Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes
This work addresses a specific bottleneck in physics-informed machine learning for researchers modeling dynamical systems, though it appears incremental.
The paper tackles the problem of learning Hamiltonian systems from a small number of long, noisy trajectories, which previous methods had not addressed, and demonstrates success in various data settings.
Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and introduce an energy-conserving shooting method that allows robust inference from both short and long trajectories. We demonstrate the method's success in learning Hamiltonian systems in various data settings.