Hamiltonian Neural Networks with Automatic Symmetry Detection

TL;DR

This paper introduces an enhanced Hamiltonian neural network framework that automatically detects and embeds symmetries using a Lie algebra approach, improving the modeling of physical systems.

Contribution

It presents a novel method combining HNN with Lie algebra to learn symmetries and energy functions simultaneously from data.

Findings

Successfully applied to pendulum and two-body astrodynamics problems.

Automatically detects symmetry groups without prior knowledge.

Preserves physical structure in learned models.

Abstract

Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.