Deep neural network Grad-Shafranov solver constrained with measured magnetic signals

A neural network solving the Grad-Shafranov equation constrained with measured magnetic signals to reconstruct magnetic equilibria in real time is developed. The database created to optimize the neural network's free parameters contains off-line EFIT results as the output of the network from 1118 KSTAR experimental discharges of two different campaigns. Input data to the network constitute magnetic signals measured by a Rogowski coil (plasma current), magnetic pick-up coils (normal and tangential components of magnetic fields) and flux loops (poloidal magnetic fluxes). The developed neural networks fully reconstruct not only the poloidal flux function phi (R, Z) but also the toroidal current density function j(phi) (R, Z) with the off-line EFIT quality. To preserve the robustness of the networks against missing input data, an imputation scheme is utilized to eliminate the required additional training sets with a large number of possible combinations of the missing inputs.