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 in the normalised domain $\approx$ $10^{-5}$). 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 (available) 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：准确预测托卡马克反应堆内的等离子体演化对于实现可持续聚变目标至关重要。快速、精确地预测等离子体时空演化的能力，使我们能够在现有托卡马克装置和未来反应堆上快速迭代设计和控制策略。使用数值求解器模拟等离子体演化通常成本高昂，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替代模型。我们展示了基于深度学习的替代建模工具——傅里叶神经算子（FNO）在模拟和实验领域对等离子体演化的准确预测能力。研究表明，在预测磁流体动力学模型模拟的等离子体动力学时，FNO 相较于传统求解器实现了六个数量级的加速，同时保持了高精度（归一化域内的均方误差 $\approx$ $10^{-5}$）。我们改进的 FNO 版本能够求解多变量偏微分方程（PDE），并能在单一模型中捕捉不同变量间的依赖关系。FNO 还能预测 MAST 托卡马克内部摄像机观测到的真实世界实验数据中的等离子体演化，即观测穿过托卡马克中心螺线管和偏滤器的摄像机数据。我们证明 FNO 能够准确预测等离子体演化，并具备部署于实时监测的潜力。我们还展示了其在预测 MAST 中整个（可用的）等离子体放电期间等离子体形状、等离子体与中心螺线管及偏滤器相互作用位置的能力。FNO 为替代建模提供了一种可行的替代方案，因为它训练和推断速度快，所需数据点更少，同时能够进行零样本超分辨率重建并获得高保真解。