularly in terms of their effectiveness across different material properties and their implications for physical interpretability.

The contributions of the study include.

• Systematically evaluated the impact of data augmentation strategies on machine learning (ML) performance for predicting size-dependent tensile properties.
• Addressed data scarcity and imbalance in experimental datasets by integrating advanced augmentation techniques with robust ML frameworks.
• Demonstrated that ensemble models, particularly Random Forest and XGBoost, achieve exceptional predictive accuracy, with correlation coefficients exceeding 0.98 on Pearson correlation coefficient for both yield strength and uniform elongation.
• Revealed that augmentation methods exhibit property-dependent effectiveness: GAN-based augmentation significantly enhances strength prediction, while SMOGN is more effective for modeling elongation behavior.

The remainder of this paper is organized as follows. Section 2 introduces the experimental datasets, including the SS316 tensile test dataset and the preprocessing procedures applied to address inconsistencies and scaling effects. Section 3 describes the machine learning frameworks and data augmentation methods, including GAN and SMOGN, as well as the implementation details of the Random Forest and XGBoost models. Section 4 and 5 present the results and discussion, focusing on model performance, comparative analysis of augmentation strategies, and their impact on predicting size-dependent tensile properties. In addition, this section examines the property-specific effectiveness of augmentation techniques and their implications for model robustness and interpretability. Finally, Section 6 summarizes the key findings of the study and outlines future research directions.

2 Experimental data

The influence of specimen dimensions and geometry on the following tensile properties is investigated in this work: yield strength (YS), ultimate tensile strength (UTS), uniform elongation (UE), and total elongation (TE). The dataset was created by our team through an extensive literature review of scientific articles and databases, targeting peer-reviewed studies on SS316 tensile testing of sub-sized specimens (Li et al., 2025b). The extracted data points were organized into a tabular format database containing 396 tensile testing records with 55 columns, including material type and composition, manufacturing information, irradiation conditions, specimen size and dimensions, and tensile properties. The number of data points for the corresponding properties before and after cleaning and preprocessing are listed in Table 1.

TABLE 1. Number of data points for the investigated tensile properties.

TABLE 2. Baseline algorithm performance across tensile properties.

The bold values provide the best performing model.

Figure 1 depicts the imbalance in the data across the tensile properties. In particular, yield strength (bottom right plot of each of the four grouped plots) has a significantly bimodal distribution with a gap from about 450 to 500 MPa. Figure 1a in the bottom right bar chart shows that the majority of the yield strength observations in the 0–250 MPa range correspond to solution annealed (post treatment temperature over 1000 °C) specimens, while the higher yield strength specimens correspond to cold-worked and stress-relieved specimens (named as heat treatment in the figure, post treatment temperature below 1000 °C). These imbalances in both the target variables (tensile properties) and the corresponding key features make it challenging to model the influence of the features on the target variables, thus hindering ML model performance.

3 Methods

3.1 Dataset and experimental design

Figure 2 provides an overview of the proposed experimental framework. The pipeline includes data cleaning and preprocessing of the sub-sized specimen tensile data, followed by augmentation strategies (GAN and SMOGN) with baseline and five augmentation ratios. Nine ML algorithms are then evaluated using 5-fold cross-validation, with Pearson correlation coefficient r, coefficient of determination R 2, and root-mean-squared error (RMSE) used as evaluation metrics to identify the optimal algorithm-augmentation combination for each tensile property. We systematically evaluated the ML algorithms for predicting the tensile properties of sub-sized specimens, utilizing datasets of varying sizes, as presented in Table 1. Specifically, for ultimate tensile strength the number of data points after data cleaning and preprocessing is n = 209, for yield strength is n = 204, for total elongation is n = 190, and for uniform elongation is n = 86. Each dataset comprises 45 input features including material composition, manufacturing/treatment parameters, irradiation conditions, specimen dimensions, and testing conditions (test temperature and strain rate).

Additionally, the initial dataset contains 187 irradiated specimens across irradiation doses ranging from 1.15 to 70 mdpa. After data cleaning to remove records with missing feature values, the number of irradiated specimens in the final training datasets was reduced to 15, 19, and 14 for UTS, YS, and TE respectively, with no irradiated specimens retained for UE.

Each ML algorithm was assessed using five-fold cross-validation with multiple data augmentation strategies at ratios of 20%, 40%, 60%, 80%, and 100% additional synthetic data, generating 396 individual model configurations to comprehensively evaluate prediction capabilities. The cross-validation splits were stratified by material grade to ensure representative sampling across different stainless-steel systems.

