ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias

Yupu Lu, Shijie Lin, Guanqi Chen, Jia Pan
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:14384-14397, 2022.

Abstract

Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-lu22c, title = {{M}od{L}a{N}ets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias}, author = {Lu, Yupu and Lin, Shijie and Chen, Guanqi and Pan, Jia}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {14384--14397}, 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/lu22c/lu22c.pdf}, url = {https://proceedings.mlr.press/v162/lu22c.html}, abstract = {Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.} }
Endnote
%0 Conference Paper %T ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias %A Yupu Lu %A Shijie Lin %A Guanqi Chen %A Jia Pan %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-lu22c %I PMLR %P 14384--14397 %U https://proceedings.mlr.press/v162/lu22c.html %V 162 %X Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.
APA
Lu, Y., Lin, S., Chen, G. & Pan, J.. (2022). ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:14384-14397 Available from https://proceedings.mlr.press/v162/lu22c.html.

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