Improving accuracy and computational efficiency of optimal design of experiments via greedy backward approach

Nonintrusive least-squares-based polynomial chaos expansion (PCE) techniques have attracted increasing attention among researchers for simple yet efficient surrogate constructions. Different sampling approaches, including optimal design of experiments (DoEs), have been developed to facilitate the least-squares-based PCE construction by reducing the number of required training samples. DoEs mainly include a random selection of the initial sample point and searching a pool of (coherence-optimal) candidate samples to iteratively select the next points based on some optimality criteria. Here, we propose a different way from the common practice to select sample points based on DoEs' optimality criteria, namely backward greedy. The proposed approach starts from a pool of coherence-optimal samples and iteratively removes the most uninfluential sample candidate among a small and randomly selected subset of the pool, instead of the whole pool. Several numerical examples are provided to demonstrate the promises of the proposed approach in improving the accuracy, robustness, and computational efficiency of DoEs. Specifically, it is observed that the proposed backward greedy approach not only improves the computational time for selecting the optimal design but also results in higher approximation accuracy. Most importantly, using the proposed approach, the choice of optimality becomes significantly less critical as different criteria yield similar accuracy when they are used in a backward procedure to select the design points.