Meshfree black hole toy evolution and excision using artificial neural networks

Abstract

We present the use of physics-informed neural networks (PINNs) for handling singularities in the context black hole singularity evolution by offering meshfree alternatives for solving partial differential equations (PDEs). This was done by implementing a spatiotemporal excision surface across the entire spacetime domain rather than iteratively excising grid points. We demonstrate a toy model of black hole evolution using a simplified form of extended conformal thin sandwich (XCTS) initial data fed into a 1D wave equation as an evolution proxy. While PINNs can learn the asymptotic behavior outside the excised surface, it failed to learn the behavior near it. Although such an implementation has a large room for improvement especially when considering the complexity of NR applications, PINN-based numerical solver piggy-backs on the advancement of neural network architectures which may lay the possibility for feasible hybrid numerical solvers.