Sparse Polynomial Chaos Expansions: Solvers, Basis Adaptivity and Meta-selection

Sparse polynomial chaos expansions (PCEs) are an efficient and widely used surrogate modeling method in uncertainty quantification. Among the many contributions aiming at computing an accurate sparse PCE while using as few model evaluations as possible, basis adaptivity is a particularly interesting approach. It consists in starting from an expansion with a small number of polynomial terms, and then parsimoniously adding and removing basis functions in an iterative fashion. We describe several state-of-the-art approaches from the recent literature and extensively benchmark them on a large set of computational models representative of a wide range of engineering problems. We investigate the synergies between sparse regression solvers and basis adaptivity schemes, and provide recommendations on which of them are most promising for specific classes of problems. Furthermore, we explore the performance of a novel cross-validation-based solver and basis adaptivity selection scheme, which consistently provides close-to-optimal results.