{"ID":2837118,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20612","arxiv_id":"2511.20612","title":"Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition","abstract":"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","short_abstract":"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/n...","url_abs":"https://arxiv.org/abs/2511.20612","url_pdf":"https://arxiv.org/pdf/2511.20612v1","authors":"[\"Yujin Kim\",\"Sarah Dean\"]","published":"2025-11-25T18:39:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SY\"]","methods":"[]","has_code":false,"code_links":[{"ID":606656,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2837118,"paper_url":"https://arxiv.org/abs/2511.20612","paper_title":"Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition","repo_url":"https://github.com/sedan-group/Stochastic-NODE-DMD","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}