STOCHASTIC SPECTRAL EMBEDDING

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