Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole

2025/06/01 by Shuyang Xiang, Xiang, Shuyang
Computer Science · Physics and Astronomy · #Astrophysical Phenomena and Observations #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Numerical Analysis (math.NA) #Pulsars and Gravitational Waves Research #Seismology and Earthquake Studies

paper · pdf · doi:10.48550/arxiv.2506.00951

openalex publication_date 2025/06/01 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We introduce a Physics-Informed Neural Networks(PINN) to solve a relativistic Burgers equation in the exterior domain of a Schwarzschild black hole. Our main contribution is a PINN architecture that is able to simulate shock wave formations in such curved spacetime, by training a shock-aware network block and introducing a Godunov-inspired residuals in the loss function. We validate our method with numerical experiments with different kinds of initial conditions. We show its ability to reproduce both smooth and discontinuous solutions in the context of general relativity.

Citations

• Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. A numerical study
• Finite volume schemes on Lorentzian manifolds

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