Learning Hamiltonians of constrained mechanical systems

TL;DR

This paper introduces new neural network-based methods for accurately learning Hamiltonian functions of constrained mechanical systems, emphasizing the preservation of system constraints during the learning process.

Contribution

It proposes novel approaches that incorporate Lie group integrators and classical schemes to better preserve constraints in Hamiltonian system learning.

Findings

Improved accuracy in Hamiltonian approximation for constrained systems

Effective constraint preservation during learning process

Enhanced modeling of physical systems with neural networks

Abstract

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined by one scalar function, the Hamiltonian. The solution trajectories are often constrained to evolve on a submanifold of a linear vector space. In this work, we propose new approaches for the accurate approximation of the Hamiltonian function of constrained mechanical systems given sample data information of their solutions. We focus on the importance of the preservation of the constraints in the learning strategy by using both explicit Lie group integrators and other classical schemes.