Advancing Interpretable Modeling with Data-Driven Decomposition and Dynamical Systems Approaches

The field of data-driven signal decomposition and dynamical systems analysis is experiencing rapid growth at the intersection of applied mathematics, physics, and data science. Researchers have developed innovative methodologies—such as Dynamic Mode Decomposition (DMD), Optimal Mode Decomposition (OMD), Dynamical Component Analysis (DyCA), and Sparse Identification of Nonlinear Dynamics (SINDy)—that enable the extraction of interpretable models and the identification of coherent structures straight from complex datasets. A significant theoretical advance in this area is the adoption of Koopman operator theory, which creates a bridge between nonlinear dynamical systems and linear spectral analysis. Recent studies have underscored the promise of these approaches, while also highlighting open questions about their applicability, robustness to noise, and interpretability across diverse scientific domains.Despite these exciting advancements, there remain critical challenges and debates in the field. Understanding the relative strengths and limitations of each method, especially regarding their mathematical guarantees, computational scalability, and suitability for nonstationary or noisy data, is a pressing need. Comparative benchmarks and real-world applications have begun to shed light on these aspects: for instance, DMD is valued for modal interpretability, OMD for low-rank optimization, DyCA for extracting deterministic structures from noise, and SINDy for sparse discovery of governing equations. However, systematic clarity on these methodological trade-offs, commonalities, and distinctions remains elusive. Unresolved issues—such as observable selection, generalization capacity, and the integration of Koopman-based perspectives—underscore the need for a comprehensive, comparative examination of these tools.This Research Topic aims to foster an integrated understanding of data-driven signal decomposition and dynamical systems analysis by gathering comparative theoretical studies, algorithmic benchmarks, and practical applications. Rather than proposing a unifying framework, the aim is to illuminate where each method excels, identify methodological gaps, and clarify how these approaches may complement one another across fundamental and applied sciences. The ultimate objective is to provide the research community with informed guidelines for method selection, reveal open questions, and inspire new advances for interpretable modeling in fields ranging from fluid dynamics to neuroscience.To gather further insights in the comparative landscape and practical applications of data-driven decomposition and dynamical systems analysis, we welcome articles addressing, but not limited to, the following themes:- Theoretical analyses connecting DMD and its variants and extensions, OMD, DyCA, system identification methods such as SINDy and its variants, Koopman and Perron-Frobenius operator theory, and related approaches- Benchmarking studies on synthetic and real-world datasets, including oscillatory, chaotic, or multiscale signals- Applications in biomechanics, fluid dynamics, control, climate science, and neuroscience- Methodological trade-offs regarding noise robustness, generalization, and computational scalability- Challenges and solutions in observable selection, integration of multiple techniques, and validation in real-world contexts Topic editors: Christian Uhl, Christopher Curtis, Frank Kwasniok Source: https://www.frontiersin.org/research-topics/80147/advancing-interpretable-modeling-with-data-driven-decomposition-and-dynamical-systems-approaches