ANOVA Gaussian process modeling for high-dimensional stochastic computational models

TL;DR

This paper introduces a novel ANOVA-Gaussian process emulator that effectively models high-dimensional PDE-based systems by decomposing inputs, applying PCA for dimension reduction, and building local GP models for improved accuracy and efficiency.

Contribution

It proposes a new ANOVA-GP framework combining input decomposition and PCA to handle high-dimensional stochastic models more effectively than existing methods.

Findings

Validated accuracy through numerical experiments

Demonstrated efficiency in high-dimensional PDE models

Provided a systematic mathematical framework for ANOVA-GP

Abstract

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. 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.