Can Neural Networks Replace Grad-Shafranov Solvers for Real-Time Tokamak Control?

A tokamak holds plasma hotter than the Sun's core inside a magnetic bottle. Keeping that bottle stable requires knowing the plasma equilibrium in real time.

Conventional Grad-Shafranov solvers calculate the equilibrium by iterating a nonlinear elliptic equation on a 2D grid. The computation takes milliseconds to seconds — too long for feedback control during a discharge. Researchers have therefore turned to AI surrogates that approximate the solver's output after a single forward pass.

The Problem: Speed Versus Precision

The preprint submitted on 24 August 2026 benchmarks five architectures under a unified protocol. The contenders include a multilayer perceptron and a convolutional neural network. A Fourier neural operator joins them. A transformer and a Kolmogorov-Arnold network complete the set. All models train on the same numerical database: 100,000 in-distribution samples and 10,000 out-of-distribution samples generated by a Grad-Shafranov code.

Accuracy is measured relative to the Grad-Shafranov solutions themselves. The surrogates achieve errors of $10^-3$-$10^-2$ relative to those solutions. The Grad-Shafranov-to-device discrepancy on EXL-50U remains at $10^-3$. This means the AI error can be comparable to or larger than the physics-model error.

Five Architectures, One Protocol

Transformer gives the best in-distribution accuracy. CNN offers the best balance of accuracy and robustness while reaching 0.7 ms TensorRT latency. CNN and FNO show the strongest extrapolation stability on unseen plasma geometries and parameter regimes with 4%-5% relative $L_2$ error. Models with weaker inductive biases degrade more substantially.

Scaling data and model capacity improves interpolation but not necessarily extrapolation. The paper reports a trade-off between capacity and out-of-distribution generalization. Larger models fit the training distribution better yet can become more brittle when geometry or parameters shift beyond the training envelope.

What the Numbers Show

Device-level validation on EXL-50U links numerical Grad-Shafranov solutions with surrogate predictions. The standard Shape Editor reference provides the third point of comparison. This chain assesses simulation-to-device consistency. The preprint does not report whether the surrogates have been deployed in a live control loop on EXL-50U.

The database size is fixed at 100,000 in-distribution and 10,000 out-of-distribution samples. The preprint does not describe how the out-of-distribution samples were constructed beyond stating they represent unseen plasma geometries and parameter regimes. It also does not specify the wall-clock training time for each architecture.

Inference latency of 0.7 ms for CNN under TensorRT is the only deployment-speed figure provided. The preprint does not give latency numbers for the other four architectures under the same inference engine. It also does not state whether the 0.7 ms includes data transfer overhead or only kernel execution.

Where the Benchmark Stops

The authors are Guoyang Shi, Zitong Zhang, Siqi Ding, Jianguo Chen, Yapeng Zhang, Jiayi Zhi, Hanyue Zhao, and Tianyuan Liu. The preprint appears on arXiv as version 1 with identifier 2608.23217v1. No journal acceptance is mentioned.

For a fusion engineer choosing a surrogate today, the practical guidance is conditional. If the operating regime stays within the training distribution, transformer yields the lowest error. CNN or FNO provide more stable extrapolation if the regime may drift or the geometry changes. If the control cycle demands sub-millisecond latency, CNN with TensorRT meets that budget. The preprint does not rank the architectures for a specific control-cycle deadline beyond the 0.7 ms figure.

The work provides a systematic, device-consistent benchmark for AI-based Grad-Shafranov prediction. It does not claim the benchmark covers all tokamak classes or all disruption-relevant scenarios. The EXL-50U validation is a single-device demonstration.