The modeling of black hole accretion disk variability represents a foundational challenge in high-energy astrophysics, requiring the integration of General Relativistic Magnetohydrodynamics (GRMHD) with chaotic, multi-scale turbulence. While traditional numerical solvers have provided significant insights into the steady-state and dynamical properties of these systems, they increasingly encounter a computational wall in the era of high-cadence, big-data observatories such as the next-generation Event Horizon Telescope (ngEHT) and the Vera C. Rubin Observatory. Traditional grid-based simulations are computationally prohibitive for real-time predictive analytics, whereas standard "black-box" deep learning models often fail to adhere to the fundamental conservation laws of General Relativity. This paper provides a comprehensive review of the evolution of accretion theory—from the classical -disk models to modern GRMHD simulations—and identifies the principal limitations in current temporal variability modeling. We then present a rigorous synthesis of these domains through a PhysicsInformed Neural Network (PINN) framework called Deep-KerrNet. By embedding the Kerr metric in horizon-penetrating Kerr–Schild coordinates, enforcing the complete set of ideal GRMHD equations (baryon-number conservation, energy-momentum conservation with ideal-MHD stress-energy tensor, Maxwell's induction equation, and the solenoidal constraint) directly into the neural network's loss function, and incorporating shock-aware residual strategies, the proposed framework enables continuous-domain forecasting of accretion variability. Deep KerrNet is designed to bridge the "modelinglatency gap" between high-fidelity GRMHD simulations and the requirements of real-time, relativistic predictive analytics for next-generation observational pipelines.
Christine Julliane Laure Reyes (Wed,) studied this question.