Learning Equations for Extrapolation and Control

TL;DR

This paper introduces a neural network-based method for learning concise, interpretable equations from data, capable of extrapolating to unseen domains and applied successfully to a cart-pendulum system with minimal data.

Contribution

It extends existing equation learning networks to include divisions and enhances model selection, enabling better learning from real-world data and successful extrapolation.

Findings

Successfully learned the cart-pendulum dynamics with only 2 rollouts.

Identified true underlying equations in many cases.

Achieved effective extrapolation to unseen domains.

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.