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

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.Comment: 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_perspectiv

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

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 [31] and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators

Normal Forms for Nonlinear Discrete Time Control Systems

We study the feedback classification of discrete-time control systems whose linear approximation around an equilibrium is controllable. We provide a normal form for systems under investigation