Koopman-Equivariant Gaussian Processes

Petar Bevanda, Max Beier, Alexandre Capone, Stefan Georg Sosnowski, Sandra Hirche, Armin Lederer
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3151-3159, 2025.

Abstract

We propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance – which we refer to as Koopman equivariance – we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-bevanda25a, title = {Koopman-Equivariant Gaussian Processes}, author = {Bevanda, Petar and Beier, Max and Capone, Alexandre and Sosnowski, Stefan Georg and Hirche, Sandra and Lederer, Armin}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3151--3159}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/bevanda25a/bevanda25a.pdf}, url = {https://proceedings.mlr.press/v258/bevanda25a.html}, abstract = {We propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance – which we refer to as Koopman equivariance – we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.} }
Endnote
%0 Conference Paper %T Koopman-Equivariant Gaussian Processes %A Petar Bevanda %A Max Beier %A Alexandre Capone %A Stefan Georg Sosnowski %A Sandra Hirche %A Armin Lederer %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-bevanda25a %I PMLR %P 3151--3159 %U https://proceedings.mlr.press/v258/bevanda25a.html %V 258 %X We propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance – which we refer to as Koopman equivariance – we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.
APA
Bevanda, P., Beier, M., Capone, A., Sosnowski, S.G., Hirche, S. & Lederer, A.. (2025). Koopman-Equivariant Gaussian Processes. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3151-3159 Available from https://proceedings.mlr.press/v258/bevanda25a.html.

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