Symbolic Regression via Neural Networks

TL;DR

This paper introduces a neural network-based method that generates symbolic expressions for dynamical system equations, combining deep learning flexibility with interpretability.

Contribution

A novel neural network architecture that produces symbolic governing equations from data, bridging deep learning and symbolic modeling.

Findings

Accurately models classical dynamical systems

Generates interpretable symbolic equations

Outperforms traditional methods in simplicity and accuracy

Abstract

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model, then show the accuracy of our algorithm across a range of classical dynamical systems.