Dynamics-aware identification of governing equations from sparse and noisy data
Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this problem, we evaluate Koopman-based upsampling techniques implemented with dynamic mode decomposition (DMD), extended DMD (EDMD), and optimized DMD. These methods learn finite-dimensional approximations of Koopman evolution on selected observables and are used to interpolate and denoise snapshots inside the observed time window before derivative estimation and sparse regression. The empirical benchma...
| Authors | Pongpisit Thanasutives, Yoshinobu Kawahara |
|---|---|
| Primary category | cs.LG |
| Published | 31 July 2026 |
| Last updated at source | 31 July 2026 |
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