Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes

Jan-Hendrik Ewering, Robin Erik Herrmann, Niklas Wahlström, Thomas B. Schön, Thomas Seel
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1875-1894, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-ewering26a, title = {Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes}, author = {Ewering, Jan-Hendrik and Herrmann, Robin Erik and Wahlstr\"om, Niklas and Sch\"on, Thomas B. and Seel, Thomas}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1875--1894}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/ewering26a/ewering26a.pdf}, url = {https://proceedings.mlr.press/v331/ewering26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes %A Jan-Hendrik Ewering %A Robin Erik Herrmann %A Niklas Wahlström %A Thomas B. Schön %A Thomas Seel %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-ewering26a %I PMLR %P 1875--1894 %U https://proceedings.mlr.press/v331/ewering26a.html %V 331 %X 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.
APA
Ewering, J., Herrmann, R.E., Wahlström, N., Schön, T.B. & Seel, T.. (2026). Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1875-1894 Available from https://proceedings.mlr.press/v331/ewering26a.html.

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