  Simulation-based plasma scenario development, optimization and control are
crucial elements towards the successful deployment of next-generation
experimental tokamaks and Fusion power plants. Current simulation codes require
extremely intensive use of HPC resources that make them unsuitable for
iterative or real time applications. Neural network based surrogate models of
expensive simulators have been proposed to speed up such costly workflows.
Current efforts in this direction in the Fusion community are mostly limited to
point estimates of quantities of interest or simple 1D PDE models, with a few
notable exceptions. While the AI literature on methods for neural PDE surrogate
models is rich, performance benchmarks for Fusion-relevant 2D fields has so far
remained flimited. In this work neural PDE surrogates are trained for the JOREK
MHD code and the STORM scrape-off layer code using the PDEArena library
(https://github.com/microsoft/pdearena). The performance of these surrogate
models is investigated as a function of training set size as well as for
long-term predictions. The performance of surrogate models that are trained on
either one variable or multiple variables at once is also considered. It is
found that surrogates that are trained on more data perform best for both long-
and short-term predictions. Additionally, surrogate models trained on multiple
variables achieve higher accuracy and more stable performance. Downsampling the
training set in time may provide stability in the long term at the expense of
the short term predictive capability, but visual inspection of the resulting
fields suggests that multiple metrics should be used to evaluate performance.
