Hamiltonian Formulation

Hamiltonian formulation, a powerful framework for describing dynamical systems, focuses on deriving and analyzing the Hamiltonian function, which encapsulates the system's energy. Current research emphasizes learning Hamiltonians from data, employing techniques like neural networks (including graph neural networks and equivariant networks) and algorithms such as WSINDy to identify and approximate Hamiltonian structures, even in high-dimensional or noisy systems. This work is significant for advancing our understanding of complex systems across diverse fields, from quantum computing and materials science to astrophysics, by enabling efficient modeling and prediction of their behavior.