Learning momenta for Hamiltonian-based models

TL;DR

This paper introduces a novel Hamiltonian-based neural network architecture that jointly learns the generalized momenta, Hamiltonian structure, and system dynamics from data, eliminating the need for known momentum expressions. It enables physics-informed modeling in real-world scenarios where momenta are analytically intractable, using only state and derivative observations. The method is validated on challenging systems like a dissipative mass-spring system, double pendulum, and rolling disk.

Why It Matters

Many real-world physical systems lack known momentum expressions, limiting the applicability of traditional Hamiltonian neural networks. This work significantly broadens the scope of physics-informed machine learning by enabling end-to-end learning of momenta, making HNNs viable for complex, real-world dynamics. It bridges a critical gap between theoretical physics and data-driven modeling.

Key Findings

• The proposed model can learn generalized momenta even when their analytical form is unknown.
• Joint learning of momenta, Hamiltonian, and dynamics improves accuracy and physical consistency in simulations.
• The method demonstrates strong performance across diverse systems, including nonholonomic and dissipative dynamics.