Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

With the ever growing importance of uncertainty and sensitivity analysis of complex model evaluations and the difficulty of their timely realizations comes a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate to map input-output relationships to investigate complex models. There is a lot of potential to increase the efficacy of the method regarding the selected sampling scheme. We examined state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1 optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the gPC regression models. The sampling schemes are thoroughly investigated by evaluating the quality of the constructed surrogate models considering distinct test cases representing different problem classes covering low, medium and high dimensional problems. Finally, the samplings schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe, which is used to measure the impedance of biological tissues at different frequencies. Due to the random nature, we compared the sampling schemes using statistical stability measures and evaluated the success rates to construct a surrogate model with an accuracy of <0.1%. We observed strong differences in the convergence properties of the methods between the analyzed test functions.