Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features
This work addresses the problem of modeling complex physical systems for researchers in computational physics and machine learning, but it is incremental as it builds on existing kernel methods with specific adaptations.
The paper tackles learning dissipative Hamiltonian dynamics from limited, noisy data by using Helmholtz decomposition with specialized kernels and random Fourier features, showing significant predictive accuracy improvements in simulations for two systems compared to a Gaussian separable kernel method.
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.