3.2 Data augmentation techniques

3.2.1 Generative Adversarial Networks (GAN)

We implemented a vanilla Generative Adversarial Network (GAN) for synthetic data generation. The generator G maps random noise vectors z ∈ R 100 to synthetic feature vectors x ̃ ∈ R 45. The generator architecture consists of four fully-connected layers with batch normalization and LeakyReLU activation (α = 0.2), followed by tanh output activation. The discriminator D comprises three fully connected layers with LeakyReLU activation and a final sigmoid activation to output a probability score. The GAN is trained using the Binary Cross-Entropy (BCE) loss, as shown in Equations 1, 2:

L D = − E l o g D x − E log ⁡ 1 − D G z (1)

L G = − E D G z (2)

The model is trained for 10,000 epochs using the Adam optimizer (β 1 = 0.5; β 2 = 0.999) and a learning rate of 2 × 10 − 4, with a 1:1 update ratio between the discriminator and generator. Input features are normalized to the range 0 , 1 using MinMax scaling. After training, synthetic samples are generated and compared to the original data using the Kolmogorov-Smirnov test to assess distributional similarity.

3.2.2 Synthetic minority oversampling using gaussian noise (SMOGN)

SMOGN generates synthetic samples through interpolation between existing samples with added Gaussian noise (Branco et al., 2017). For each sample x i with target y i, synthetic samples are created based on Equations 3, 4: where x j is a randomly selected k-nearest neighbor (k = 3), α ∼ U 0 , 1, ε ∼ N 0 , σ x 2 I with σ x = 0.1 * std X, and η ∼ N 0 , σ y 2 with σ y = 0.05 * std y . A custom relevance matrix is constructed by dividing the target variable into quantiles and identifying the sparsest region for oversampling. SMOGN is applied iteratively until the dataset size doubles. Synthetic samples are constrained to physically realistic ranges, and composition features are normalized to sum to 100%. A Kolmogorov-Smirnov test is used to assess the similarity between the original and augmented distributions.

x s y n t h = x i + α x j − x i + ε (3)

y s y n t h = y i + α y j − y i + η (4)

3.2.3 Kolmogorov-smirnov test

The two-sample Kolmogorov–Smirnov (KS) test was applied to compare the distributions of both target and non-target features against the original dataset and evaluate the quality of synthetic datasets generated using SMOGN and GAN. Across the four target variables including ultimate tensile strength, yield strength, ultimate elongation, and total elongation, GAN produced lower KS statistics for elongation-related target variables (0.093 and 0.347, respectively) and correspondingly higher p-values, indicating closer agreement with the marginal distributions of the original data. In contrast, SMOGN yielded better performance for ultimate tensile strength, with a lower KS statistic (0.354 vs. 0.451), while GAN outperformed SMOGN for yield strength despite both showing significant divergence from the original distribution. A recurring pattern across all SMOGN-generated datasets showed exact distributional alignment (KS = 0, p = 1.0) for several elemental and geometric features, including Al, V, Mg, Y, Zr, Zn, W, Sn, and H, suggesting that no observable variation was introduced by the synthetic sampling process for these variables in the generated dataset. Conversely, GAN introduced broader distributional shifts, particularly in elemental features such as C, Si, Mo, Cu, Zn, and Co., which frequently exhibited large KS statistics (>0.7) and correspondingly low p-values. These results characterize the distributional properties of synthetic data generated by GAN and SMOGN. It is important to note that the KS test evaluates univariate (marginal) distribution similarity and does not capture multivariate dependencies or feature-target relationships that govern predictive performance. Therefore, the KS results are reported as a descriptive characterization of synthetic data properties, while the selection of augmentation strategies was based on experimental predictive performance presented in Tables 3–6.

TABLE 3. Data augmentation results for ultimate tensile strength.

The bold values provide the best performing model.

TABLE 4. Data augmentation results for yield strength.

The bold values provide the best performing model.

TABLE 5. Data augmentation results for total elongation.

The bold values provide the best performing model.

TABLE 6. Data augmentation results for uniform elongation.

The bold values provide the best performing model.

3.3 Machine learning algorithms

We evaluated nine algorithms representing different ML-based learning paradigms: Extreme Gradient Boosting (XGBoost), Random Forest, Decision Tree, K-Nearest Neighbors, Support Vector Machine, Gaussian Process Regression, Neural Network, Simple Tabular Transformer, and Materials-Informed Transformer.

