  Constructing approximations that can accurately mimic the behavior of complex
models at reduced computational costs is an important aspect of uncertainty
quantification. Despite their flexibility and efficiency, classical surrogate
models such as Kriging or polynomial chaos expansions tend to struggle with
highly non-linear, localized or non-stationary computational models. We hereby
propose a novel sequential adaptive surrogate modeling method based on
recursively embedding locally spectral expansions. It is achieved by means of
disjoint recursive partitioning of the input domain, which consists in
sequentially splitting the latter into smaller subdomains, and constructing a
simpler local spectral expansions in each, exploiting the trade-off complexity
vs. locality. The resulting expansion, which we refer to as "stochastic
spectral embedding" (SSE), is a piece-wise continuous approximation of the
model response that shows promising approximation capabilities, and good
scaling with both the problem dimension and the size of the training set. We
finally show how the method compares favorably against state-of-the-art sparse
polynomial chaos expansions on a set of models with different complexity and
input dimension.
