Stochastic spectral embedding
This addresses the problem of efficient uncertainty quantification for engineers and scientists dealing with computationally intensive models, though it appears incremental as an enhancement to existing surrogate modeling techniques.
The paper tackles the challenge of approximating complex models with non-linear or non-stationary behavior by proposing a sequential adaptive surrogate modeling method called stochastic spectral embedding (SSE), which recursively partitions the input domain and uses local spectral expansions, showing promising accuracy and scalability compared to state-of-the-art methods.
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.