Learning Equations for Extrapolation and Control

Subham Sahoo, Christoph Lampert, Georg Martius
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4442-4450, 2018.

Abstract

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-sahoo18a, title = {Learning Equations for Extrapolation and Control}, author = {Sahoo, Subham and Lampert, Christoph and Martius, Georg}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {4442--4450}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf}, url = {https://proceedings.mlr.press/v80/sahoo18a.html}, abstract = {We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.} }
Endnote
%0 Conference Paper %T Learning Equations for Extrapolation and Control %A Subham Sahoo %A Christoph Lampert %A Georg Martius %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-sahoo18a %I PMLR %P 4442--4450 %U https://proceedings.mlr.press/v80/sahoo18a.html %V 80 %X We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.
APA
Sahoo, S., Lampert, C. & Martius, G.. (2018). Learning Equations for Extrapolation and Control. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:4442-4450 Available from https://proceedings.mlr.press/v80/sahoo18a.html.

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