Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery

TL;DR

This paper introduces an integrated neural network framework combining symbolic regression with deep learning, enabling models to learn interpretable equations and generalize better for scientific discovery tasks.

Contribution

It presents a novel end-to-end trainable system that incorporates the Equation Learner (EQL) network into deep learning architectures for symbolic regression.

Findings

EQL-based models can learn the form of functions from data.

The integrated system performs well on MNIST arithmetic tasks.

The approach enables better extrapolation outside training data.

Abstract

Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved amazing levels of accuracy on image recognition and natural language processing tasks, but are often seen as black-box models that are difficult to interpret and typically extrapolate poorly. Here we use a neural network-based architecture for symbolic regression called the Equation Learner (EQL) network and integrate it with other deep learning architectures such that the whole system can be trained end-to-end through backpropagation. To demonstrate the power of such systems, we study their performance on several substantially different tasks. First, we show that the neural network can perform symbolic regression and learn the form of several functions. Next, we present an MNIST arithmetic task where a separate part of the neural network extracts the digits. Finally, we demonstrate prediction of dynamical systems where an unknown parameter is extracted through an encoder. We find that the EQL-based architecture can extrapolate quite well outside of the training data set compared to a standard neural network-based architecture, paving the way for deep learning to be applied in scientific exploration and discovery.