# Automated discovery of interpretable gravitational-wave population models

arXiv: https://arxiv.org/abs/2207.12409 · HTML: https://mlsanity.com/paper/2207.12409/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 25 Jul 2022.

## Builds on (most cited first, 3 of 3)

- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [AutoML-Zero: Evolving Machine Learning Algorithms From Scratch](https://mlsanity.com/paper/2003.03384/) (2020)

## Built on by (most cited first, 6 of 6)

- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Normalizing Flows for Hierarchical Bayesian Analysis: A Gravitational Wave Population Study](https://mlsanity.com/paper/2211.09008/) (2022)
- [Discovering equations from data: symbolic regression in dynamical systems](https://mlsanity.com/paper/2508.20257/) (2025)
- [Approximating neutron-star radii using gravitational-wave only measurements with symbolic regression](https://mlsanity.com/paper/2504.19962/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling](https://mlsanity.com/paper/2604.12806/) (2026)

## Abstract (arXiv)

We present an automatic approach to discover analytic population models for gravitational-wave (GW) events from data. As more gravitational-wave (GW) events are detected, flexible models such as Gaussian Mixture Models have become more important in fitting the distribution of GW properties due to their expressivity. However, flexible models come with many parameters that lack physical motivation, making interpreting the implication of these models challenging. In this work, we demonstrate symbolic regression can complement flexible models by distilling the posterior predictive distribution of such flexible models into interpretable analytic expressions. We recover common GW population models such as a power-law-plus-Gaussian, and find a new empirical population model which combines accuracy and simplicity. This demonstrates a strategy to automatically discover interpretable population models in the ever-growing GW catalog, which can potentially be applied to other astrophysical phenomena.