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

Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately