Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition
This work addresses the problem of modeling complex, real-world dynamic systems for scientific machine learning, offering a probabilistic and interpretable method that is incremental over existing DMD approaches.
The paper tackled the challenge of reconstructing continuous spatiotemporal fields from sparse, noisy observations in dynamic systems like wind fields, introducing Stochastic NODE-DMD, which achieved higher reconstruction accuracy than baselines when trained on only 10% observation density and recovered dynamical structures with calibrated uncertainty quantification.
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