3.3.1 Simple tabular transformer

The Simple Tabular Transformer architecture (Hollmann et al., 2025) treats each input feature as an individual token in the sequence. For a tabular input with n features, in Equation 5 each scalar feature x i is transformed into a d m o d e l-dimensional embedding through:where P i ∈ R d m o d e l represents a learnable positional embedding specific to feature i. The embedded feature representations are then processed through a standard transformer encoder consisting of 2 layers, each with d m o d e l = 64 dimensions, 4 attention heads, and a feed-forward network dimension of 128. Dropout regularization with probability p = 0.1 is applied throughout the network. The final prediction layer concatenates all transformed feature representations by flattening the encoder output from batch _ size , n features , d model to batch _ size , n features × d model followed by a single linear transformation to produce the scalar output. This approach enables the model to learn both feature-specific representations and cross-feature interactions through the self-attention mechanism while maintaining computational efficiency for tabular data processing.

E i = Linear 1 , d m o d e l x i + P i (5)

3.3.2 Materials-informed transformer (MIT)

MIT organizes input features into physics-based groups reflecting the underlying materials science domain: material information, manufacturing/treatment information, irradiation conditions, specimen dimensions and tensile test conditions. Additional features beyond the predefined 36 are automatically assigned to an “additional features” group to accommodate varying input dimensions.

For each feature group G g containing | G g | features, the group embedding is computed as Equation 6: where x G g represents the subset of input features belonging to group g, T g ∈ R d m o d e l is a learnable group-type embedding that encodes the semantic category of each group, and P g ∈ R d m o d e l is a learnable positional embedding. The group-type embeddings are implemented through an embedding layer that maps each of the distinct feature groups to a d m o d e l-dimensional representation.

E g = L i n e a r G g , d m o d e l x G g + T g + P g (6)

The architecture employs identical hyperparameters to the Simple Tabular Transformer (d m o d e l = 64, 4 attention heads, 2 encoder layers) but applies self-attention across feature groups rather than individual features, reducing the sequence length from the number of input features to the number of semantic groups (typically 5 or 6). The final prediction is generated through a two-layer regression head with ReLU activation and dropout regularization, which first projects the flattened group representations to d m o d e l/2 dimensions before producing the scalar output. This hierarchical approach enables the model to capture both intra-group feature interactions within each physical domain and inter-group relationships across different aspects of the materials testing process.

3.3.3 Physics-informed neural networks (PINNs)

We implemented PINNs incorporating Barba’s Law and Bertella-Oliver formula as physical constraints for total elongation prediction (Li et al., 2025a). Barba’s Law is expressed as Equation 7:

e t B a r b a = c + d √ A L (7)

The Bertella-Oliver formula is given in Equation 8:where A is cross-sectional area, L is gauge length, and c, d, m, n are material-dependent parameters predicted by separate neural networks. The PINN model employed in this study is a fully-connected feedforward architecture designed to predict total elongation from material features. It consists of three hidden layers, each comprising 256 neurons. The RELU activation function is applied after each hidden layer to introduce non-linearity and improve learning capacity. To enhance generalization and mitigate overfitting, dropout regularization is optionally applied with a dropout probability of 0.25, randomly deactivating a subset of neurons during training. Additionally, residual connections are incorporated between hidden layers, allowing the network to learn identity mappings and facilitating gradient flow during backpropagation. This design helps stabilize training and improves convergence, especially in deeper networks. The final output layer is a single neuron with a linear activation function, producing a continuous prediction corresponding to the total elongation (%) of the material. The total loss combines data fidelity with physics constraints using predictions using Barba’s Law and Bertella-Oliver formula, as shown in Equations 9, 10.

e t O l i v e r = m √ A L n (8)

L t o t a l = λ d a t a L d a t a + λ B a r b a L B a r b a (9)

L t o t a l = λ d a t a L d a t a + λ O l i v e r L O l i v e r (10)

The training phase used the Adam optimizer (l r = 1 × 10 − 3) with loss weights λ d a t a = λ B a r b a = λ O l i v e r = 0.5. Reference parameters were derived from literature: c r e f = 34.07, d r e f = 234.41, m r e f = 136.34, n r e f = 0.38 (Li et al., 2025a).

3.4 Evaluation metrics

All models were evaluated using 5-fold cross-validation with Pearson correlation coefficient (r), coefficient of determination (R 2), and root-mean-square error (RMSE). Results are reported as mean ± standard deviation across folds.

