Published In

OpenReview.net

Document Type

Article

Publication Date

2025

Subjects

Differential equations

Abstract

Learning a nonparametric system of ordinary differential equations from trajectories in a -dimensional state space requires learning functions of variables. Explicit formulations often scale quadratically in unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach, the multivariate occupation kernel method (MOCK), using the implicit formulation provided by vector-valued reproducing kernel Hilbert spaces. The solution for the vector field relies on multivariate occupation kernel functions associated with the trajectories and scales linearly with the dimension of the state space. We validate through experiments on a variety of simulated and real datasets ranging from 2 to 1024 dimensions, and provide an example with a divergence-free vector field. MOCK outperforms all other comparators on 3 of the 9 datasets on full trajectory prediction and 4 out of the 9 datasets on next-point prediction.

Rights

Copyright (c) 2025 The Authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Persistent Identifier

https://archives.pdx.edu/ds/psu/44298

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