Class Symbolic Regression: Gotta Fit 'Em All

TL;DR

This paper presents 'Class Symbolic Regression', a novel hierarchical framework that automatically finds a single analytical form fitting multiple datasets with unique parameters, extending previous symbolic regression methods and demonstrating its utility in astrophysics.

Contribution

The paper introduces the first Class SR framework for multi-dataset symbolic regression, extending prior work with a hierarchical approach and a new benchmark for evaluation.

Findings

Successfully applied to synthetic physical challenges

Demonstrated utility in astrophysics for galaxy potential estimation

Established a new benchmark for Class SR algorithms

Abstract

We introduce 'Class Symbolic Regression' (Class SR) a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization ($\Phi$-SO) framework for Symbolic Regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.