4 Experimental results

4.1 Baseline algorithm performance analysis

Table 2 presents the baseline performance (without data augmentation) for all algorithms across the four tensile properties. Figures 3–6 illustrate the baseline performance of all nine algorithms across the four tensile properties using Pearson r, R 2, and RMSE metrics, providing a visual comparison of algorithm effectiveness. The evaluation revealed distinct performance hierarchies that vary significantly across different properties, with notable patterns in algorithm effectiveness and cross-validation stability.

For ultimate tensile strength prediction, Random Forest achieved the highest baseline performance with r = 0.934 and R M S E = 48.802 M P a, followed by Gaussian Process Regressor (r = 0.929; R M S E = 50.904 M P a) and Extreme Gradient Boosting (r = 0.926; R M S E = 50.179 M P a). kNN exhibited the poorest performance (r = 0.880; R M S E = 65.840 M P a) among all evaluated algorithms.

Yield strength predictions showed exceptionally high accuracy across multiple algorithms, with Random Forest achieving the best performance (r = 0.987; R M S E = 32.601 M P a), closely followed by Extreme Gradient Boosting (r = 0.983; R M S E = 37.768 M P a) and Decision Tree (r = 0.981; R M S E = 38.840 M P a). The Simple Transformer also demonstrated strong performance (r = 0.979; R M S E = 41.575 M P a), while Support Vector Machine showed the lowest accuracy (r = 0.892; R M S E = 114.577 M P a).

Total elongation presented moderate prediction complexity, with Extreme Gradient Boosting achieving the highest correlation (r = 0.930; R M S E = 7.454 %), followed by Simple Transformer (r = 0.920; R M S E = 8.276 %) and Random Forest (r = 0.918; R M S E = 8.056 %). The Materials-Informed Transformer achieved competitive performance (r = 0.883; R M S E = 10.006%), while Support Vector Machine showed the poorest results (r = 0.856; R M S E = 11.266 %).

Uniform elongation achieved the highest prediction accuracy across all properties, despite having the smallest dataset n = 86. Extreme Gradient Boosting delivered exceptional performance (r = 0.989; R M S E = 3.414 %), followed by Random Forest (r = 0.982; R M S E = 4.077 %) and Simple Transformer (r = 0.961; R M S E = 6.101 %). Even Support Vector Machine achieved reasonable accuracy for this property (r = 0.934; R M S E = 8.732 %).

4.1.1 Tree-based algorithm analysis

Random Forest consistently achieved top-tier performance for strength properties, demonstrating remarkable stability with the lowest RMSE for ultimate tensile strength (48.802 M P a) and exceptional correlation for yield strength (r = 0.987). The algorithm’s ensemble averaging effectively captured the complex, non-linear relationships characteristic of materials property dependencies.

XGBoost emerged as the single best performer for total elongation (r = 0.930) and uniform elongation (r = 0.989), with the lowest RMSE values for both properties (7.454% and 3.414% respectively). The gradient boosting approach proved particularly effective for capturing the systematic geometric scaling relationships governing ductility behavior.

4.1.2 Transformer architecture analysis

Simple Tabular Transformer demonstrated remarkable property-specific performance variation, achieving exceptional results for yield strength (r = 0.979, ranking third) while showing poor performance for ultimate tensile strength (r = 0.857, ranking eighth). This 14% performance gap reveals the algorithm’s sensitivity to the underlying data structure and relationship complexity. The feature-wise tokenization approach effectively captured the systematic strengthening mechanisms governing yield behavior but struggled with the multi-factorial complexity of ultimate strength determination.

The Simple Transformer’s strong performance for total elongation (r = 0.920, ranking second) and competitive results for uniform elongation (r = 0.961, ranking fourth) indicate that attention mechanisms can effectively model ductility relationships when provided with appropriate feature representations. The consistent performance across elongation properties (cross-validation std <0.07) suggests stable learning of geometric scaling effects.

Materials-Informed Transformer (MIT) showed consistently lower performance across all properties, with correlations ranging from 0.824–0.945, representing 2%–15% degradation compared to the Simple Transformer. This result indicates that the physics-based feature grouping strategy did not improve model performance. To investigate this result, ablation experiments were conducted comparing three MIT configurations, presented in Table 11. The negligible performance differences across all configurations indicate that feature grouping granularity is not the primary factor behind MIT’s underperformance relative to Simple Transformer.

