Constraint-based graph network simulator

Yulia Rubanova, Alvaro Sanchez-Gonzalez, Tobias Pfaff, Peter Battaglia
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:18844-18870, 2022.

Abstract

In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states. However, many traditional simulation engines instead model the constraints of the system and select the state which satisfies them. Here we present a framework for constraint-based learned simulation, where a scalar constraint function is implemented as a graph neural network, and future predictions are computed by solving the optimization problem defined by the learned constraint. Our model achieves comparable or better accuracy to top learned simulators on a variety of challenging physical domains, and offers several unique advantages. We can improve the simulation accuracy on a larger system by applying more solver iterations at test time. We also can incorporate novel hand-designed constraints at test time and simulate new dynamics which were not present in the training data. Our constraint-based framework shows how key techniques from traditional simulation and numerical methods can be leveraged as inductive biases in machine learning simulators.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-rubanova22a, title = {Constraint-based graph network simulator}, author = {Rubanova, Yulia and Sanchez-Gonzalez, Alvaro and Pfaff, Tobias and Battaglia, Peter}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {18844--18870}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/rubanova22a/rubanova22a.pdf}, url = {https://proceedings.mlr.press/v162/rubanova22a.html}, abstract = {In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states. However, many traditional simulation engines instead model the constraints of the system and select the state which satisfies them. Here we present a framework for constraint-based learned simulation, where a scalar constraint function is implemented as a graph neural network, and future predictions are computed by solving the optimization problem defined by the learned constraint. Our model achieves comparable or better accuracy to top learned simulators on a variety of challenging physical domains, and offers several unique advantages. We can improve the simulation accuracy on a larger system by applying more solver iterations at test time. We also can incorporate novel hand-designed constraints at test time and simulate new dynamics which were not present in the training data. Our constraint-based framework shows how key techniques from traditional simulation and numerical methods can be leveraged as inductive biases in machine learning simulators.} }
Endnote
%0 Conference Paper %T Constraint-based graph network simulator %A Yulia Rubanova %A Alvaro Sanchez-Gonzalez %A Tobias Pfaff %A Peter Battaglia %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-rubanova22a %I PMLR %P 18844--18870 %U https://proceedings.mlr.press/v162/rubanova22a.html %V 162 %X In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states. However, many traditional simulation engines instead model the constraints of the system and select the state which satisfies them. Here we present a framework for constraint-based learned simulation, where a scalar constraint function is implemented as a graph neural network, and future predictions are computed by solving the optimization problem defined by the learned constraint. Our model achieves comparable or better accuracy to top learned simulators on a variety of challenging physical domains, and offers several unique advantages. We can improve the simulation accuracy on a larger system by applying more solver iterations at test time. We also can incorporate novel hand-designed constraints at test time and simulate new dynamics which were not present in the training data. Our constraint-based framework shows how key techniques from traditional simulation and numerical methods can be leveraged as inductive biases in machine learning simulators.
APA
Rubanova, Y., Sanchez-Gonzalez, A., Pfaff, T. & Battaglia, P.. (2022). Constraint-based graph network simulator. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:18844-18870 Available from https://proceedings.mlr.press/v162/rubanova22a.html.

Related Material