Symbolic regression aims to find optimal functional representation of datasets, with broad applications across science. This is traditionally done using a “genetic algorithm” which stochastically searches function space using an evolution-inspired method for generating new trial functions. Motivated by the uncertainties inherent in this approach — and its failure on seemingly simple test cases — I will describe a new method which exhaustively searches and evaluates function space. Coupled to a model selection principle based on minimum description length, Exhaustive Symbolic Regression is guaranteed to find the simple equations that optimally balance simplicity with accuracy on any dataset. I will describe how the method works and showcase it on Hubble rate measurements and dynamical galaxy data.

Based on work with Deaglan Bartlett and Pedro G. Ferreira:
https://arxiv.org/abs/2211.11461
https://arxiv.org/abs/2301.04368