Exploration-oriented sampling strategies for global surrogate modeling: A comparison between one-stage and adaptive methods

Abstract

Studying complex phenomena in detail by performing real experiments is often an unfeasible task. Virtual experiments using simulations are usually used to support the development process. However, numerical simulations are limited by their computational cost. Metamodeling techniques are commonly used to mimic the behavior of unknown solver functions, especially for expensive black box optimizations. If a good correlation between the surrogate model and the black box function is obtained, expensive numerical simulations can be significantly reduced. The sampling strategy, which selects a subset of samples that can adequately predict the behavior of expensive black box functions, plays an important role in the fidelity of the surrogate model. Achieving the desired metamodel accuracy with as few solver calls as possible is the main goal of global surrogate modeling. In this paper, exploration-oriented adaptive sampling strategies are compared with commonly used one-stage sampling approaches, such as Latin Hypercube Design (LHD). The difference in the quality of approximation is tested on benchmark functions from 2 up to 30 variables. Two novel sampling algorithms to get fine-grained quasi-LHDs will be proposed and an improvement to a well-known, pre-existing sequential input algorithm will be discussed. Finally, these methods are applied to a crash box design to investigate the performance when approximating highly non-linear crashworthiness problems. It is found that adaptive sampling approaches outperform one-stage methods both in terms of mathematical properties and in terms of metamodel accuracy in the majority of the tests. A proper stopping algorithm should also be employed with adaptive methods to avoid oversampling.