In computationally intensive studies, such as model calibration and
uncertainty quantification, surrogate models are usually employed instead of
full physical models. However, surrogate construction for high-dimensional
models is challenged in two major ways: a) obtaining sufficient number of
training model simulations becomes prohibitively expensive, and b)
non-adaptive surrogate basis selection rules lead to excessively large basis
sets. To alleviate these difficulties, select state-of-the-art tools are
ported from statistical learning to build efficient sparse surrogate
representations, with quantified uncertainty, for high-dimensional complex
models. Specifically, Bayesian compressive sensing techniques are enhanced by
iterative basis growth and weighted regularization. Application to an
80-dimensional climate land model shows promising results, leading to
efficient global sensitivity analysis and dimensionality reduction.