Bayesian neural regression and classification on GRRT images: uncertainties and limitations

ABSTRACT We investigate a Bayes-by-Backprop multitask neural network applied to general relativistic ray-traced (GRRT) black hole shadow images, with the aim of estimating black hole and accretion flow parameters. The network simultaneously classifies accretion regimes – magnetically arrested discs and standard and normal evolution – and discrete black hole spin states while predicting continuous parameters such as black hole mass, inclination, position angle, total flux, ion–electron temperature ratio, and mass accretion rate. The model employs probabilistic layers to capture both aleatoric and epistemic uncertainties. We train the network on a library of GRRT images from general relativistic magnetohydrodynamic (GRMHD) simulations and evaluate performance as a function of training-set size and across independent data sets with varying time spans and resolutions. The classifier achieves robust accretion-state identification ($\ge 97 {{\ \rm per\ cent}}$ accuracy). Spin classification is more challenging: extreme prograde and retrograde states are recovered with accuracies of $\sim 90 {{\ \rm per\ cent}}$, while intermediate spins reach $\sim 80 {{\ \rm per\ cent}}$, with most misclassifications occurring between neighbouring classes. By training directly on pure GRRT images that exclude observational systematics, we can isolate how the Gaussian likelihood interacts with intrinsically non-Gaussian, multimodal, or discretized target distributions. An analysis of probability integral transform distributions and Kolmogorov–Smirnov statistics indicates systematic miscalibration in the regression outputs. The Gaussian likelihood tends to underestimate the true dispersion, basically for parameters with sparse or discrete label distributions. Although absolute calibration is imperfect, relative uncertainty structure remains informative and allows the network to identify ambiguous, low-informative, or noisy images.