Neural Posterior Estimation for UHECR source inference from 3D propagation simulations

TL;DR

This paper introduces a simulation-based inference framework using deep learning to accurately estimate the properties of ultra-high energy cosmic ray sources from 3D propagation simulations.

Contribution

It presents a novel scalable Bayesian inference method combining Deep Set encoders and normalizing flows trained on extensive simulations for UHECR source characterization.

Findings

All source parameters are recovered without systematic bias.

Directional parameters are best constrained, source distance is most uncertain.

Primary composition classification achieves over 98.2% accuracy.

Abstract

The identification of ultra-high energy cosmic ray sources is one of the open challenges of high-energy astrophysics. As charged particles travel through the Universe, they are deflected by extragalactic magnetic fields and lose energy through interactions with background radiation, making source inference highly non-trivial. Existing approaches either rely on simplified propagation models or on computationally prohibitive Monte Carlo methods. Here we present a simulation-based inference framework trained on three-dimensional \texttt{CRPropa~3} propagation simulations that produces calibrated posterior distributions over source energy, distance, direction, and primary composition for individual UHECR events. The model combines a Deep Set encoder, handling the variable number of detected secondary particles, with a normalizing flow, and is trained on approximately 5 million simulated events covering a broad range of extragalactic magnetic field configurations. Validated on held-out simulations, all source parameters are recovered without systematic bias, with directional parameters best constrained and source distance most uncertain, consistent with the underlying propagation physics. Primary composition classification achieves $\geq$~98.2\% accuracy across all mass groups. This framework provides a scalable and physically interpretable interface between detailed propagation simulations and Bayesian source inference relevant for current UHECR data.