Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 24, 2022 | Submitted
Report Open

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


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.

Additional Information

Attribution 4.0 International (CC BY 4.0).

Attached Files

Submitted - 2111.13037.pdf


Files (1.2 MB)
Name Size Download all
1.2 MB Preview Download

Additional details

August 20, 2023
October 24, 2023