Lengthscale-adaptivity in Gaussian process emulation with sparse grids
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Gaussian process emulation is a commonly employed method of surrogate modelling in which the aim is to cheaply approximate outputs of computer models whilst also keeping track of the uncertainty in these predictions. Emulators, however, fall prey to the curse of dimensionality, and so much work is done to find optimal experimental designs for high-dimensional models. For functions in certain mixed Sobolev spaces, Sparse grid designs have been shown to have improved rates of convergence - depending only logarithmically on the dimension. For large dimensions (>10), however, these methods still quickly become unfeasible. We introduce a novel sparse grid construction for which, by adapting to the lengthscale in each dimension, we are able to emulate in arbitrarily large dimensions for functions exhibiting sufficient anisotropy.