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快速且可靠的等离子体平衡预测对于托卡马克的实时运行与控制至关重要，然而传统的Grad-Shafranov (GS) 求解器计算成本过高，无法直接部署于实时控制中。为此，本文开发了一个AI代理框架，并在包含100,000个独立同分布（IID）样本和10,000个分布外（OOD）样本的数值GS数据库上，对五种主流神经网络架构（MLP、CNN、FNO、Transformer 和 KAN）进行了全面的基准测试。

通过统一的评估协议，该研究系统地评估了各个模型的准确性、推理效率、缩放行为（scaling behaviors）以及鲁棒性。此外，研究人员通过将数值GS解、AI代理预测结果与标准的Shape Editor参考进行对比，在 EXL-50U 托卡马克 装置上进行了设备级验证，从而确认了从仿真到实体装置的一致性。该工作为基于AI的GS预测提供了系统化、装置一致的基准，并为实时等离子体控制及聚变应用中可靠代理模型的选择提供了具有实用价值的指导。

AI Surrogate Modeling for Real-Time Tokamak Equilibrium Prediction: Benchmarking Neural Architectures and Validation on EXL-50U

Authors: Guoyang Shi, Zitong Zhang, Siqi Ding, Jianguo Chen, Yapeng Zhang, Jiayi Zhi, Hanyue Zhao, Tianyuan Liu
Subjects: Plasma Physics (physics.plasm-ph); Artificial Intelligence (cs.AI)
arXiv: 2608.23217 [physics.plasm-ph]
Submitted: August 24, 2026
License: Creative Commons Attribution-NonCommercial-ShareAlike 4.0

📌 Summary

快速且可靠的等离子体平衡预测对于实时托卡马克运行和控制至关重要，然而传统的 Grad-Shafranov (GS) 求解器在计算上过于昂贵，难以用于实时部署。本文开发了一个 AI 代理框架，并在包含 100,000 个 IID 和 10,000 个 OOD 样本的数值 GS 数据库上，对五种神经网络架构（MLP、CNN、FNO、Transformer 和 KAN）进行了基准测试。

通过统一的评估协议，该研究评估了模型的准确性、推理效率、缩放行为和鲁棒性。此外，研究人员通过连接数值 GS 解、AI 代理预测以及标准的 Shape Editor 参考，在 EXL-50U 托卡马克上建立了设备级验证，以验证仿真到设备的一致性。

Fast and reliable plasma equilibrium prediction is vital for real-time tokamak operation and control, yet traditional Grad-Shafranov (GS) solvers are computationally too expensive for real-time deployment. This paper develops an AI surrogate framework that benchmarks five neural architectures (MLP, CNN, FNO, Transformer, and KAN) across a numerical GS database comprising 100,000 IID and 10,000 OOD samples.

Using a unified evaluation protocol, the study assesses model accuracy, inference efficiency, scaling behaviors, and robustness. Furthermore, the researchers establish device-level validation on the EXL-50U tokamak by linking numerical GS solutions, AI surrogate predictions, and standard Shape Editor references to verify simulation-to-device consistency.

