# Gradient-Based Active Learning with Gaussian Processes for Global Sensitivity Analysis

Guerlain Lambert, Céline Helbert, Claire Lauvernet

<figure><img src="image_1.png" /></figure>

## To cite this version:

Guerlain Lambert, Céline Helbert, Claire Lauvernet. Gradient-Based Active Learning with Gaussian Processes for Global Sensitivity Analysis. ENBIS, Sep 2025, Athènes, Greece. hal-05312298

HAL Id: hal-05312298

https://hal.science/hal-05312298v1

Submitted on 13 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_3.png" /></figure>

Abstract ID: 62

# Gradient-Based Active Learning with Gaussian Processes for Global Sensitivity Analysis

## Content

In recent decades, numerical experimentation has established itself as a valuable and cost-effective alternative to traditional field trials for investigating physical phenomena and evaluating the environmental impact of human activities. Nevertheless, high-fidelity simulations often remain computationally prohibitive due to the detailed modelling required and the complexity of parameter selection. To overcome these challenges, surrogate models constructed from a limited number of complex model evaluations are commonly used to drastically reduce computational costs and quantify uncertainties. In this context, we propose an active learning approach that, for a fixed evaluation budget, intelligently reduce the dimension of the input space to optimize surrogate model performance.

Specifically, our methodology builds on new advances in active learning for sensitivity analysis—such as Sobol indices and Derivative-based Global Sensitivity Measures (DGSM)—by leveraging derivatives obtained from a Gaussian Process (GP) surrogate. The benefits of our approach are demonstrated through several case studies, ranging from synthetic benchmark functions to a real-world environmental application involving physically-based modelling of pesticide transfer. Our results highlight the potential of this strategy to enhance sensitivity analysis in computationally intensive modelling scenarios.

## Special/ Invited session

### Classification

Both methodology and application

### Keywords

Active Learning, Gaussian Process, Sensitivity Analysis

**Primary author:** LAMBERT, Guerlain (Ecole Centrale de Lyon)

**Co-authors:** HELBERT, Celine (Ecole Centrale de Lyon); LAUVERNET, Claire (INRAE, Riverly)

**Presenter:** LAMBERT, Guerlain (Ecole Centrale de Lyon)

**Track Classification:** Statistical/Stochastic Modelling

Submitted by LAMBERT, Guerlain on Friday, 23 May 2025