Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces
This work addresses the problem of accurately modeling Hamiltonian systems for researchers in physics and machine learning, but it is incremental as it builds on existing kernel methods with specific modifications.
The paper tackled learning Hamiltonian dynamics from limited data by using a regularized optimization method in a reproducing kernel Hilbert space with symplectic kernels, and simulations showed improved accuracy and energy-preservation in two Hamiltonian systems.
This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently Hamiltonian, and where the vector field is required to be odd or even. This is done with a symplectic kernel, and it is shown how this symplectic kernel can be modified to be odd or even. The performance of the method is validated in simulations for two Hamiltonian systems. The simulations show that the learned dynamics reflect the energy-preservation of the Hamiltonian dynamics, and that the restriction to symplectic and odd dynamics gives improved accuracy over a large domain of the phase space.