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.

Development of the VGF Crystal Growth Recipe: Intelligent Solutions of Ill‐Posed Inverse Problems using Images and Numerical Data

“…In view of this, the low prediction accuracy when using only images as input data is not only a consequence of the non-singularity of the solution but also of the nature of this data-driven method, the number and location of the input data in the parameter space, as reported in the literature. [23] When considering the Kriging interpolation model with both images and numerical data for solving inverse tasks, the system behavior was fully captured as shown in the parity plots for 6 outputs in Figure 7.…”

“…In view of this, the low prediction accuracy when using only images as input data is not only a consequence of the non‐singularity of the solution but also of the nature of this data‐driven method, the number and location of the input data in the parameter space, as reported in the literature. [ 23 ]…”

An adaptive sampling algorithm for reduced‐order models using Isomap

“…Our algorithm is also applicable to both non‐intrusive and projection‐based ROMs, whereas previous works have focused exclusively on non‐intrusive ROMs. A wide range of adaptive sampling algorithms is compared in a work 11 by Karcher and Franz. When applied to two external aerodynamics problems, our results show that the proposed adaptive sampling algorithm outperforms using LHS alone in predicting physical fields and integral quantities of lift and drag.…”