  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.
