Interpretable Analytic Formulae for GWTC-4 Binary Black Hole Population Properties via Symbolic Regression

Abstract

Recent LIGO-Virgo-KAGRA analyses have revealed complex structure in the binary black hole population, including distinct features in the primary mass spectrum and nontrivial spin-mass correlations. However, phenomenological models used to capture these features often lack analytic transparency, making it difficult to isolate robust physical laws from modeling artifacts. This paper applies symbolic regression to posterior predictive samples from the GWTC-4 catalog, producing ensembles of closed-form surrogate expressions for merger-rate evolution with redshift, spin-population trends, and conditional mass-ratio distributions associated with the 10 and 35 solar-mass primary-mass peaks. The resulting formulae enable exact analytic gradient diagnostics and compact surrogate summaries for flexible population posteriors.

The paper demonstrates how symbolic regression can compress flexible numerical population models into interpretable mathematical expressions. Those expressions can be differentiated exactly, compared across population features, and reused in forecasting, formation-channel studies and stochastic-background calculations.

Fig. 1: BBH comoving merger rate R(z) as a function of redshift. Shaded bands show the GWTC-4 90% credible intervals, while dashed lines show the corresponding PySR symbolic-regression median fits.

Dr. Chayan Chatterjee

AI for New Messengers Postdoctoral Fellow

Dr. Chayan Chatterjee is the A.I. for New Messengers Postdoctoral Fellow at Vanderbilt University. His research focuses on applying machine learning, frontier AI and interpretable inference to gravitational waves and multimessenger astronomy.