Learning Closure of Dynamical Systems with Kernel Ridge Regression
We develop a closure modeling framework for identifying missing components of dynamical systems using Kernel Ridge Regression (KRR). The framework addresses two classes of closure problems: difference-equation closures arising in ODE and PDE settings, and algebraic closures arising from moment closure in kinetic equations. For the first class, we derive an error bound in an ODE setting that quantifies contributions from time integration, approximation of unresolved scales, and interpolation required to couple unresolved-scale effects to the resolved solver. Numerical experiments on the Lorenz-63 system and the Kuramoto-Sivashinsky equation demonstrate accurate long-horizon predictions and...
| Authors | Evan Habbershaw, John Harlim, Senwei Liang |
|---|---|
| Primary category | math.NA |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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