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Published July 2021 | public
Journal Article

Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows


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 (Owhadi and Yoo, 2019) and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators.

Additional Information

© 2020 Elsevier. Received 4 July 2020, Revised 3 December 2020, Accepted 5 December 2020, Available online 5 February 2021. B.H. thanks the European Commission for funding through the Marie Curie fellowship STALDYS-792919 (Statistical Learning for Dynamical Systems). H.O. gratefully acknowledges support by the Air Force Office of Scientific Research, USA under award number FA9550-18-1-0271 (Games for Computation and Learning). We thank Deniz Eroğlu, Yoshito Hirata, Jeroen Lamb, Edmilson Roque, Gabriele Santin and Yuzuru Sato for useful comments. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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August 22, 2023
October 23, 2023