Title: Least Squares Polynomial Chaos Expansion: A Review of Sampling Strategies,
Abstract: As non-institutive polynomial chaos expansion (PCE) techniques have gained
growing popularity among researchers, we here provide a comprehensive review of
major sampling strategies for the least squares based PCE. Traditional sampling
methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal
design of experiments (ODE), Gaussian quadratures, as well as more recent
techniques, such as coherence-optimal and randomized quadratures are discussed.
We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal,
that employs the so-called alphabetic optimality criteria used in the context
of ODE in conjunction with coherence-optimal samples. A comparison between the
empirical performance of the selected sampling methods applied to three
numerical examples, including high-order PCE's, high-dimensional problems, and
low oversampling ratios, is presented to provide a road map for practitioners
seeking the most suitable sampling technique for a problem at hand. We observed
that the alphabetic-coherence-optimal technique outperforms other sampling
methods, specially when high-order ODE are employed and/or the oversampling
ratio is low.