Learning Equations for Extrapolation and Control
This work addresses the challenge of interpretable and generalizable modeling for control tasks, though it is incremental as it builds on a recently proposed equation learning network.
The paper tackles the problem of identifying concise equations from data to understand functional relations and extrapolate to unseen domains, achieving the swing-up task on a cart-pendulum system with only 2 random rollouts.
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.