Learning Trajectories of Hamiltonian Systems with Neural Networks
This work addresses the challenge of accurately simulating Hamiltonian systems in physics and engineering, though it is incremental as it builds on existing HNN methods.
The authors tackled the problem of modeling conservative systems with neural networks by enhancing Hamiltonian neural networks (HNNs) with a continuous-time trajectory estimation using a deep hidden physics model, resulting in improved performance with low sampling rates, noisy, and irregular observations.
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.