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ANOVA Gaussian process modeling for high-dimensional stochastic computational models. (English) Zbl 1437.62286
Summary: In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. The Gaussian process (GP) is a widely used surrogate modeling strategy, but it can become invalid when the inputs are high-dimensional. In this new ANOVA-GP strategy, high-dimensional inputs are decomposed into unions of local low-dimensional inputs, and principal component analysis (PCA) is applied to provide dimension reduction for each ANOVA term. We then systematically build local GP models for PCA coefficients based on ANOVA decomposition to provide an emulator for the overall high-dimensional problem. We present a general mathematical framework of ANOVA-GP, validate its accuracy and demonstrate its efficiency with numerical experiments.
MSC:
62J10 Analysis of variance and covariance (ANOVA)
65C20 Probabilistic models, generic numerical methods in probability and statistics
60G15 Gaussian processes
35R60 PDEs with randomness, stochastic partial differential equations
76M35 Stochastic analysis applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
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