  The past few years have witnessed an increased interest in learning
Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on
physical laws, Hamiltonian dynamics endow neural networks with accurate
long-term prediction, interpretability, and data-efficient learning. However,
Hamiltonian dynamics also bring energy conservation or dissipation assumptions
on the input data and additional computational overhead. In this paper, we
systematically survey recently proposed Hamiltonian neural network models, with
a special emphasis on methodologies. In general, we discuss the major
contributions of these models, and compare them in four overlapping directions:
1) generalized Hamiltonian system; 2) symplectic integration, 3) generalized
input form, and 4) extended problem settings. We also provide an outlook of the
fundamental challenges and emerging opportunities in this area.
