Hierarchical adaptive polynomial chaos expansions

Chu V. Mai (1, 2) , Bruno Sudret (1, 2)

1 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact significant. Taking into account the sparse structure of the model, advanced techniques such as sparse PCE (SPCE), have been recently proposed to alleviate the computational issue. In this paper, we propose a novel approach to SPCE, which allows one to exploit the model's hierarchical structure. The proposed approach is based on the adaptive enrichment of the polynomial basis using the so-called principle of heredity. As a result, one can reduce the computational burden related to a large pre-defined candidate set while obtaining higher accuracy with the same computational budget.

Mots clés: hierarchical adaptive polynomial chaos expansions; heredity principle; sparsity principle; hierarchy principle; high dimensional problems.

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]

Chu V. Mai, Bruno Sudret. Hierarchical adaptive polynomial chaos expansions. 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering, May 2015, Crete, Greece. ⟨hal-01158502⟩