🔑 Key Findings & Architecture Benchmarking

  • 准确性与误差范围： 与标准 GS 解相比，AI 代理实现了 \(10^{-3}\) 到 \(10^{-2}\) 之间的相对误差，而基准 GS 到设备的差异保持在 \(10^{-3}\) 水平。
  • 表现最佳的模型：
  • Transformer 在分布内（In-Distribution, IID）数据集上实现了最高的准确率。
  • CNN 在准确性、鲁棒性和计算速度之间取得了最佳平衡，实现了高性能的 0.7 ms TensorRT 推理延迟。
  • 泛化与外推： 在未见过的等离子体几何形状和参数区间（分布外/OOD）中，CNN 和 FNO 表现出优异的外推稳定性（维持 4%–5% 的相对 \(L_2\) 误差），而缺乏强归纳偏置的模型则经历了显著的性能下降。
  • 缩放权衡（Scaling Trade-offs）： 增加数据量和模型容量虽然增强了内插能力，但并不能从根本上改善 OOD 泛化能力，这凸显了网络容量与稳健外推之间的明显权衡。
  • Accuracy & Error Margins: AI surrogates achieve relative errors between \(10^{-3}\) and \(10^{-2}\) compared to standard GS solutions, while the baseline GS-to-device discrepancy remains at \(10^{-3}\).
  • Top Performers:
  • Transformer achieves the highest accuracy on In-Distribution (IID) datasets.
  • CNN strikes the optimal balance between accuracy, robustness, and computational speed, delivering a high-performance 0.7 ms TensorRT latency.
  • Generalization & Extrapolation: On unseen plasma geometries and parameter regimes (Out-of-Distribution/OOD), CNN and FNO demonstrate superior extrapolation stability (maintaining 4%–5% relative \(L_2\) errors), whereas models lacking strong inductive biases experience significant performance degradation.
  • Scaling Trade-offs: While increasing data volume and model capacity enhances interpolation capabilities, it does not inherently improve OOD generalization, highlighting a distinct trade-off between network capacity and robust extrapolation.

📄 Abstract

快速且可靠的等离子体平衡预测对于实时托卡马克运行和控制至关重要，但常规的 Grad-Shafranov (GS) 求解器对于实时部署而言计算代价往往过高。我们开发了一个 AI 代理框架，并在包含 100,000 个 IID 和 10,000 个 OOD 样本的数值 GS 数据库上对五种架构（MLP、CNN、FNO、Transformer 和 KAN）进行了基准测试。在统一的协议下，我们评估了准确性、推理效率、模型缩放和鲁棒性。我们还通过连接数值 GS 解、代理预测以及标准的 Shape Editor 参考，在 EXL-50U 托卡马克上建立了设备级验证，以评估仿真到设备的一致性。相对于 GS 解，代理模型的误差达到了 \(10^{-3}\)-\(10^{-2}\)，而 GS 到设备的差异保持在 \(10^{-3}\)。Transformer 提供了最佳的 IID 准确率，而 CNN 提供了准确性、鲁棒性和速度的最佳平衡，达到了 0.7 ms 的 TensorRT 延迟。在未见过的等离子体几何形状和参数区间上，CNN 和 FNO 显示出最强的外推稳定性，相对 \(L_2\) 误差为 4%-5%，而归纳偏置较弱的模型性能下降更为明显。缩放数据和模型容量改善了内插，但不一定能改善外推，这揭示了容量与 OOD 泛化之间的权衡。总的来说，这项工作为基于 AI 的 GS 预测提供了系统性的、设备一致的基准，并为选择用于实时等离子体控制和聚变应用的可靠代理模型提供了实用指导。

Fast and reliable plasma equilibrium prediction is essential for real-time tokamak operation and control, but conventional Grad-Shafranov (GS) solvers are often too costly for real-time deployment. We develop an AI surrogate framework and benchmark five architectures (MLP, CNN, FNO, Transformer, and KAN) on a numerical GS database with 100,000 IID and 10,000 OOD samples. Under a unified protocol, we evaluate accuracy, inference efficiency, model scaling, and robustness. We also establish device-level validation on the EXL-50U tokamak by linking numerical GS solutions, surrogate predictions, and the standard Shape Editor reference to assess simulation-to-device consistency. The surrogates achieve errors of \(10^{-3}\)-\(10^{-2}\) relative to GS solutions, while the GS-to-device discrepancy remains at \(10^{-3}\). Transformer gives the best IID accuracy, whereas CNN offers the best balance of accuracy, robustness, and speed, reaching 0.7 ms TensorRT latency. On unseen plasma geometries and parameter regimes, CNN and FNO show the strongest extrapolation stability, with 4%-5% relative \(L_2\) error, while models with weaker inductive biases degrade more substantially. Scaling data and model capacity improves interpolation but not necessarily extrapolation, revealing a trade-off between capacity and OOD generalization. Overall, this work provides a systematic, device-consistent benchmark for AI-based GS prediction and practical guidance for selecting reliable surrogates for real-time plasma control and fusion applications.

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