AGN X-ray Reflection Spectroscopy with ML MYTORUS:Neural Posterior Estimation with Training on Observation-Driven Parameter Grids

Abstract

X-ray spectroscopy of active galactic nuclei (AGN) reveals key information about circumnuclear geometry. Many AGN show a narrow Fe K-alpha line at 6.4 keV and associated Compton-scattered continua, produced by primary continuum scattering in cold, neutral material far from the central supermassive black hole. We present a novel approach based on Simulation-Based Inference with Neural Posterior Estimation (SBI-NPE) to train a machine-learning (ML) model using NuSTAR spectral fitting results from the literature, adopting the physically motivated MYTORUS-decoupled model, which separates line-of-sight and global equivalent hydrogen column densities (NH_Z and NH_S). To overcome limitations of traditional frequentist fitting such as local minima, limited automation, reproducibility, and computational cost, we employ normalizing flows and autoregressive networks to learn flexible posterior distributions from simulated spectra. From 34 NuSTAR spectral fits, we generate 34,000 synthetic spectra using uniform and Gaussian parameter distributions, showing that the latter is more strongly observationally driven. The network is trained to infer four MYTORUS parameters: NH_Z, NH_S, the photon index Gamma, and the relative normalization AS. Mutual information analysis identifies optimal spectral regions and motivates the inclusion of redshift, exposure time, and Galactic absorption. The observation-based grid significantly outperforms uniform sampling, achieving predictive accuracies above 90 percent for NH_S and AS, 89 percent for NH_Z, and 82 percent for Gamma within one sigma, with a joint accuracy of 70 percent for all parameters. We publicly release ML MYTORUS with a web interface enabling fast, reproducible inference from NuSTAR spectra. An application to NGC 4388 illustrates the promise of this approach.