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

TL;DR

This paper presents a neural network-based solver for the Grad-Shafranov equation that reconstructs magnetic equilibria in real time using measured magnetic signals, matching EFIT quality.

Contribution

It introduces a neural network constrained by measured signals to accurately reconstruct magnetic equilibria, with an innovative imputation scheme for missing data.

Findings

Reconstructs poloidal flux and current density with EFIT accuracy

Uses measured magnetic signals from KSTAR discharges

Robust against missing input data through imputation

Abstract

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.