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

Fri, 07 Aug 2026 00:00:00 +0000

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.

Interpretable Binary Black Hole Population Inference

Fri, 07 Aug 2026 00:00:00 +0000

This project develops interpretable analytic summaries of binary black hole population properties inferred from the GWTC-4 catalog. Instead of treating flexible population models as opaque numerical objects, symbolic regression is used to learn closed-form surrogate expressions for merger-rate evolution, spin-population trends and mass-ratio structure near the primary-mass peaks.

The resulting formulae make it possible to inspect gradients exactly, compare features across model families and pass compact population summaries into downstream calculations such as rate forecasting, formation-channel comparisons and stochastic-background estimates.


Fig. 1: Symbolic-regression surrogates reproduce GWTC-4 binary black hole merger-rate trends while preserving posterior uncertainty across model families.

Population Inference | Chayan Chatterjee

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

Interpretable Binary Black Hole Population Inference