Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling

Franck Djeumou, Cyrus Neary, Eric Goubault, Sylvie Putot, Ufuk Topcu
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:263-277, 2022.

Abstract

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or from the system’s design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system’s vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model’s training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems – including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-djeumou22a, title = {Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling}, author = {Djeumou, Franck and Neary, Cyrus and Goubault, Eric and Putot, Sylvie and Topcu, Ufuk}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {263--277}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/djeumou22a/djeumou22a.pdf}, url = {https://proceedings.mlr.press/v168/djeumou22a.html}, abstract = {Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or from the system’s design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system’s vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model’s training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems – including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.} }
Endnote
%0 Conference Paper %T Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling %A Franck Djeumou %A Cyrus Neary %A Eric Goubault %A Sylvie Putot %A Ufuk Topcu %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-djeumou22a %I PMLR %P 263--277 %U https://proceedings.mlr.press/v168/djeumou22a.html %V 168 %X Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or from the system’s design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system’s vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model’s training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems – including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.
APA
Djeumou, F., Neary, C., Goubault, E., Putot, S. & Topcu, U.. (2022). Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:263-277 Available from https://proceedings.mlr.press/v168/djeumou22a.html.

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