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

A neural network solving Grad-Shafranov equation constrained with measured magnetic signals to reconstruct magnetic equilibria in real time is developed. Database created to optimize the neural network's free parameters contain off-line EFIT results as the output of the network from $1,118$ 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 $\psi\left( R, Z\right)$ but also the toroidal current density function $j_\phi\left( R, Z\right)$ with the off-line EFIT quality. To preserve robustness of the networks against a few missing input data, an imputation scheme is utilized to eliminate the required additional training sets with large number of possible combinations of the missing inputs.