  Understanding natural symmetries is key to making sense of our complex and
ever-changing world. Recent work has shown that neural networks can learn such
symmetries directly from data using Hamiltonian Neural Networks (HNNs). But
HNNs struggle when trained on datasets where energy is not conserved. In this
paper, we ask whether it is possible to identify and decompose conservative and
dissipative dynamics simultaneously. We propose Dissipative Hamiltonian Neural
Networks (D-HNNs), which parameterize both a Hamiltonian and a Rayleigh
dissipation function. Taken together, they represent an implicit Helmholtz
decomposition which can separate dissipative effects such as friction from
symmetries such as conservation of energy. We train our model to decompose a
damped mass-spring system into its friction and inertial terms and then show
that this decomposition can be used to predict dynamics for unseen friction
coefficients. Then we apply our model to real world data including a large,
noisy ocean current dataset where decomposing the velocity field yields useful
scientific insights.
