Neural-Network solver of ideal MHD equilibria

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria byparametrizing Fourier modes with artificial neuralnetworks and compare it to equilibria computedby conventional solvers. The full nonlinear globalforce residual across the volume in real space is thenminimized with first order optimizers. Already, weobserve competitive computational cost to arriveat the same minimum residuals computed by exist-ing codes. With increased computational cost, lowerminima of the residual are achieved by the neuralnetworks, establishing a new lower bound for theforce residual. We use minimally complex neuralnetworks, and we expect significant improvementsfor solving not only single equilibria with neuralnetworks, but also for computing neural networkmodels valid over continuous distributions of equi-libria.