Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes

Andreas Geist, Sebastian Trimpe
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:225-234, 2020.

Abstract

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model’s data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere Gauss’ principle of least constraint. In return, predictions of the system’s acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-geist20a, title = {Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes}, author = {Geist, Andreas and Trimpe, Sebastian}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {225--234}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/geist20a/geist20a.pdf}, url = {https://proceedings.mlr.press/v120/geist20a.html}, abstract = {The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model’s data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere Gauss’ principle of least constraint. In return, predictions of the system’s acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations. } }
Endnote
%0 Conference Paper %T Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes %A Andreas Geist %A Sebastian Trimpe %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-geist20a %I PMLR %P 225--234 %U https://proceedings.mlr.press/v120/geist20a.html %V 120 %X The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model’s data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere Gauss’ principle of least constraint. In return, predictions of the system’s acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.
APA
Geist, A. & Trimpe, S.. (2020). Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:225-234 Available from https://proceedings.mlr.press/v120/geist20a.html.

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