Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

2023/03/03 by Magnus Ross, Markus Heinonen, Ross, Magnus +1 · 2 citations
Computer Science · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.2303.01925

openalex publication_date 2023/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
• Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data

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