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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 (2023) Learning dynamical systems from data: A simple cross-validation perspective, Part III: Irregularly-sampled time series. Physica D, 443 . Art. No. 133546. ISSN 0167-2789. doi:10.1016/j.physd.2022.133546.

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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) (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). 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 approximating a generalization of the flow map 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:Article
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URLURL TypeDescription
De Brouwer, Edward0000-0003-0608-0155
Hamzi, Boumediene0000-0002-9446-2614
Owhadi, Houman0000-0002-5677-1600
Additional Information:HO and BH gratefully acknowledges partial support by the Air Force Office of Scientific Research under MURI award number FA9550-20-1-0358 (Machine Learning and Physics-Based Modeling and Simulation) and JPL/NASA (Greenland contribution to sea level by 2050: The role of meltwater in shaping the future ice sheet evolution, UQ-aware Machine Learning for Uncertainty Quantification). EDB is funded by a FWO-SB grant.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-20-1-0358
Fonds Wetenschappelijk Onderzoek (FWO)UNSPECIFIED
Record Number:CaltechAUTHORS:20221122-564647900.3
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117990
Deposited By: Research Services Depository
Deposited On:06 Dec 2022 00:46
Last Modified:06 Dec 2022 17:27

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