Learning Hamiltonians of constrained mechanical systems
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.
Code (1)
Similar Papers 제목 키워드 기반
Geometric PID Controller for Stabilization of Nonholonomic Mechanical Systems on Lie Groups
The PID controller is an elegant and versatile controller for set point tracking in double integrator systems of which mechanical systems evolving on Euclidean space constitute a large class. But since mechanical systems…
Point TrackingData-driven Bayesian Control of Port-Hamiltonian Systems
Port-Hamiltonian theory is an established way to describe nonlinear physical systems widely used in various fields such as robotics, energy management, and mechanical engineering. This has led to considerable research in…
energy managementGaussian ProcessesManagementUncertainty QuantificationScalable Quantum Optimisation using HADOF: Hamiltonian Auto-Decomposition Optimisation Framework
Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadr…
Predictive Free Energy Simulations Through Hierarchical Distillation of Quantum Hamiltonians
Obtaining the free energies of condensed phase chemical reactions remains computationally prohibitive for high-level quantum mechanical methods. We introduce a hierarchical machine learning framework that bridges this ga…
Scalably learning quantum many-body Hamiltonians from dynamical data
The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measure…
Tensor Networks