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

arXiv: https://arxiv.org/abs/1911.02882 · HTML: https://mlsanity.com/paper/1911.02882/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2019.

## Built on by (most cited first, 7 of 7)

- [Neural net modeling of equilibria in NSTX-U](https://mlsanity.com/paper/2202.13915/) (2022)
- [Grad-Shafranov equilibria via data-free physics informed neural networks](https://mlsanity.com/paper/2311.13491/) (2023)
- [A machine-learning-based tool for last closed-flux surface reconstruction on tokamaks](https://mlsanity.com/paper/2207.05695/) (2022)
- [Improving ideal MHD equilibrium accuracy with physics-informed neural networks](https://mlsanity.com/paper/2507.03119/) (2025)
- [Machine-Learning enabled analysis of ELM filament dynamics in KSTAR](https://mlsanity.com/paper/2201.07941/) (2022)
- [Evaluation and Verification of Physics-Informed Neural Models of the Grad-Shafranov Equation](https://mlsanity.com/paper/2504.21155/) (2025)
- [Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator](https://mlsanity.com/paper/2606.15512/) (2026)

## Abstract (arXiv)

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 psileft( R, Zright) but also the toroidal current density function jφleft( R, Zright) 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.