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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03325 |
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| _version_ | 1866913975998873600 |
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| author | Bistrian, D. A. |
| author_facet | Bistrian, D. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced Order Data-driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning Bistrian, D. A. Numerical Analysis 00A71, 46N40, 34A45 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. |
| title | Reduced Order Data-driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning |
| topic | Numerical Analysis 00A71, 46N40, 34A45 |
| url | https://arxiv.org/abs/2508.03325 |