Physics-Informed Neural-Network Surrogate Model for the Inverse Equilibrium Solution in the EAST Tokamak.

A free-boundary equilibrium (FBE) solver has been recently developed by using finite-difference and Picard-iteration methods to solve both the direct (plasma condition + poloidal-field (PF) coil currents -> 2D poloidal-flux map) and the inverse (plasma condition + desired plasma shape -> needed PF coil currents + 2D poloidal-flux map) equilibrium problems in tokamaks. With the ultimate goal of accelerating calculations, which is critical when using the FBE solver for scenario optimization, a physics-informed neural network (PINN) surrogate model has been developed in this work for the inverse-mode FBE solver. The NN employs a fully-connected multi-layer perceptron (MLP) architecture. The physical constraint encoded into the loss function is the Grad-Shafranov equation, ensuring a correct relationship between the plasma condition, PF coil currents and 2D poloidal-flux map. The dataset, which is used for training and as ground truth for performance analysis, has been generated by selecting various combinations of parameters for the plasma condition (plasma current, poloidal beta) and its shape (minor and major radii, triangularity, elongation). The trained NN can reproduce the inverse-mode FBE output with high accuracy while also significantly reducing computational time.