The MIT’s poorest performance for ultimate tensile strength ( r = 0.824, ranking ninth) and relatively moderate yield strength performance (r = 0.950, ranking fifth) suggest that the prescribed physics-based attention structure conflicts with the data-driven patterns that Simple Transformer successfully identified. However, the more competitive performance for elongation properties (r = 0.883 − 0.945) indicates that geometric feature grouping may be more aligned with physical reality for ductility prediction.

4.1.3 Classical algorithm performance patterns

Support Vector Machine consistently ranked in the bottom three across all properties (r = 0.856 − 0.934), with particularly poor yield strength performance (r = 0.892; R M S E = 114.577 M P a). The 27% higher RMSE compared to Random Forest quantifies the inadequacy of linear separation for materials property relationships, even with kernel transformations.

K-Nearest Neighbors showed moderate performance with high variability (CV std > 0.02), indicating sensitivity to local data distribution. The algorithm’s poor performance for yield strength (r = 0.922) compared to elongation properties reflects the different neighborhood structures required for systematic strengthening mechanisms versus geometric scaling relationships.

Gaussian Process Regressor achieved competitive performance for strength properties (r > 0.929) but showed degraded performance for elongation properties, indicating that the Gaussian kernel effectively captured composition-dependent strengthening but struggled with specimen geometry effects.

4.2 Data augmentation effects and algorithm selection analysis

The selection of algorithms for detailed augmentation analysis (Tables 3–6) was based on three criteria: (1) baseline performance ranking, (2) algorithmic diversity to represent different learning paradigms, and (3) preliminary screening showing significant augmentation sensitivity. For each property, we selected the top 3-4 performing baseline algorithms plus algorithms demonstrating notable augmentation responses.

4.2.1 Ultimate tensile strength analysis

Algorithm Selection Rationale: Random Forest and XGBoost were selected as top baseline performers; KNN was included due to expected high sensitivity to synthetic data quality based on distance-based learning; SVM was included to demonstrate failure modes of linear approaches with augmentation.

Random Forest demonstrated exceptional stability across all GAN ratios (r = 0.934 − 0.935, <0.1% variation), indicating robust handling of synthetic data without ensemble degradation. However, SMOGN caused significant degradation (7.8% drop to r = 0.856 − 0.861), revealing sensitivity to interpolative augmentation that may violate ensemble independence assumptions for ultimate tensile strength property. XGBoost achieved peak performance at 60% GAN augmentation (r = 0.935), representing a 1.0% improvement over baseline. This enhancement demonstrates successful integration of realistic synthetic samples that complement existing training patterns. SMOGN caused substantial degradation (11.3% drop to r = 0.820 − 0.823), indicating that gradient boosting is particularly sensitive to interpolative noise in high-dimensional feature spaces. K-Nearest Neighbors showed progressive improvement with GAN augmentation, achieving 1.4% enhancement at 100% ratio (r = 0.880 → 0.892). This improvement contradicts conventional expectations about KNN sensitivity to synthetic data, suggesting that GANs generate samples that improve local neighborhood quality rather than introducing artifacts. Support Vector Machine exhibited systematic performance degradation with both augmentation types (8.0% decline under GAN, 8.7% decline under SMOGN), confirming that linear separation approaches cannot effectively leverage synthetic data in complex materials feature spaces.

4.2.2 Yield strength: systematic relationship stability

Algorithm Selection Rationale: Top three baseline performers (Random Forest, XGBoost, Simple Transformer) were selected for stability analysis; Neural Network was included due to largest potential for improvement based on poor baseline performance.

Random Forest maintained exceptional stability (r = 0.984 − 0.987, <0.3% variation) across all augmentation conditions, demonstrating that ensemble methods effectively handle yield strength’s systematic relationships regardless of augmentation strategy. XGBoost showed remarkable consistency across all conditions (r = 0.983 − 0.986), with slight improvements under both augmentation types. Stability reflects the algorithm’s effective capture of systematic strengthening mechanisms through gradient boosting optimization. Simple Transformer achieved some improvements with both augmentation types, reaching peak performance at 60%–100% SMOGN (r = 0.986). The 0.7% improvement demonstrates that attention mechanisms can effectively leverage additional training diversity for systematic relationships. Neural Network exhibited notable improvement, with GAN augmentation increasing performance by 1.2%. This enhancement indicates that synthetic augmentation provided the sample diversity necessary for effective learning of yield strength relationships.

4.2.3 Total elongation analysis

Algorithm Selection Rationale: XGBoost selected as baseline leader, Random Forest as robust ensemble comparator, Simple Transformer and MIT included to examine transformer sensitivity to total elongation property.

