Estimation and model errors in Gaussian-process-based Sensitivity Analysis of functional outputs

TL;DR

This paper introduces an efficient algorithm for estimating errors in Gaussian-process-based sensitivity analysis of functional outputs, significantly reducing computational time and improving accuracy in Sobol and generalized sensitivity indices.

Contribution

The work presents a novel algorithm that estimates model and sampling errors in GP-based sensitivity analysis, leveraging basis coefficients and vector-valued PF estimation for efficiency.

Findings

Achieved 15-fold reduction in computational time.

Validated methodology on analytical and hydraulic flow models.

Improved accuracy of sensitivity indices estimation.

Abstract

Global sensitivity analysis (GSA) of functional-output models is usually performed by combining statistical techniques, such as basis expansions, metamodeling and sampling based estimation of sensitivity indices. By neglecting truncation error from basis expansion, two main sources of errors propagate to the final sensitivity indices: the metamodeling related error and the sampling-based, or pick-freeze (PF), estimation error. This work provides an efficient algorithm to estimate these errors in the frame of Gaussian processes (GP), based on the approach of Le Gratiet et al. [16]. The proposed algorithm takes advantage of the fact that the number of basis coefficients of expanded model outputs is significantly smaller than output dimensions. Basis coefficients are fitted by GP models and multiple conditional GP trajectories are sampled. Then, vector-valued PF estimation is used to speed-up the estimation of Sobol indices and generalized sensitivity indices (GSI). We illustrate the methodology on an analytical test case and on an application in non-Newtonian hydraulics, modelling an idealized dam-break flow. Numerical tests show an improvement of 15 times in the computational time when compared to the application of Le Gratiet et al. [16] algorithm separately over each output dimension.