Learning Hamiltonians of constrained mechanical systems
This work addresses the modelling of physical systems with neural networks for researchers in computational physics and machine learning, but it appears incremental as it builds on existing methods for Hamiltonian systems.
The paper tackled the problem of accurately approximating the Hamiltonian function of constrained mechanical systems from sample data, achieving improved accuracy by preserving constraints in the learning strategy using explicit Lie group integrators and classical schemes.
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.