XGBoost showed modest but consistent improvements, with peak SMOGN performance at 80% (r = 0.936), representing 0.6% enhancement. The improvement indicates successful capture of geometric scaling relationships through interpolative augmentation. Random Forest demonstrated similar modest improvements, with 0.4% enhancement under SMOGN at 80%–100% ratios (r = 0.922 − 0.923). The improvement pattern confirms that elongation benefits from interpolative rather than generative augmentation. Simple Transformer achieved significant improvements with both augmentation types, reaching peak GAN performance at 60% (r = 0.936) and consistent SMOGN improvements (r = 0.930 − 0.940). The 1.7%–2.2% enhancement demonstrates that attention mechanisms effectively capture the multi-factorial nature of total elongation when provided with sufficient data diversity. Materials-Informed Transformer showed the largest relative improvements, with 3.3% enhancement under GAN at 100% (r = 0.912) and 4.4% improvement under SMOGN (r = 0.922). This substantial improvement suggests that physics-based feature grouping becomes more effective when provided with sufficient training diversity to learn optimal attention patterns within groups.

4.2.4 Uniform elongation analysis

Algorithm Selection Rationale: XGBoost selected as exceptional baseline performer; Random Forest as ensemble comparator; Decision Tree included due to expected high augmentation sensitivity; Simple Transformer included to examine attention mechanism effectiveness.

As shown in the Table 6, XGBoost maintained exceptional performance (r = 0.987 − 0.989, <0.2% variation) across all conditions, demonstrating that the algorithm has already captured ultimate elongation relationships optimally at baseline. Random Forest showed contrasting behavior between augmentation types: slight degradation with GAN (r = 0.974 − 0.980) but improvement with SMOGN (r = 0.987). This pattern suggests that uniform elongation relationships benefit from interpolative rather than generative augmentation. Decision Tree exhibited dramatic augmentation sensitivity, with exceptional improvement under SMOGN at 60% ratio (r = 0.994, +1.7%) but degradation under GAN. The exceptional SMOGN performance indicates that moderate interpolative augmentation provides optimal decision boundary placement without overfitting. Simple Transformer showed modest improvements across conditions (r = 0.955 − 0.974), with best performance under SMOGN at 60% (r = 0.974). The consistent improvements demonstrate that attention mechanisms benefit from additional training diversity for learning ultimate elongation relationships.

To further assess whether the exceptional performance of XGBoost for uniform elongation reflects genuine learning rather than overfitting, a mean baseline was established by predicting the training set mean value for all test samples. As shown in Table 10, the mean baseline achieved an RMSE of 21.714% and R 2 of −0.181, compared to XGBoost’s RMSE of 3.414% and R 2 of 0.969, demonstrating that the model substantially outperforms a simple reference predictor despite the limited sample size (n = 86). Furthermore, a permutation importance analysis presented in Figure 7 reveals that the most influential features are heat treatment condition and test temperature, which have well-established physical relevance to uniform elongation behavior, confirming that the model has learned meaningful material-property relationships rather than spurious correlations.

4.2.5 Best and worst performance under data augmentation

Supplementary Figures S2–S9 in illustrate how nine algorithms behave under different GAN and SMOGN augmentation ratios.

Several algorithms exhibited significant performance degradations that provide important insights into augmentation strategy limitations. Support Vector Machine showed systematic degradation across all properties and augmentation types, with the most severe decline for ultimate tensile strength under SMOGN augmentation (8.7% drop from r = 0.900 to r = 0.822). This degradation reveals fundamental incompatibility between linear kernel approaches and the non-linear synthetic data distributions generated by both GAN and SMOGN methods. Despite excellent GAN stability, Random Forest showed unexpected sensitivity to SMOGN augmentation, particularly for ultimate tensile strength (8.1% degradation). This selective sensitivity suggests that ensemble averaging assumptions could be compromised by interpolative augmentation, which introduces artificial feature correlations that do not exist in the original materials data. Decision Tree with GAN exhibited 1.7% degradation for uniform elongation under GAN augmentation (r = 0.977 → 0.960), suggesting that synthetic data generation introduces noise that disrupts optimal decision boundary placement for this single-tree approach.

