Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce the computational burden, provided that the design of computer experiments is enriched efficiently. In this context, we propose an active learning approach that, for a fixed evaluation budget, targets the most informative regions of the input space to improve sensitivity analysis accuracy. More specifically, our method builds on recent advances in active learning for sensitivity analysis (Sobol' indices and derivative-based global sensitivity measures, DGSM) that exploit derivatives obtained from a Gaussian process (GP) surrogate. By leveraging the joint posterior distribution of the GP gradient, we develop acquisition functions that better account for correlations between partial derivatives and their impact on the response surface, leading to a more comprehensive and robust methodology than existing DGSM-oriented criteria. The proposed approach is first compared to state-of-the-art methods on standard benchmark functions, and is then applied to a real environmental model of pesticide transfers.

翻译：复杂数值模拟器的全局敏感性分析通常受限于可负担的少量模型评估。在此类场景下，基于有限模拟构建的代理模型可显著减轻计算负担，前提是计算机实验设计能被高效地丰富。在此背景下，我们提出一种主动学习方法，该方法在固定评估预算下，针对输入空间中最具信息量的区域以提高敏感性分析的准确性。具体而言，我们的方法建立在敏感性分析（Sobol指数和基于导数的全局敏感性度量，DGSM）主动学习的最新进展之上，这些进展利用了从高斯过程（GP）代理模型获得的导数。通过利用GP梯度的联合后验分布，我们开发了能更好考虑偏导数间相关性及其对响应面影响的采集函数，从而形成比现有DGSM导向准则更全面、更稳健的方法论。所提出的方法首先在标准基准函数上与最先进方法进行比较，随后应用于农药迁移的真实环境模型。