Learning dynamical systems from data: a simple cross-validation perspective
This work provides an incremental improvement for researchers in dynamical systems modeling by offering a straightforward approach to kernel selection in data-driven emulators.
The authors tackled the problem of learning surrogate models for dynamical systems from observed data by introducing cross-validation variants to select kernels for kernel-based emulators, resulting in a method that simplifies kernel selection without specifying performance metrics.
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.