Researchers from Seoul National University and the Korea Institute of Fusion Energy (KFE) have developed a deep neural network, GS-DeepNet, capable of solving the Grad–Shafranov equation for tokamak plasma equilibria in milliseconds. This physics-informed neural network (PINN) achieves a computational speedup of 100,000 to one million times compared to established iterative solvers like EFIT. The model was trained on a dataset of over 10,000 equilibrium states generated from the KSTAR tokamak, demonstrating a relative L2 error of just 0.0019 in predicting the poloidal magnetic flux distribution. This advance, detailed in a peer-reviewed paper in *Scientific Reports*, directly addresses the computational bottleneck that has limited real-time plasma control and analysis. Source: Nature

The Grad–Shafranov (GS) equation is a fundamental component of magnetohydrodynamics, describing the static equilibrium of a plasma confined within an axisymmetric magnetic field, such as in a tokamak. Solving this nonlinear, second-order partial differential equation is essential for determining the plasma's shape, position, and internal magnetic structure. Conventional numerical methods are computationally intensive, requiring iterative calculations that can take from minutes to hours. This latency makes them unsuitable for dynamic control tasks, such as responding to plasma instabilities or predicting disruptions, which evolve on much faster timescales. The GS-DeepNet model bypasses this iterative process by learning the direct mapping from plasma parameters to the equilibrium state. Source: Nature

Solving this nonlinear, second-order partial differential equation is essential for determining the plasma's shape, position, and internal magnetic structure.

GS-DeepNet's architecture is a PINN, which embeds the governing physical equations—in this case, the GS equation—directly into the neural network's loss function during training. This approach ensures that the model's predictions are not merely statistical correlations but are also physically consistent solutions. The network was trained using data from the KSTAR tokamak, a superconducting device known for its long-pulse, high-performance plasma operations. By learning from a wide range of KSTAR's operational scenarios, the model has demonstrated its ability to generalize and accurately reconstruct equilibria for previously unseen plasma conditions, a critical requirement for its deployment in active feedback control systems. Source: Nature

The primary impact of this computational advance lies in its potential to enable real-time, model-based plasma control. With equilibrium solutions available in milliseconds, control systems can make rapid adjustments to magnetic fields to optimize plasma performance and prevent disruptions before they terminate a discharge. This capability is particularly vital for next-generation devices like ITER, where avoiding disruptions is a high-priority operational and safety requirement. Beyond control, the rapid solver can accelerate integrated modeling workflows, which couple multiple physics simulations, and expedite the post-shot analysis of experimental data, improving the efficiency of research campaigns. Source: Nature

Future work will likely focus on validating GS-DeepNet's performance in a live experimental setting on KSTAR or other tokamaks. Integrating the model into a real-time plasma control system will be the definitive test of its robustness and accuracy under dynamic conditions. Researchers will also need to assess its applicability to a wider range of plasma shapes and operational regimes, including those with strong shaping, high beta, or internal transport barriers. The successful deployment of such AI-driven tools represents a significant step toward the sophisticated, autonomous control systems required for a commercially viable fusion power plant. Source: Nature