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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.12103 |
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| _version_ | 1866917406051401728 |
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| author | Chakrabarti, Ananda Saleh, Haitham H. Nayak, Indranil Shanker, Balasubramaniam Teixeira, Fernando L. Goswami, Debdipta |
| author_facet | Chakrabarti, Ananda Saleh, Haitham H. Nayak, Indranil Shanker, Balasubramaniam Teixeira, Fernando L. Goswami, Debdipta |
| contents | We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems Chakrabarti, Ananda Saleh, Haitham H. Nayak, Indranil Shanker, Balasubramaniam Teixeira, Fernando L. Goswami, Debdipta Systems and Control Machine Learning We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces. |
| title | Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2604.12103 |