Abstract: The Galactic Center Excess (GCE) in GeV gamma rays has been debated for over a decade, with the possibility that it might be due to dark matter annihilation or undetected point sources such as millisecond pulsars (MSPs). This study investigates how the gamma-ray emission model (-yEM) used in Galactic center analyses affects the interpretation of the GCE's nature. To address this issue, we construct an ultra-fast and powerful inference pipeline based on convolutional Deep Ensemble Networks. We explore the two main competing hypotheses for the GCE using a set of-yEMs with increasing parametric freedom. We calculate the fractional contribution (fsrc) of a dim population of MSPs to the total luminosity of the GCE and analyze its dependence on the complexity of the ryEM. For the simplest ryEM, we obtain fsrc = 0.10 f 0.07, while the most complex model yields fsrc = 0.79 f 0.24. In conclusion, we find that the statement about the nature of the GCE (dark matter or not) strongly depends on the assumed ryEM. The quoted results for fsrc do not account for the additional uncertainty arising from the fact that the observed gamma-ray sky is out-of-distribution concerning the investigated ryEM iterations. We quantify the reality gap between our ryEMs using deep-learning-based One-Class Deep Support Vector Data Description networks, revealing that all employed ryEMs have gaps to reality. Our study casts doubt on the validity of previous conclusions regarding the GCE and dark matter, and underscores the urgent need to account for the reality gap and consider previously overlooked “out of domain” uncertainties in future interpretations.

Abstract: We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that forces the model to partially ignore high-gradients in the physical variables, achieved by introducing a suitable weighting function. The method relies on a set of hyperparameters that control how gradients are treated in the physical loss. The performance of our methodology is demonstrated by solving Riemann problems in special relativistic hydrodynamics, extending earlier studies with PINNs in the context of the classical Euler equations. The solutions obtained with the GA-PINN model correctly describe the propagation speeds of discontinuities and sharply capture the associated jumps. We use the relative l(2) error to compare our results with the exact solution of special relativistic Riemann problems, used as the reference ''ground truth'', and with the corresponding error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by the GA-PINN model is comparable to that obtained with a shock-capturing scheme, achieving a performance superior to that of the baseline PINN algorithm in general. An additional benefit worth stressing is that our PINN-based approach sidesteps the costly recovery of the primitive variables from the state vector of conserved variables, a well-known drawback of grid-based solutions of the relativistic hydrodynamics equations. Due to its inherent generality and its ability to handle steep gradients, the GA-PINN methodology discussed in this paper could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions.