Pseudo Hamiltonian

Pseudo-Hamiltonian methods aim to leverage the structure of Hamiltonian systems—those governed by energy conservation principles—to improve the learning and modeling of dynamical systems, even when energy is not perfectly conserved. Current research focuses on developing neural network architectures, such as pseudo-Hamiltonian neural networks (PHNNs) and Hamiltonian graph neural networks (HGNNs), to learn these systems from data, often incorporating techniques like symmetric integration schemes to enhance robustness to noise. This approach offers advantages in system identification, particularly when dealing with complex systems exhibiting damping or external forces, and shows promise for applications ranging from discovering symbolic laws from physical trajectories to solving computationally challenging problems like finding Hamiltonian cycles in graphs.