Projection pursuit adaptation on polynomial chaos expansions

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