Neural-Network solver of ideal MHD equilibria
This addresses the challenge of solving ideal MHD equilibria for plasma physics, offering an incremental improvement over conventional solvers.
The paper tackles the problem of computing three-dimensional Magnetohydrodynamic equilibria by using artificial neural networks to parametrize Fourier modes and minimizing the force residual with optimizers, achieving competitive computational cost and establishing a new lower bound for the residual with increased cost.
We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.