Enhancing Machine Learning of the Grad-Shafranov Equation with EFIT's Green's Function Tables

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using Principal Component Analysis of plasma toroidal current densities (J_t) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for poloidal flux (ψ) and diagnostics generated from the toroidal current. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. Results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J_t with median R² = 0.9995 and R² = 0.973, respectively. A simple neural network (NN) is also employed to predict the coefficients of the basis functions. The NN demonstrates better performance compared to the least squares method with median R² = 0.9997 and 0.988 for J_t and ψ respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.