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.

Abstract: The XENON1T experiment uses a time projection chamber (TPC) with liquid xenon to search for weakly interacting massive particles (WIMPs), a proposed dark matter particle, via direct detection. As this experiment relies on capturing rare events, the focus is on achieving a high recall of WIMP events. Hence the ability to distinguish between WIMP and the background is extremely important. To accomplish this, we suggest using convolutional neural networks (CNNs); a machine learning procedure mainly used in image recognition tasks. To explore this technique we use XENON collaboration open-source software to simulate the TPC graphical output of dark matter signals and main backgrounds. A CNN turns out to be a suitable tool for this purpose, as it can identify features in the images that differentiate the two types of events without the need to manipulate or remove data in order to focus on a particular region of the detector. We find that the CNN can distinguish between the dominant background events (ER) and 500 GeV WIMP events with a recall of 93.4%, precision of 81.2% and an accuracy of 87.2%.