  The optimisation of scenarios and design of real-time-control in tokamaks,
especially for machines still in design phase, requires a comprehensive
exploration of solutions to the Grad-Shafranov (GS) equation over a
high-dimensional space of plasma and coil parameters. Emulators can bypass the
numerical issues in the GS equation, if a large enough library of equilibria is
available. We train an ensemble of neural networks to emulate the typical
shape-control targets (separatrix at midplane, X-points, divertor strike point,
flux expansion, poloidal beta) as a function of plasma parameters and active
coil currents for the range of plasma configurations relevant to spherical
tokamaks with a super-X divertor, with percent-level accuracy. This allows a
quick calculation of the classical-control shape matrices, potentially allowing
real-time calculation at any point in a shot with sub-ms latency. We devise a
hyperparameter sampler to select the optimal network architectures and quantify
uncertainties on the model predictions. To generate the relevant training set,
we devise a Markov-Chain Monte Carlo algorithm to produce large libraries of
forward Grad-Shafranov solutions without the need for user intervention. The
algorithm promotes equilibria with desirable properties, while avoiding
parameter combinations resulting in problematic profiles or numerical issues in
the integration of the GS equation.
