Geometric Contact Flows: Contactomorphisms for Dynamics and Control

Andrea Testa, Søren Hauberg, Tamim Asfour, Leonel Rozo
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:59259-59284, 2025.

Abstract

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system’s behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-testa25a, title = {Geometric Contact Flows: Contactomorphisms for Dynamics and Control}, author = {Testa, Andrea and Hauberg, S{\o}ren and Asfour, Tamim and Rozo, Leonel}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {59259--59284}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/testa25a/testa25a.pdf}, url = {https://proceedings.mlr.press/v267/testa25a.html}, abstract = {Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system’s behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.} }
Endnote
%0 Conference Paper %T Geometric Contact Flows: Contactomorphisms for Dynamics and Control %A Andrea Testa %A Søren Hauberg %A Tamim Asfour %A Leonel Rozo %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-testa25a %I PMLR %P 59259--59284 %U https://proceedings.mlr.press/v267/testa25a.html %V 267 %X Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system’s behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.
APA
Testa, A., Hauberg, S., Asfour, T. & Rozo, L.. (2025). Geometric Contact Flows: Contactomorphisms for Dynamics and Control. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:59259-59284 Available from https://proceedings.mlr.press/v267/testa25a.html.

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