Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition

• URL: http://arxiv.org/abs/2511.20612v1
• Date: Tue, 25 Nov 2025 18:39:50 GMT
• Title: Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition
• Authors: Yujin Kim, Sarah Dean,
• Abstract summary: Many real-world systems, like wind fields and ocean currents, are dynamic and hard to model.<n> Dynamic Mode Decomposition (DMD) provides a simple, data-driven approximation, but practical use is limited by sparse/noisy observations.<n>We introduce NODE-DMD, a probabilistic extension of DMD that models continuous-time, nonlinear dynamics while remaining interpretable.
• Score: 12.812771670043212
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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