Contemporary Symbolic Regression Methods and their Relative Performance

TL;DR

This paper introduces a comprehensive, open-source benchmarking platform for symbolic regression, evaluating 14 methods across diverse datasets to identify the most effective approaches and promote reproducibility in the field.

Contribution

It provides a standardized, reproducible benchmarking framework for symbolic regression and assesses multiple methods on real-world and synthetic problems, highlighting the best performing techniques.

Findings

Genetic algorithms combined with parameter estimation excel in real-world tasks.

Deep learning and genetic algorithms perform similarly on noisy synthetic problems.

The benchmarking platform facilitates transparent comparison and future method development.

Abstract

Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no known model form as well as ground-truth benchmark problems, including physics equations and systems of ordinary differential equations. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method's ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that deep learning and genetic algorithm-based approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.