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The Gaussian process is a standard tool for building emulators for bothdeterministic and stochastic computer experiments. However, application ofGaussian process models is greatly limited in practice, particularly forlarge-scale and many-input computer experiments that have become typical. Wepropose a multi-resolution functional ANOVA model as a computationally feasibleemulation alternative. More generally, this model can be used for large-scaleand many-input non-linear regression problems. An overlapping group lassoapproach is used for estimation, ensuring computational feasibility in alarge-scale and many-input setting. New results on consistency and inferencefor the (potentially overlapping) group lasso in a high-dimensional setting aredeveloped and applied to the proposed multi-resolution functional ANOVA model.Importantly, these results allow us to quantify the uncertainty in ourpredictions. Numerical examples demonstrate that the proposed model enjoysmarked computational advantages. Data capabilities, both in terms of samplesize and dimension, meet or exceed best available emulation tools while meetingor exceeding emulation accuracy.

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments