Learning and Interpreting Potentials for Classical Hamiltonian Systems
This work addresses the challenge of interpretability in physics-based machine learning for classical Hamiltonian systems, though it appears incremental as it applies existing techniques to new test cases.
The paper tackles the problem of learning interpretable potential energy functions from Hamiltonian system trajectories by constructing a neural network model and extracting closed-form algebraic expressions, showing close agreement with ground truth potentials, such as learning the correct effective potential for a central force problem.
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network model of the potential and then applies an equation discovery technique to extract from the neural potential a closed-form algebraic expression. We demonstrate this approach for several systems, including oscillators, a central force problem, and a problem of two charged particles in a classical Coulomb potential. Through these test problems, we show close agreement between learned neural potentials, the interpreted potentials we obtain after training, and the ground truth. In particular, for the central force problem, we show that our approach learns the correct effective potential, a reduced-order model of the system.