Neural network tokamak equilibria with incompressible flows

We present several numerical solutions to a generalized Grad-Shafranov equation (GGSE), which governs axisymmetric plasma equilibria with incompressible flows of arbitrary direction, using fully connected, feed-forward, deep neural networks, also known as multi-layer perceptrons. Such artificial network (ANNs) are trained approximate tokamak-relevant upon minimizing the GGSE mean squared residual in volume and poloidal flux function on boundary. Solutions for Solovev general linearizing ansatz free functions involved obtained benchmarked against analytic solutions. construct non-linear equilibrium incorporating characteristics relevant high confinement mode. In our experiments it was observed that changing radial distribution training points has surprisingly small effect accuracy solution. particular is shown localizing at edge results ANN describe quite accurately entire magnetic configuration, thus demonstrating interpolation capabilities ANNs.