Speaker
Description
The gravitational collapse of magnetized astrophysical fluids underlies a wide range of phenomena, from protostellar formation to large-scale structure evolution. These systems are governed by magnetohydrodynamic (MHD) equations, a nonlinear and tightly coupled set of partial differential equations that pose significant challenges for traditional numerical solvers. High-resolution finite-volume methods accurately capture shocks and discontinuities but scale poorly as spatial and temporal resolution increases, especially in multi-dimensional simulations.
This work investigates Physics-Informed Neural Networks (PINNs) as a complementary framework for solving well-established MHD benchmark problems without conventional time-marching schemes. Three representative cases are considered. In one dimension, PINNs are applied to the Brio–Wu shock tube and the slowly moving shock variant to test recovery of discontinuous solutions governed by the ideal MHD equations. In two dimensions, the method is extended to gravitationally stratified MHD systems exhibiting magnetic buoyancy, including the Parker instability. As a third component, PINNs are explored as solvers for the elliptic Poisson equation governing the gravitational potential of a thin disk, using established polar-coordinate and convolution-based formulations as reference solutions.
In each case, the governing equations are embedded directly into the network loss function, and the physical variables are represented by continuous neural approximations. The results are compared with numerical solutions and purely data-driven models to evaluate accuracy and stability in shock-dominated flows, instability evolution, and elliptic gravitational field calculations. These comparisons provide a quantitative assessment of PINN performance on classical MHD benchmark problems relative to conventional numerical approaches, highlighting both their capabilities and current limitations.
| Keyword-1 | Magnetohydrodynamics |
|---|---|
| Keyword-2 | Neural Networks |
| Keyword-3 | Computational Astrophysics |