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Neural networks are being extensively used for modelling data, especially inthe case where no likelihood can be formulated. Although in the case of X-rayspectral fitting, the likelihood is known, we aim to investigate the neuralnetworks ability to recover the model parameters but also their associateduncertainties, and compare its performance with standard X-ray spectralfitting, whether following a frequentist or Bayesian approach. We applySimulation-Based Inference with Neural Posterior Estimation (SBI-NPE) to X-rayspectra. We train a network with simulated spectra, and then it learns themapping between the simulated spectra and their parameters and returns theposterior distribution. The model parameters are sampled from a predefinedprior distribution. To maximize the efficiency of the training of the neuralnetwork, yet limiting the size of the training sample to speed up theinference, we introduce a way to reduce the range of the priors, either througha classifier or a coarse and quick inference of one or multiple observations.SBI-NPE is demonstrated to work equally well as standard X-ray spectralfitting, both in the Gaussian and Poisson regimes, both on simulated and realdata, yielding fully consistent results in terms of best fit parameters andposterior distributions. The inference time is comparable to or smaller thanthe one needed for Bayesian inference. On the other hand, once properlytrained, an amortized SBI-NPE network generates the posterior distributions inno time. We show that SBI-NPE is less sensitive to local minima trapping thanstandard fit statistic minimization techniques. We find that the neural networkcan be trained equally well on dimension-reduced spectra, via a PrincipalComponent Decomposition, leading to a shorter inference time. Neural posteriorestimation thus adds up as a complementary tool for X-ray spectral fitting.(abridged).

Simulation-Based Inference with Neural Posterior Estimation applied to  X-ray spectral fitting: Demonstration of working principles down to the  Poisson regime