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Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series

Lee, Jonghyeon and De Brouwer, Edward and Hamzi, Boumediene and Owhadi, Houman (2021) Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220524-180315371

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Abstract

A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field 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) [34] (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). Despite its previous successes, this strategy (based on interpolating the vector field driving the dynamical system) breaks down when the observed time series is not regularly sampled in time. In this work, we propose to address this problem by directly approximating the vector field of the dynamical system by incorporating time differences between observations in the (KF) data-adapted kernels. We compare our approach with the classical one over different benchmark dynamical systems and show that it significantly improves the forecasting accuracy while remaining simple, fast, and robust.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/2111.13037arXivDiscussion Paper
ORCID:
AuthorORCID
De Brouwer, Edward0000-0003-0608-0155
Hamzi, Boumediene0000-0002-9446-2614
Owhadi, Houman0000-0002-5677-1600
Additional Information:Attribution 4.0 International (CC BY 4.0).
Record Number:CaltechAUTHORS:20220524-180315371
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220524-180315371
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114899
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:24 May 2022 20:08
Last Modified:24 May 2022 20:08

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