Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (MSE $\approx$ $10^{-5}$). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations (PDE), and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e., cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

翻译：预测托卡马克反应堆内等离子体的演化对于实现可持续聚变的目标至关重要。快速准确地预测等离子体时空演化的能力，使我们能够快速迭代当前托卡马克装置及未来反应堆的设计与控制策略。使用数值求解器对等离子体演化进行建模通常成本高昂，需在超级计算机上耗费大量时间，因此我们需要替代性的低成本代理模型。我们通过基于深度学习的代理建模工具——傅里叶神经算子（FNO），展示了在模拟和实验领域中对等离子体演化的精确预测。结果表明，FNO在预测基于磁流体动力学模型模拟的等离子体动力学时，速度比传统求解器快六个数量级，同时保持高精度（均方误差 $\approx$ $10^{-5}$）。我们改进后的FNO版本能够求解多变量偏微分方程，并在单一模型中捕捉不同变量之间的依赖关系。FNO还可基于MAST托卡马克内摄像头（即观察中央螺线管和偏滤器的摄像头）观测到的真实实验数据预测等离子体演化。研究表明，FNO能够准确预测等离子体演化，并具备部署用于实时监测的潜力。我们还展示了其在MAST托卡马克等离子体放电全过程中预测等离子体形状，以及等离子体与中央螺线管、偏滤器相互作用位置的能力。FNO训练和推理速度快，所需数据量少，同时具备零样本超分辨率能力并生成高保真解，因此为代理建模提供了可行的替代方案。