再生核ヒルベルト空間とランダム特徴を用いたハミルトン力学の学習
Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features
限られたノイズを含むデータからハミルトン力学を学習するため、奇数シンプレクティックカーネルとランダム特徴近似を提案し、予測精度とデータ効率の向上を実証した。
著者: Torbjørn Smith, Olav Egeland
分類: cs.LG, cs.RO, cs.SY, eess.SY
原文アブストラクト
A method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular, odd Hamiltonian vector fields. This is done with a symplectic kernel, and it is shown how the kernel can be modified to an odd symplectic kernel to impose the odd symmetry. A random feature approximation is developed for the proposed odd kernel to reduce the problem size. The performance of the method is validated in simulations for three Hamiltonian systems. It is demonstrated that the use of an odd symplectic kernel improves prediction accuracy and data efficiency, and that the learned vector fields are Hamiltonian and exhibit the imposed odd symmetry characteristics.
