2020/04/09 by Stefano Marelli, Marelli, S., Paul‐Remo Wagner +5 · 2 citations
Computer Science · Decision Sciences · Physics and Astronomy · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2004.04480
openalex publication_date 2020/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.