🤖 AI Summary
This work proposes a gradient-based active learning method to enhance the accuracy of global sensitivity analysis under limited computational budgets. By leveraging the posterior gradient distribution of a Gaussian process surrogate model, the approach introduces a novel acquisition function that explicitly accounts for correlations among partial derivatives, enabling intelligent selection of the most informative input samples within a constrained simulation budget. Compared to existing derivative-based global sensitivity measures (DGSM)-oriented strategies, the proposed method offers a more comprehensive and robust framework. Experimental results on multiple benchmark test functions and a real-world pesticide transport environmental model demonstrate that the method significantly outperforms state-of-the-art approaches, yielding notably improved estimates of both Sobol’ indices and DGSM sensitivity measures.
📝 Abstract
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.