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

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.

File uploaded on arxiv on Sunday, July 5th, 2020. Got delayed due to tex problems on ArXiv. Original version at https://www.researchgate.net/publication/342693818_Learning_dynamical_systems_from_data_a_simple_cross-validation_perspective

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• Symplectic Gaussian Process Regression of Hamiltonian Flow Maps
• Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification
• Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series
• A Note on A Priori Forecasting and Simplicity Bias in Time Series
• Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
• Recovering sparse networks: Basis adaptation and stability under extensions
• Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
• Learning of discrete models of variational PDEs from data
• Analysis of Structured Deep Kernel Networks
• Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods
• Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
• Dual-moon forced dynamics and nonlinear aggregation in Saturn's F ring: From quasi-periodicity to modulated oscillations