Disk mass predictions for binary neutron star mergers: limitations of proposed symbolic regression models

TL;DR

This paper critically evaluates the effectiveness of symbolic regression models for predicting disk mass in binary neutron star mergers, highlighting their limitations and advocating for physics-informed formulas in data analysis.

Contribution

The paper demonstrates that symbolic regression models do not significantly outperform existing physics-based models and can produce unphysical results, emphasizing the need for physics input in fitting formulae.

Findings

Symbolic regression models do not outperform existing models when optimized with the same error measure.

Many symbolic regression formulae yield unphysical results across relevant parameter ranges.

Physics-based fitting formulae remain safer and more reliable for data analysis.

Abstract

Modeling disk formation and mass ejection in binary neutron star systems is an important component in the construction of models for the electromagnetic signals powered by these events. Most models rely on analytical formulae for the disk mass and dynamical ejecta that are fitted to the results of numerical simulations, yet these fits have large uncertainties that significantly limit our ability to extract information from merger observations. In a recent manuscript, Darc et al claim that disk mass formulae constructed using symbolic regression outperform existing formulae and robustly extend to regions of the parameter space outside of the fitting region. I show here that the improvement over the most directly comparable existing model comes mostly from the use of different error measures in optimizing the fitting parameters. For the limited training data used so far, that existing fitting formula has a performance similar to symbolic regression models when optimized over the same error measure. More importantly, I show that many of the formulae obtained through symbolic regression provide unphysical results when used over the whole range of parameters relevant to the modeling of binary neutron star mergers, making them dangerous to use within parameter estimation pipelines. I conclude that fitting formulae with more physics input (e.g. Lund et al 2025), albeit certainly imperfect, remain safer to use in data analysis than these symbolic regression results. Symbolic regression results used in conjunction with careful physics-based vetting may however outperform them in the future.