Hamiltonian System

Hamiltonian systems, describing energy-conserving physical processes, are a central focus in scientific computing, with research aiming to accurately model and predict their behavior, particularly in high-dimensional settings. Current efforts concentrate on developing neural network architectures, such as Hamiltonian Neural Networks (HNNs) and Symplectic Graph Neural Networks (SympGNNs), that incorporate the inherent symplectic structure of these systems to improve accuracy and long-term stability, often employing symplectic integrators and Lie-Poisson methods. These advancements are crucial for accurate simulations and predictions across diverse fields, from molecular dynamics to astrophysics, enabling more efficient and reliable modeling of complex physical phenomena.