Exploring Multi-view Symbolic Regression methods in physical sciences

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and careful observations. A modern alternative is to automate part of this process with symbolic regression (SR). The SR algorithms search for a function that adequately fits the observed data while trying to enforce sparsity, in the hopes of generating an interpretable equation. A particularly interesting extension to these algorithms is the Multi-view Symbolic Regression (MvSR). It searches for a parametric function capable of describing multiple datasets generated by the same phenomena, which helps to mitigate the common problems of overfitting and data scarcity. Recently, multiple implementations added support to MvSR with small differences between them. In this paper, we test and compare MvSR as supported in Operon, PySR, phy-SO, and eggp, in different real-world datasets. We show that they all often achieve good accuracy while proposing solutions with only few free parameters. However, we find that certain features enable a more frequent generation of better models. We conclude by providing guidelines for future MvSR developments.