Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features

TL;DR

This paper introduces a novel approach for learning dissipative Hamiltonian systems from limited, noisy data by decomposing the vector field into symplectic and dissipative parts using specialized kernels and random Fourier features.

Contribution

It proposes a new kernel-based method leveraging Helmholtz decomposition and random Fourier features to improve learning of dissipative Hamiltonian dynamics from small datasets.

Findings

Significantly improved predictive accuracy over Gaussian kernel methods.

Effective learning of dissipative Hamiltonian systems with limited data.

Validation through simulations on two dissipative Hamiltonian systems.

Abstract

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.