Simulation-based inference with neural posterior estimation applied to X-ray spectral fitting

II. High-resolution spectroscopy with Athena X-IFU

Institut de Recherche en Astrophysique et Planétologie, 9 avenue du Colonel Roche, Toulouse 31028, France

^★ Corresponding author: sdupourque@irap.omp.eu

Received: 18 April 2025
Accepted: 5 June 2025

Abstract

Context. X-ray spectral fitting in high-energy astrophysics can be reliably accelerated using machine learning. Simulation-based inference (SBI) produces accurate posterior distributions in the Gaussian and Poisson regimes for low-resolution spectra much more efficiently than other exact approaches, such as Monte Carlo Markov chains or nested sampling (NS).

Aims. We aim to highlight the capabilities of SBI for high-resolution spectra, anticipating the data provided by the newAthena X-ray Integral Field Unit (X-IFU) instrument. The large number of channels encourages us to use compressed representations of the spectra and take advantage of the likelihood-free inference aspect of SBI.

Methods. We explored two compression schemes, using either simple summary statistics, such as the counts in arbitrary bins or ratios between these bins, or automatically learning compressed representation using dense neural networks. We benchmarked the efficiency of these approaches using simulated X-IFU spectra with various spectral models, including smooth Comptonised spectra, relativistic reflexion models, and plasma emission models.

Results. We find that using simple and meaningful summary statistics is much more efficient than working directly with the full spectrum or automatically-learned summary statistics. This approach can allow us to derive posterior distributions comparable to the results of exact computations with NS. In particular, multi-round inference converges quickly to the appropriate solution. Amortised single-round inference requires more simulations and, thus, a longer training time, but it can be used to infer model parameters from many observations afterwards. We show an application where it can be used to explore the sensitivity of an observation to a model, for which the parameters spreads around the targeted model. Information from the emission lines must be accounted for using dedicated summary statistics.

Conclusions. The SBI approach for X-ray spectral fitting is a robust technique that delivers well-calibrated posteriors. Although it is still in its early days of development, the method shows great promise for high-resolution spectra and the potential to assist in the scientific exploitation of X-IFU. We plan to apply the method to the current era of high-resolution telescopes and further challenge this approach on the basis of real data.