Simulation-Based Inference for Direction Reconstruction of Ultra-High-Energy Cosmic Rays with Radio Arrays

TL;DR

This paper presents a simulation-based inference method using graph neural networks and normalizing flows to accurately reconstruct the directions of ultra-high-energy cosmic rays from radio array data, providing well-calibrated uncertainties and rapid analysis.

Contribution

It introduces a novel inference pipeline combining physics-informed GNNs and normalizing flows for unbiased, calibrated direction reconstruction of cosmic rays from radio signals.

Findings

Achieved sub-degree median angular resolution.

68% highest-posterior-density contours capture 71% of true directions.

Method is fast, interpretable, and well-calibrated for upcoming experiments.

Abstract

Ultra-high-energy cosmic-ray (UHECR) observatories require unbiased direction reconstruction to enable multi-messenger astronomy with sparse, nanosecond-scale radio pulses. Explicit likelihood methods often rely on simplified models, which may bias results and understate uncertainties. We introduce a simulation-based inference pipeline that couples a physics-informed graph neural network (GNN) to a normalizing-flow posterior within the Learning the Universe Implicit Likelihood Inference framework. Each event is seeded by an analytic plane-wavefront fit; the GNN refines this estimate by learning spatiotemporal correlations among antenna signals, and its frozen embedding conditions an eight-block autoregressive flow that returns the full Bayesian posterior. Trained on about $8,000$ realistic UHECR air-shower simulations generated with the ZHAireS code, the posteriors are temperature-calibrated to meet empirical coverage targets. We demonstrate a sub-degree median angular resolution on test UHECR events, and find that the nominal 68% highest-posterior-density contours capture $71\% \pm 2\%$ of true arrival directions, indicating a mildly conservative uncertainty calibration. This approach provides physically interpretable reconstructions, well-calibrated uncertainties, and rapid inference, making it ideally suited for upcoming experiments targeting highly inclined events, such as GRAND, AugerPrime Radio, and BEACON.