Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processes

TL;DR

This paper introduces FOAGP, a novel Gaussian process model for data-driven orthogonal effect decomposition in functional-output computer experiments, enabling flexible sensitivity analysis without strong distributional assumptions.

Contribution

It proposes a new orthogonal additive Gaussian process framework that captures complex nonlinear relationships and provides analytical sensitivity indices, advancing functional-output sensitivity analysis.

Findings

Effective in orthogonal effect decomposition demonstrated through simulations.

Accurate variance decomposition validated on real fuselage shape data.

Enables comprehensive local and global sensitivity analysis.

Abstract

Functional ANOVA (FANOVA) is a widely used variance-based sensitivity analysis tool. However, studies on functional-output FANOVA remain relatively scarce, especially for black-box computer experiments, which often involve complex and nonlinear functional-output relationships with unknown data distribution. Conventional approaches often rely on predefined basis functions or parametric structures that lack the flexibility to capture complex nonlinear relationships. Additionally, strong assumptions about the underlying data distributions further limit their ability to achieve a data-driven orthogonal effect decomposition. To address these challenges, this study proposes a functional-output orthogonal additive Gaussian process (FOAGP) to efficiently perform the data-driven orthogonal effect decomposition. By enforcing a conditional orthogonality constraint on the separable prior process, the proposed functional-output orthogonal additive kernel enables data-driven orthogonality without requiring prior distributional assumptions. The FOAGP framework also provides analytical formulations for local Sobol' indices and expected conditional variance sensitivity indices, enabling comprehensive sensitivity analysis by capturing both global and local effect significance. Validation through two simulation studies and a real case study on fuselage shape control confirms the model's effectiveness in orthogonal effect decomposition and variance decomposition, demonstrating its practical value in engineering applications.