2023/09/14 by Zhi-Han Li, Li, Zhi-Han, Chen-Qi Li +3 · 1 citation
Computer Science · Physics and Astronomy · #Astrophysical Phenomena and Observations #Computational Physics (physics.comp-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Nuclear Theory (nucl-th) #Pulsars and Gravitational Waves Research #Seismology and Earthquake Studies
paper · pdf · doi:10.48550/arxiv.2309.07397
openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Einstein field equations are notoriously challenging to solve due to their complex mathematical form, with few analytical solutions available in the absence of highly symmetric systems or ideal matter distribution. However, accurate solutions are crucial, particularly in systems with strong gravitational field such as black holes or neutron stars. In this work, we use neural networks and auto differentiation to solve the Einstein field equations numerically inspired by the idea of physics-informed neural networks (PINNs). By utilizing these techniques, we successfully obtain the Schwarzschild metric and the charged Schwarzschild metric given the energy-momentum tensor of matter. This innovative method could open up a different way for solving space-time coupled Einstein field equations and become an integral part of numerical relativity.