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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2511.20612 |
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| _version_ | 1866911286642606080 |
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| author | Kim, Yujin Dean, Sarah |
| author_facet | Kim, Yujin Dean, Sarah |
| contents | Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD) provides a simple, data-driven approximation, but practical use is limited by sparse/noisy observations from continuous fields, reliance on linear approximations, and the lack of principled uncertainty quantification. To address these issues, we introduce Stochastic NODE-DMD, a probabilistic extension of DMD that models continuous-time, nonlinear dynamics while remaining interpretable. Our approach enables continuous spatiotemporal reconstruction at arbitrary coordinates and quantifies predictive uncertainty. Across four benchmarks, a synthetic setting and three physics-based flows, it surpasses a baseline in reconstruction accuracy when trained from only 10% observation density. It further recovers the dynamical structure by aligning learned modes and continuous-time eigenvalues with ground truth. Finally, on datasets with multiple realizations, our method learns a calibrated distribution over latent dynamics that preserves ensemble variability rather than averaging across regimes. Our code is available at: https://github.com/sedan-group/Stochastic-NODE-DMD |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition Kim, Yujin Dean, Sarah Machine Learning Systems and Control Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD) provides a simple, data-driven approximation, but practical use is limited by sparse/noisy observations from continuous fields, reliance on linear approximations, and the lack of principled uncertainty quantification. To address these issues, we introduce Stochastic NODE-DMD, a probabilistic extension of DMD that models continuous-time, nonlinear dynamics while remaining interpretable. Our approach enables continuous spatiotemporal reconstruction at arbitrary coordinates and quantifies predictive uncertainty. Across four benchmarks, a synthetic setting and three physics-based flows, it surpasses a baseline in reconstruction accuracy when trained from only 10% observation density. It further recovers the dynamical structure by aligning learned modes and continuous-time eigenvalues with ground truth. Finally, on datasets with multiple realizations, our method learns a calibrated distribution over latent dynamics that preserves ensemble variability rather than averaging across regimes. Our code is available at: https://github.com/sedan-group/Stochastic-NODE-DMD |
| title | Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2511.20612 |