Projection pursuit adaptation on polynomial chaos expansions

Zeng, Xiaoshu; Ghanem, Roger

doi:10.1016/j.cma.2022.115845

Projection pursuit adaptation on polynomial chaos expansions

Journal Article · Thu Dec 21 00:00:00 EST 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2022.115845· OSTI ID:2421877

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Univ. of Southern California, Los Angeles, CA (United States)

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Southern California, Los Angeles, CA (United States)

Sponsoring Organization:: US Department of the Navy, Office of Naval Research (ONR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: SC0021307

Other Award/Contract Number:: N00014-21-1-2475

OSTI ID:: 2421877

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 405; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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