Set-based Implicit Likelihood Inference of Galaxy Cluster Mass

TL;DR

This paper introduces a set-based machine learning method combining Deep Sets and normalizing flows to accurately infer galaxy cluster masses from galaxy dynamics, reducing scatter and improving uncertainty calibration.

Contribution

It develops a novel set-based inference framework that enhances galaxy cluster mass estimation by integrating positional and velocity data with improved interpretability.

Findings

Significantly reduces scatter in mass estimates.

Provides well-calibrated uncertainties across mass range.

Outperforms traditional dynamical methods.

Abstract

We present a set-based machine learning framework that infers posterior distributions of galaxy cluster masses from projected galaxy dynamics. Our model combines Deep Sets and conditional normalizing flows to incorporate both positional and velocity information of member galaxies to predict residual corrections to the $M$-$\sigma$ relation for improved interpretability. Trained on the Uchuu-UniverseMachine simulation, our approach significantly reduces scatter and provides well-calibrated uncertainties across the full mass range compared to traditional dynamical estimates.