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

Francois Foucart

TL;DR

The paper challenges the claim that symbolic regression (SR) automatically yields superior and more robust disk-mass fits for binary neutron star mergers. It shows that the apparent SR advantage in Darc et al. largely arises from using a different error metric than the one underlying traditional fits, and that when evaluated with a common metric, SR performance is comparable to existing, physics-inspired fits. The analysis reveals that many SR formulas extrapolate unphysically outside the training region, especially at high lower-star compactness $C_1$, making them risky for parameter estimation pipelines. It argues that physics-informed fits, such as Lund 2025, remain safer with current data, though SR could become useful with more data and careful physics-based vetting for higher-dimensional models. The study uses training data from Kruger 2020 and testing data from Nedora 2020, emphasizes the role of parameter space coverage and error modeling, and ultimately advocates a cautious, multi-model approach to quantify modeling uncertainty in EM counterparts of mergers.

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.

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

TL;DR

The paper challenges the claim that symbolic regression (SR) automatically yields superior and more robust disk-mass fits for binary neutron star mergers. It shows that the apparent SR advantage in Darc et al. largely arises from using a different error metric than the one underlying traditional fits, and that when evaluated with a common metric, SR performance is comparable to existing, physics-inspired fits. The analysis reveals that many SR formulas extrapolate unphysically outside the training region, especially at high lower-star compactness , making them risky for parameter estimation pipelines. It argues that physics-informed fits, such as Lund 2025, remain safer with current data, though SR could become useful with more data and careful physics-based vetting for higher-dimensional models. The study uses training data from Kruger 2020 and testing data from Nedora 2020, emphasizes the role of parameter space coverage and error modeling, and ultimately advocates a cautious, multi-model approach to quantify modeling uncertainty in EM counterparts of mergers.

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.

Paper Structure

This paper contains 6 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Numerical data and Simulated Parameter Space
  3. Models depending on the lower star's compactness
  4. Model robustness
  5. AI-driven symbolic regression
  6. Conclusions

Figures (2)

  • Figure 1: Behavior of three one-parameter models for $M_{\rm disk}$. We show the best symbolic regression model from Darc:2025set (D25), and the two models derived here by minimizing the MSE (K20 MSE) and by using the errors from Eq. \ref{['eq:err']} (K20 Var $\sigma$), based on our previous model Kruger:2020gig. We use black circles for the training data, and gray circle for the testing data. Vertical dashed lines show the range of compactness in the training set.
  • Figure 2: Same as Fig.1, but now for all models from Darc:2025set (D25) that only depend on $C_1$, as well as the model derived here by minimizing the MSE (K20 MSE) and the existing model from 2025ApJ...987...56L.