Reduced Order Data-Driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning

Diana Alina Bistrian ()
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Diana Alina Bistrian: Department of Electrical Engineering and Industrial Informatics, University Politehnica Timisoara, 300006 Timisoara, Romania

Mathematics, 2025, vol. 13, issue 17, 1-32

Abstract: This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity and no manual parameter adjustment. The method integrates a novel algorithm with Pareto front analysis to construct a compact, high-fidelity reduced-order model that balances accuracy and efficiency. An explainable NLARX deep learning framework enables real-time, adaptive calibration and prediction, while a key innovation—computing orthogonal Koopman modes via randomized orthogonal projections—ensures optimal data representation. This approach for data-driven twin modeling is fully self-consistent, avoiding heuristic choices and enhancing interpretability through integrated explainable learning techniques. The proposed method is demonstrated on shock wave phenomena using three experiments of increasing complexity accompanied by a qualitative analysis of the resulting data-driven twin models.

Keywords: data-driven twin model; Koopman randomized orthogonal decomposition; nonlinear PDE; explainable deep learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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