Hamiltonian Dynamic

Hamiltonian dynamics, describing the evolution of systems governed by a Hamiltonian function, is a core concept in physics and is increasingly central to machine learning. Current research focuses on developing and analyzing algorithms, such as Hamiltonian Monte Carlo (HMC) and its variants, and neural network architectures (e.g., Hamiltonian Neural Networks) that efficiently learn and simulate Hamiltonian systems, often incorporating symplectic integration for accuracy. These advancements are improving the efficiency of sampling methods in Bayesian inference and enabling more accurate and robust modeling of complex dynamical systems in robotics, control theory, and other fields. The ability to accurately learn and simulate Hamiltonian dynamics from limited data holds significant promise for various scientific and engineering applications.