Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics

Pingchuan Ma, Peter Yichen Chen, Bolei Deng, Joshua B. Tenenbaum, Tao Du, Chuang Gan, Wojciech Matusik
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:23279-23300, 2023.

Abstract

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method’s ability to learn constitutive laws from videos.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ma23a, title = {Learning Neural Constitutive Laws from Motion Observations for Generalizable {PDE} Dynamics}, author = {Ma, Pingchuan and Chen, Peter Yichen and Deng, Bolei and Tenenbaum, Joshua B. and Du, Tao and Gan, Chuang and Matusik, Wojciech}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {23279--23300}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ma23a/ma23a.pdf}, url = {https://proceedings.mlr.press/v202/ma23a.html}, abstract = {We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method’s ability to learn constitutive laws from videos.} }
Endnote
%0 Conference Paper %T Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics %A Pingchuan Ma %A Peter Yichen Chen %A Bolei Deng %A Joshua B. Tenenbaum %A Tao Du %A Chuang Gan %A Wojciech Matusik %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ma23a %I PMLR %P 23279--23300 %U https://proceedings.mlr.press/v202/ma23a.html %V 202 %X We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method’s ability to learn constitutive laws from videos.
APA
Ma, P., Chen, P.Y., Deng, B., Tenenbaum, J.B., Du, T., Gan, C. & Matusik, W.. (2023). Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:23279-23300 Available from https://proceedings.mlr.press/v202/ma23a.html.

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