Learning dynamical systems from data: A simple cross-validation perspective, part IV: Case with partial observations

Abstract

A simple and interpretable way to learn a dynamical system from data is to interpolate its governing equations with a kernel. In particular, this strategy is highly efficient (both in terms of accuracy and complexity) when the kernel is data-adapted using Kernel Flows (KF) (Owhadi and Yoo, 2019), (which uses gradient-based optimization to learn a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used for interpolation). In this work, we extend previous work on learning dynamical systems using Kernel Flows (Hamzi and Owhadi, 2021; Darcy et al. 2021; Lee et al. 2023; Darcy et al. 2023; Owhadi and Romit Maulik, 2021) to the case of learning vector-valued dynamical systems from time-series observations that are partial/incomplete in the state space. The method combines Kernel Flows with Computational Graph Completion.