K-Nearest Neighbors demonstrated the most dramatic improvement observed across all experiments due to augmentation, achieving a 4.4% enhancement for yield strength (r = 0.922 → 0.963) and 1.4% improvement for ultimate tensile strength (r = 0.880 → 0.892) with GAN augmentation at 100% ratio. This finding contradicts conventional expectations about distance-based algorithms’ sensitivity to synthetic data, instead revealing that properly trained GANs generate chemically realistic intermediate compositions that enhance local neighborhood quality rather than introducing artifacts. The progressive improvement with increasing GAN ratios demonstrates that synthetic data generation can fill critical gaps in materials property space while maintaining proper element correlations, effectively increasing training density without degrading prediction accuracy.

MIT for Total Elongation achieved substantial improvements under both augmentation types (3.3% with GAN, 4.4% with SMOGN), indicating that physics-based attention mechanisms require sufficient training diversity to learn optimal within-group attention patterns for complex geometric-material interactions. Decision Tree for Uniform Elongation with SMOGN demonstrated exceptional improvement with minimal augmentation (1.4% enhancement at 20% SMOGN, reaching r = 0.991), suggesting that uniform elongation relationships benefit from precise interpolative enhancement without overfitting synthetic artifacts.

4.3 Physics-informed neural network performance

Table 7 presents the PINN performance results with Barba’s law and Bertella-Oliver formula for total elongation prediction. The implementation of physics-informed neural networks for total elongation prediction yielded results inferior to standard neural network approaches. The standard Neural Network achieved r = 0.897 with RMSE = 9.87%. In contrast, the Physics-Informed Neural Network incorporating Barba’s Law achieved r = 0.800 with RMSE = 16.0%, representing a 10.8% decrease in correlation. The Physics-Informed Neural Network with Bertella-Oliver formula achieved r = 0.809 with RMSE = 15.4%, showing a 9.8% correlation decrease.

TABLE 7. PINN performance with Barba’s law and Bertella-Oliver formula.

The bold values provide the best performing model.

Both physics-informed approaches demonstrated higher cross-validation variance and significantly increased prediction errors compared to the standard neural network approach.

4.4 Cross-validation stability analysis

Cross-validation stability analysis reveals critical reliability differences essential for nuclear materials qualification. Extreme Gradient Boosting achieved great stability (σ = 0.03 − 0.051) combined with top-tier performance, establishing it as optimal for safety-critical applications requiring both accuracy and reliability. Random Forest demonstrated similar robustness while maintaining competitive performance and interpretability. In contrast, Neural Network showed the highest variability across all properties (σ = 0.029 − 0.048) despite achieving reasonable performance, highlighting that accuracy alone is insufficient for nuclear applications where prediction reliability is paramount for safety margins and regulatory compliance.

5 Discussion

This study provides several key insights into the interplay between ML methods, data augmentation strategies, and the underlying physics of material properties. From an application perspective, the high predictive accuracy achieved for yield strength and uniform elongation (r > 0.98) demonstrates the potential of ML to reduce reliance on costly and time-intensive irradiation experiments in nuclear materials research. The consistently strong performance of Random Forest and XGBoost highlights the importance of aligning model structure with the hierarchical and threshold-driven nature of materials behavior. Cross-validation stability analysis presented in Table 8 reveals that tree-based methods generally demonstrate lower standard deviations, with XGBoost achieving the highest stability for uniform elongation (standard deviation of 0.003) and Random Forest for yield strength (standard deviation of 0.009). Many material properties exhibit discontinuities at critical composition or temperature points, and tree-based models effectively capture these transitions, leading to robust and interpretable predictions. In contrast, the weaker performance of Support Vector Machine underscores the highly non-linear and coupled nature of the feature space, which is not well represented by linear decision boundaries, particularly when augmented data introduces additional complexity.

TABLE 8. Cross-validation stability analysis based on standard deviation of correlation coefficients.

Beyond tree-based and kernel-based methods, the remaining algorithms exhibited distinct performance patterns consistent with their underlying model structures. Gaussian Process Regressor achieved competitive results for strength properties but showed lower performance for elongation, reflecting the limitations of kernel-based methods in capturing the geometric scaling relationships that govern ductility behavior. Decision Tree showed higher cross-validation variance than Random Forest and XGBoost, confirming that ensemble aggregation is essential for stable predictions in sparse and imbalanced datasets. Neural Network showed moderate performance with higher variance, suggesting that the limited dataset size constrains effective learning of deep representations. Among transformer-based architectures, Simple Transformer outperformed MIT across most properties, with ablation experiments ruling out feature grouping granularity as the primary factor, suggesting that other architectural differences between the two models merit further exploration.

