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

Abstract

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters. A neural network (NN)-based approach is investigated that facilitates such a process. Both multilayer perceptron (MLP)-based NN and 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, an initial CNN with one convolutional layer is found to perform better than an initial MLP model. In particular, a 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 a good initial guess for iterative equilibrium solvers, where the desired input quantity is the safety factor instead of the plasma current density.