PFEM-GP-dPHS : a finite element framework for combining Gaussian processes and infinite-dimensional port-Hamiltonian systems

Florian Courteville, Iain Henderson, Denis MATIGNON, Sylvain Dubreuil
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1396-1417, 2026.

Abstract

In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the functional hyperparameters of the GP prior over the Hamiltonian functional is chosen independently from the discretization of the dPHS, thus reducing the numerical complexity of our method. We next model the mean of the GP prior of the Hamiltonian as a quadratic form, enabling the GP kernel to focus on the nonlinear part of a given dPHS. We illustrate our method on a nonlinear one dimensional wave equation with unknown physical parameters (tension and linear mass).

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-courteville26a, title = {PFEM-GP-dPHS : a finite element framework for combining Gaussian processes and infinite-dimensional port-Hamiltonian systems}, author = {Courteville, Florian and Henderson, Iain and MATIGNON, Denis and Dubreuil, Sylvain}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1396--1417}, 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/courteville26a/courteville26a.pdf}, url = {https://proceedings.mlr.press/v331/courteville26a.html}, abstract = {In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the functional hyperparameters of the GP prior over the Hamiltonian functional is chosen independently from the discretization of the dPHS, thus reducing the numerical complexity of our method. We next model the mean of the GP prior of the Hamiltonian as a quadratic form, enabling the GP kernel to focus on the nonlinear part of a given dPHS. We illustrate our method on a nonlinear one dimensional wave equation with unknown physical parameters (tension and linear mass).} }
Endnote
%0 Conference Paper %T PFEM-GP-dPHS : a finite element framework for combining Gaussian processes and infinite-dimensional port-Hamiltonian systems %A Florian Courteville %A Iain Henderson %A Denis MATIGNON %A Sylvain Dubreuil %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-courteville26a %I PMLR %P 1396--1417 %U https://proceedings.mlr.press/v331/courteville26a.html %V 331 %X In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the functional hyperparameters of the GP prior over the Hamiltonian functional is chosen independently from the discretization of the dPHS, thus reducing the numerical complexity of our method. We next model the mean of the GP prior of the Hamiltonian as a quadratic form, enabling the GP kernel to focus on the nonlinear part of a given dPHS. We illustrate our method on a nonlinear one dimensional wave equation with unknown physical parameters (tension and linear mass).
APA
Courteville, F., Henderson, I., MATIGNON, D. & Dubreuil, S.. (2026). PFEM-GP-dPHS : a finite element framework for combining Gaussian processes and infinite-dimensional port-Hamiltonian systems. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1396-1417 Available from https://proceedings.mlr.press/v331/courteville26a.html.

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