  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.
