X-ray spectral fitting with Monte Carlo dropout neural networks

¹ Istituto Nazionale di Astrofisica INAF IASF Palermo, Via Ugo La Malfa 153, Palermo 90146, Italy
² ICSC – Centro Nazionale di Ricerca in HPC, Big Data e Quantum Computing, Italy
³ Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-Sestu, KM 0.7, Monserrato, 09042 Italy
⁴ Dipartimento di Fisica e Chimica – Emilio Segrè, Università di Palermo, via Archirafi 36, 90123 Palermo, Italy
⁵ INAF – Osservatorio Astronomico di Roma, Via Frascati 33, 00076 Monte Porzio Catone (RM), Italy
⁶ Istituto Nazionale di Fisica Nucleare Sezione di Catania, Via Santa Sofia 64, 95123 Catania, Italy

^★ Corresponding author; antonio.tutone@inaf.it

Received: 7 January 2025
Accepted: 10 March 2025

Abstract

Context. The analysis of X-ray spectra often encounters challenges due to the tendency of frequentist approaches to be trapped in local minima, affecting the accuracy of spectral parameter estimation. Bayesian methods offer a solution to this issue, though computational time significantly increases, limiting their scalability. In this context, neural networks have emerged as a powerful tool for efficiently addressing these challenges, providing a balance between accuracy and computational efficiency.

Aims. This work aims to explore the potential of neural networks to recover model parameters and quantify their uncertainties. We benchmark their accuracy and computational time performance against traditional X-ray spectral fitting methods based on frequentist and Bayesian approaches. This study serves as a proof of concept for data analysis of future astronomical missions, producing extensive datasets that could benefit from the proposed methodology.

Methods. We applied Monte Carlo dropout to a range of neural network architectures to analyze X-ray spectra. Our networks are trained on simulated spectra derived from a multiparameter source emission model convolved with an instrument response. This allows them to learn the relationship between the spectra and their corresponding parameters while generating posterior distributions. The model parameters are drawn from a predefined prior distribution. To illustrate the method, we used data simulated with the response matrix of the X-ray instrument NICER. We focus on simple X-ray emission models with up to five spectral parameters for this proof of concept.

Results. Our approach delivers well-defined posterior distributions, comparable to those produced by Bayesian inference analysis, while achieving an accuracy similar to traditional spectral fitting. It is significantly less prone to falling into local minima, thus reducing the risk of selecting parameter outliers. Moreover, this method substantially improves computational speed compared to other Bayesian approaches, with computational time reduced by roughly an order of magnitude.

Conclusions. Our method offers a robust alternative to the traditional spectral fitting procedures. Despite some remaining challenges, this approach can potentially be a valuable tool in X-ray spectral analysis, providing fast, reliable, and interpretable results with reduced risk of convergence to local minima, effectively scaling with data volume.