Pré-Publication, Document De Travail Année : 2025

Gradient-enhanced global sensitivity analysis with Poincaré chaos expansions

Résumé

Chaos expansions are widely used in global sensitivity analysis (GSA), as they leverage orthogonal bases of L2 spaces to efficiently compute Sobol' indices, particularly in data-scarce settings. When derivatives are available, we argue that a desirable property is for the derivatives of the basis functions to also form an orthogonal basis. We demonstrate that the only basis satisfying this property is the one associated with weighted Poincaré inequalities and Sturm-Liouville eigenvalue problems, which we refer to as the Poincaré basis. We then introduce a comprehensive framework for gradient-enhanced GSA that integrates recent advances in sparse, gradient-enhanced regression for surrogate modeling with the construction of weighting schemes for derivative-based sensitivity analysis. The proposed methodology is applicable to a broad class of probability measures and supports various choices of weights. We illustrate the effectiveness of the approach on a challenging flood modeling case study, where Sobol' indices are accurately estimated using limited data.

Fichier principal
Vignette du fichier
main.pdf (763.82 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05266237 , version 1 (02-10-2025)

Licence

Identifiants

  • HAL Id : hal-05266237 , version 1

Citer

O Roustant, N Lüthen, David Heredia, B Sudret. Gradient-enhanced global sensitivity analysis with Poincaré chaos expansions. 2025. ⟨hal-05266237⟩
108 Consultations
189 Téléchargements

Partager

  • More