  The tritium breeding ratio (TBR) is an essential quantity for the design of
modern and next-generation D-T fueled nuclear fusion reactors. Representing the
ratio between tritium fuel generated in breeding blankets and fuel consumed
during reactor runtime, the TBR depends on reactor geometry and material
properties in a complex manner. In this work, we explored the training of
surrogate models to produce a cheap but high-quality approximation for a Monte
Carlo TBR model in use at the UK Atomic Energy Authority. We investigated
possibilities for dimensional reduction of its feature space, reviewed 9
families of surrogate models for potential applicability, and performed
hyperparameter optimisation. Here we present the performance and scaling
properties of these models, the fastest of which, an artificial neural network,
demonstrated $R^2=0.985$ and a mean prediction time of $0.898\ \mu\mathrm{s}$,
representing a relative speedup of $8\cdot 10^6$ with respect to the expensive
MC model. We further present a novel adaptive sampling algorithm,
Quality-Adaptive Surrogate Sampling, capable of interfacing with any of the
individually studied surrogates. Our preliminary testing on a toy TBR theory
has demonstrated the efficacy of this algorithm for accelerating the surrogate
modelling process.
