Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes

Fuente: arXiv
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Autori principali: Ewering, Jan-Hendrik, Herrmann, Robin E., Wahlström, Niklas, Schön, Thomas B., Seel, Thomas
Natura: Preprint
Pubblicazione: 2025
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author Ewering, Jan-Hendrik
Herrmann, Robin E.
Wahlström, Niklas
Schön, Thomas B.
Seel, Thomas
author_facet Ewering, Jan-Hendrik
Herrmann, Robin E.
Wahlström, Niklas
Schön, Thomas B.
Seel, Thomas
contents Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements.
format Preprint
id arxiv_https___arxiv_org_abs_2511_05330
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
Ewering, Jan-Hendrik
Herrmann, Robin E.
Wahlström, Niklas
Schön, Thomas B.
Seel, Thomas
Machine Learning
Systems and Control
Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements.
title Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
topic Machine Learning
Systems and Control
url https://arxiv.org/abs/2511.05330