Deep learning approaches to recover plasma current density profile from safety factor based on Grad-Shafranov solutions across multiple tokamaks

Abstract

Many magnetohydrodynamic stability analysis requires generation of a set of equilibria with fixed safety factor q-profile while varying other plasma parameters. A neural network (NN)-based approach is investigated that facilitates such a process. Both the multi-layer perceptron (MLP) based NN and the convolutional neural network (CNN) models are trained to map the q-profile to the plasma current density J-profile and vice versa, while satisfying the Grad-Shafranov radial force balance constraint. When the initial target models are trained, using a database of semi-analytically constructed numerical equilibria, the initial CNN with one convolutional layer is found to perform better than the initial MLP model. In particular, the trained initial CNN model can also predict the q- or J-profile for experimental tokamak equilibria. The performance of both initial target models is further improved by fine-tuning the training database, i.e., by adding realistic experimental equilibria with Gaussian noise. The fine-tuned target models, referred to as fine-tuned MLP and fine-tuned CNN, well reproduce the target q- or J-profile across multiple tokamak devices. As an important application, these NN-based equilibrium profile convertors can be utilized to provide good initial guess for iterative equilibrium solvers, where the desired input quantity is the safety factor instead of the plasma current density.