Variational Integrator Networks for Physically Structured Embeddings

Steindor Saemundsson, Alexander Terenin, Katja Hofmann, Marc Deisenroth
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3078-3087, 2020.

Abstract

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-saemundsson20a, title = {Variational Integrator Networks for Physically Structured Embeddings}, author = {Saemundsson, Steindor and Terenin, Alexander and Hofmann, Katja and Deisenroth, Marc}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3078--3087}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/saemundsson20a/saemundsson20a.pdf}, url = {https://proceedings.mlr.press/v108/saemundsson20a.html}, abstract = {Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.} }
Endnote
%0 Conference Paper %T Variational Integrator Networks for Physically Structured Embeddings %A Steindor Saemundsson %A Alexander Terenin %A Katja Hofmann %A Marc Deisenroth %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-saemundsson20a %I PMLR %P 3078--3087 %U https://proceedings.mlr.press/v108/saemundsson20a.html %V 108 %X Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.
APA
Saemundsson, S., Terenin, A., Hofmann, K. & Deisenroth, M.. (2020). Variational Integrator Networks for Physically Structured Embeddings. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3078-3087 Available from https://proceedings.mlr.press/v108/saemundsson20a.html.

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