Learning dynamical systems from data: a simple cross-validation perspective

TL;DR

This paper introduces cross-validation techniques, including Kernel Flows and MMD-based methods, to improve kernel selection in data-driven dynamical system modeling, enhancing the accuracy of surrogate models.

Contribution

It proposes simple cross-validation variants for selecting kernels in dynamical system regression, connecting kernel learning with system stability and discrepancy measures.

Findings

Cross-validation improves kernel choice for dynamical systems.

Kernel Flows and MMD-based methods effectively select kernels.

Enhanced surrogate models for dynamical systems.

Abstract

Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. We present variants of cross-validation (Kernel Flows \cite{Owhadi19} and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators.