Learning Nonparametric Differential Equations via Multivariate Occupation Kernel Functions
Abstract: Learning a nonparametric system of ordinary differential equations from trajectories in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations often scale quadratically in $d$ unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach, the occupation kernel method (OCK), 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. The OCK method outperforms all other comparators on 3 of the 9 datasets on full trajectory predictions, and 4 out of the 9 datasets on next point prediction.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We rearranged the author names but no other changes were made..
Assigned Action Editor: ~Tongliang_Liu1
Submission Number: 2929
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