Symplectic Group

Symplectic groups are fundamental mathematical structures crucial for modeling Hamiltonian systems, which describe many physical phenomena where energy is conserved. Current research focuses on developing neural network architectures, such as Symplectic Graph Neural Networks (SympGNNs) and Hamiltonian Neural Networks (HNNs), that learn these systems while preserving their inherent symplectic structure, often using symplectic integrators for improved accuracy and long-term prediction. This work is significant because accurately modeling Hamiltonian systems is vital for applications ranging from molecular dynamics simulations to robotics and control systems, and these new methods offer improved accuracy and efficiency compared to traditional approaches. The development of novel metrics, like the Symplecticity Metric (SyMetric), is also improving the evaluation and comparison of these models.