Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately
This addresses the challenge of modeling complex physical systems with mixed dynamics, such as friction and energy conservation, for applications in scientific domains like fluid dynamics, though it appears incremental as an extension of HNNs.
The paper tackled the problem of learning both conservative and dissipative dynamics from data, which Hamiltonian Neural Networks (HNNs) struggle with when energy is not conserved, by proposing Dissipative Hamiltonian Neural Networks (D-HNNs) that separate these effects, demonstrating successful decomposition and prediction on a damped mass-spring system and real-world ocean current data.
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.