Guerlain Lambert | Searcharxiv

arXiv2026

Gradient-based Active Learning with Gaussian Processes for Global Sensitivity Analysis

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.

stat.ML↗

arXiv2024

Quantization-based LHS for dependent inputs : application to sensitivity analysis of environmental models

Numerical modeling is essential for comprehending intricate physical phenomena in different domains. To handle complexity, sensitivity analysis, particularly screening, is crucial for identifying influential input parameters. Kernel-based methods, such as the Hilbert Schmidt Independence Criterion (HSIC), are valuable for analyzing dependencies between inputs and outputs. Moreover, due to the computational expense of such models, metamodels (or surrogate models) are often unavoidable. Implementing metamodels and HSIC requires data from the original model, which leads to the need for space-filling designs. While existing methods like Latin Hypercube Sampling (LHS) are effective for independent variables, incorporating dependence is challenging. This paper introduces a novel LHS variant, Quantization-based LHS, which leverages Voronoi vector quantization to address correlated inputs. The method ensures comprehensive coverage of stratified variables, enhancing distribution across marginals. The paper outlines expectation estimators based on Quantization-based LHS in various dependency settings, demonstrating their unbiasedness. The method is applied on several models of growing complexities, first on simple examples to illustrate the theory, then on more complex environmental hydrological models, when the dependence is known or not, and with more and more interactive processes and factors. The last application is on the digital twin of a French vineyard catchment (Beaujolais region) to design a vegetative filter strip and reduce water, sediment and pesticide transfers from the fields to the river. Quantization-based LHS is used to compute HSIC measures and independence tests, demonstrating its usefulness, especially in the context of complex models.

stat.ME↗