Abstract: The KM3NeT neutrino telescope is currently being deployed at two different sites in the Mediterranean Sea. First searches for astrophysical neutrinos have been performed using data taken with the partial detector configuration already in operation. The paper presents the results of two independent searches for neutrinos from compact binary mergers detected during the third observing run of the LIGO and Virgo gravitational wave interferometers. The first search looks for a global increase in the detector counting rates that could be associated with inverse beta decay events generated by MeV-scale electron anti -neutrinos. The second one focuses on upgoing track -like events mainly induced by muon (anti -)neutrinos in the GeV-TeV energy range. Both searches yield no significant excess for the sources in the gravitational wave catalogs. For each source, upper limits on the neutrino flux and on the total energy emitted in neutrinos in the respective energy ranges have been set. Stacking analyses of binary black hole mergers and neutron star -black hole mergers have also been performed to constrain the characteristic neutrino emission from these categories.

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.