Structure-Preserving Learning Using Gaussian Processes and Variational Integrators

Jan Brüdigam, Martin Schuck, Alexandre Capone, Stefan Sosnowski, Sandra Hirche
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:1150-1162, 2022.

Abstract

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some generic discretization technique, which might however disregard properties of the underlying physical system. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation and satisfaction of explicit kinematic constraints. In this work, we present a novel structure-preserving learning-based modelling approach that combines a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with general theoretical results and demonstrates exact constraint satisfaction for constrained dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-brudigam22a, title = {Structure-Preserving Learning Using Gaussian Processes and Variational Integrators}, author = {Br\"udigam, Jan and Schuck, Martin and Capone, Alexandre and Sosnowski, Stefan and Hirche, Sandra}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {1150--1162}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/brudigam22a/brudigam22a.pdf}, url = {https://proceedings.mlr.press/v168/brudigam22a.html}, abstract = {Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some generic discretization technique, which might however disregard properties of the underlying physical system. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation and satisfaction of explicit kinematic constraints. In this work, we present a novel structure-preserving learning-based modelling approach that combines a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with general theoretical results and demonstrates exact constraint satisfaction for constrained dynamical systems.} }
Endnote
%0 Conference Paper %T Structure-Preserving Learning Using Gaussian Processes and Variational Integrators %A Jan Brüdigam %A Martin Schuck %A Alexandre Capone %A Stefan Sosnowski %A Sandra Hirche %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-brudigam22a %I PMLR %P 1150--1162 %U https://proceedings.mlr.press/v168/brudigam22a.html %V 168 %X Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some generic discretization technique, which might however disregard properties of the underlying physical system. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation and satisfaction of explicit kinematic constraints. In this work, we present a novel structure-preserving learning-based modelling approach that combines a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with general theoretical results and demonstrates exact constraint satisfaction for constrained dynamical systems.
APA
Brüdigam, J., Schuck, M., Capone, A., Sosnowski, S. & Hirche, S.. (2022). Structure-Preserving Learning Using Gaussian Processes and Variational Integrators. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:1150-1162 Available from https://proceedings.mlr.press/v168/brudigam22a.html.

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