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Learning equations for extrapolation and control


Conference Paper


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.

Author(s): Subham S. Sahoo and Christoph H. Lampert and Georg Martius
Book Title: Proc. 35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, 2018
Year: 2018
Publisher: {PMLR}

Department(s): Autonomous Learning
Research Project(s): Learning physics: extrapolation and learning equations
Bibtex Type: Conference Paper (inproceedings)

How Published: ArXiv preprint: \url{https://arxiv.org/abs/1806.07259}
Note: to appear


  title = {Learning equations for extrapolation and control},
  author = {Sahoo, Subham S. and Lampert, Christoph H. and Martius, Georg},
  booktitle = {Proc.\ 35th International Conference on Machine Learning, {ICML} 2018, Stockholm, Sweden, 2018},
  howpublished = {ArXiv preprint: \url{https://arxiv.org/abs/1806.07259}},
  publisher = {{PMLR}},
  year = {2018},
  note = {to appear}