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

• URL: http://arxiv.org/abs/2111.13037v2
• Date: Thu, 03 Oct 2024 21:30:36 GMT
• Title: Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series
• Authors: Jonghyeon Lee, Edward De Brouwer, Boumediene Hamzi, Houman Owhadi,
• Abstract summary: A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a kernel. Despite its previous successes, this strategy breaks down when the observed time series is not regularly sampled in time. We propose to address this problem by directly approxing the vector field of the dynamical system by incorporating time differences in the (KF) data-adapted kernels.
• Score: 8.918419734720613
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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)\cite{Owhadi19} (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.

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