A central finding is that the effectiveness of data augmentation is strongly property-dependent as shown in the algorithm-augmentation selection in Table 9. GAN-based augmentation is more effective for strength-related properties, which are governed by discrete and competing mechanisms, while SMOGN performs better for elongation, where deformation behavior follows smoother, more continuous trends. This distinction provides a broader implication: data augmentation strategies must be selected based on the underlying physics of the target property, rather than applied uniformly. At the same time, these results highlight the sensitivity of augmentation methods to dataset limitations. GAN may generate physically inconsistent samples when data coverage is insufficient, while SMOGN may fail to enhance poorly represented regions lacking local structure.

TABLE 9. Algorithm-augmentation selection for tensile properties.

TABLE 10. Comparison of XGBoost and mean baseline performance for uniform elongation (n = 86). The mean baseline predicts the training set mean value for all test samples, providing a simple reference to assess whether the model has learned meaningful patterns beyond trivial prediction.

TABLE 11. Ablation study results for MIT feature grouping configurations on UTS (baseline, ratio = 0).

While GAN training on small datasets (n = 86 − 209) may introduce some distributional limitations, as shown in the PCA visualization in Figure 8, GAN-generated samples generally cover the main regions in the feature space of the real data distribution, with the degree of coverage varying across properties depending on the available dataset size. The experimental results demonstrate that GAN augmentation consistently improved strength property prediction, suggesting that even partially overlapping synthetic samples can provide useful training signal for tree-based ensemble methods.

The analysis of physics-informed neural networks (PINNs) further emphasizes the importance of consistency between imposed constraints and dataset characteristics. The reduced performance of PINNs indicates that simplified empirical laws are not appropriate for this heterogeneous dataset, which spans multiple alloys and processing conditions. This finding suggests that rigid, globally applied physics constraints can degrade performance when their assumptions are violated. More broadly, it underscores the need for flexible, data-adaptive physics integration, such as learning material-dependent parameters or using soft constraints, rather than enforcing fixed relationships.

Despite these contributions, several limitations should be acknowledged. First, the dataset remains relatively small, sparse, and potentially biased, which may limit generalizability. Second, while augmentation improves performance, it can introduce artificial correlations or distributional shifts that do not fully reflect real physical behavior. Third, the interpretation of model performance as evidence of physical mechanisms should be treated cautiously, as machine learning captures correlations rather than causality. Finally, the conclusions are constrained to the current feature space and material system, and may not directly extend to other alloys or loading conditions.

6 Conclusion

This study systematically demonstrates that ML algorithms, when appropriately selected and combined with suitable data augmentation strategies, can achieve exceptional accuracy in predicting the tensile properties of sub-sized specimens, even with limited experimental data. Ensemble models, particularly Random Forest and Extreme Gradient Boosting, consistently delivered optimal performance across most properties, achieving Pearson correlation coefficients exceeding 0.98 for yield strength and uniform elongation, highlighting their strong alignment with underlying materials behavior. A key insight is the property-dependent effectiveness of data augmentation methods. GAN-based approaches are more effective for strength properties governed by complex, nonlinear compositional relationships, while SMOGN performs better for elongation properties associated with smoother, continuous deformation mechanisms. This distinction not only improves predictive performance but also enhances model robustness and reduces bias in underrepresented regions, revealing meaningful connections between statistical learning and physical behavior. The proposed framework provides practical guidance for selecting ML algorithms and augmentation strategies based on underlying physics, enabling reliable property prediction from sparse data. This capability addresses a critical bottleneck in nuclear materials research, where experimental constraints are significant, and establishes a foundation for physics-informed materials informatics that supports accelerated yet reliable materials development for safety-critical applications.

Future work will focus on extending the proposed framework in several key directions. First, building upon the identified key factors, future studies will investigate size effects on mechanical properties under controlled conditions by fixing dominant variables, enabling a more isolated and physically interpretable understanding of size-dependent behavior. Second, optimization of testing parameters will be explored to maximize mechanical performance, leveraging machine learning models to identify optimal combinations of geometry, loading conditions, and material configurations. Third, expanding the experimental dataset to include a broader range of materials, compositions, and testing conditions will further improve model robustness, generalization, and applicability. Together, these efforts will enhance the predictive capability and practical utility of the framework for advanced materials design and evaluation.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmtec.2026.1811951/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Krishna Kishore Mugada, Sardar Vallabhbhai National Institute of Technology Surat, India

Reviewed by: Subraya Krishna Bhat, Manipal Institute of Technology, India

Mustafa Al-karkhi, University of Technology, Iraq