Physics-constrained learning for PDE systems with uncertainty quantified port-Hamiltonian models

Kaiyuan Tan, Peilun Li, Thomas Beckers
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1753-1764, 2024.

Abstract

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-tan24a, title = {Physics-constrained learning for {PDE} systems with uncertainty quantified port-{H}amiltonian models}, author = {Tan, Kaiyuan and Li, Peilun and Beckers, Thomas}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {1753--1764}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/tan24a/tan24a.pdf}, url = {https://proceedings.mlr.press/v242/tan24a.html}, abstract = {Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.} }
Endnote
%0 Conference Paper %T Physics-constrained learning for PDE systems with uncertainty quantified port-Hamiltonian models %A Kaiyuan Tan %A Peilun Li %A Thomas Beckers %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-tan24a %I PMLR %P 1753--1764 %U https://proceedings.mlr.press/v242/tan24a.html %V 242 %X Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.
APA
Tan, K., Li, P. & Beckers, T.. (2024). Physics-constrained learning for PDE systems with uncertainty quantified port-Hamiltonian models. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1753-1764 Available from https://proceedings.mlr.press/v242/tan24a.html.

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