Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes

TL;DR

This paper introduces novel active learning methods tailored for derivative-based global sensitivity analysis using Gaussian processes, significantly improving efficiency in estimating sensitivity measures for expensive black-box functions.

Contribution

It develops the first active learning acquisition functions directly targeting DGSMs, enhancing sample efficiency and accuracy in sensitivity analysis with limited evaluations.

Findings

Active learning strategies substantially improve DGSM estimation efficiency.

Proposed methods outperform traditional sampling in synthetic and real-world tests.

Enhances sensitivity analysis for expensive black-box functions in engineering applications.

Abstract

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models. We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.