Adaptive sampling strategies for reduced-order modeling

Abstract

Reduced-order models (ROMs) become increasingly popular in industrial design and optimization processes, since they allow to approximate expensive high fidelity computational fluid dynamics (CFD) simulations in near real-time. The quality of ROM predictions highly depends on the placement samples in the spanned parameter space. Adaptive sampling strategies allow to identify regions of interest, which feature e.g. nonlinear responses with respect to the parameters, and therefore enable the sensible placement of new samples. By introducing more samples in these regions, the ROM prediction accuracy should increase. In this contribution we investigate different adaptive sampling strategies based on cross-validation, Gaussian mean-squared error, two methods exploiting the CFD residual and a two manifold embedding methods. The performance of those strategies is evaluated and measured by their ability to successfully identify the regions of interest and the resulting sample placement in terms of different quantitative statistical values. We further discuss the reduction of the ROM prediction error over the adaptive sampling iterations and show that depending on the adaptive sampling strategy, the number of required samples can be reduced by 35–44% without deteriorating model quality compared to a Halton sequence sampling plan.