Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces
Torbjørn Smith Olav Egeland
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. It is shown
that the learned dynamics are Hamiltonian, and that the learned Hamiltonian
vector field can be prescribed to be odd or even.