Variational Principle and Variational Integrators for Neural Symplectic Forms

Yuhan Chen, Baige Xu, Takashi Matsubara, Takaharu Yaguchi

Keywords: variational principle, variational integrator, symplectic form, Hamiltonian equation

TL;DR: We investigate the variational principle that derives neural symplectic forms. This shows that this model admits the physical properties, particularly the Noether theorem. We also propose the variational integrator for this model.

Abstract:

In this study, we investigate the variational principle for neural symplectic forms, thereby designing the variational integrators for this model. In recent years, neural networks models for physical phenomena have been attracting much attention. In particular, the neural symplectic form is a method that can model general Hamiltonian systems, which are not necessary in the canonical form.
In this paper, we make the following two contributions regarding this model. Firstly, we show that this model is derived from a variational principle and hence admits the Noether theorem.
Secondly, when the trained models are used for simulations, they must be discretized using numerical integrators; however, unless carefully designed, numerical integrators destroy physical laws.

Submission Number: 116