Separable Hamiltonian Neural Networks
This work addresses a specific bottleneck in physics-informed machine learning for dynamical systems, offering incremental improvements over existing HNNs.
The authors tackled the problem of improving Hamiltonian neural networks (HNNs) for modeling dynamical systems by embedding additive separability biases, resulting in more accurate regression of Hamiltonians and vector fields, with better prediction of dynamics and energy conservation.
Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.