A gradient-enhanced partition-of-unity surrogate model and adaptive sampling strategy for non-analytic functions

We present a gradient-enhanced, partition-of-unity surrogate model and an associated adaptive sampling procedure that performs well for functions with low regularity or rapid variation over short distances. The approach reconstructs local quadratic models at each training point using function and gr...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2023-07, Vol.66 (7), p.167, Article 167
Main Authors: Bedonian, Garo, Hicken, Jason E., Forster, Edwin
Format: Article
Language:English
Subjects:
Accuracy
Adaptive sampling
Analytic functions
Approximation
Basis functions
Computational Mathematics and Numerical Analysis
Design optimization
Engineering
Engineering Design
Mathematical analysis
Meta-analysis
Regularity
Research Paper
Sampling methods
Smoothness
Theoretical and Applied Mechanics
Training
Unity
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Summary:We present a gradient-enhanced, partition-of-unity surrogate model and an associated adaptive sampling procedure that performs well for functions with low regularity or rapid variation over short distances. The approach reconstructs local quadratic models at each training point using function and gradient data from neighboring points, and partition-of-unity basis functions blend these local models. We apply the proposed method to a suite of analytical test functions and a coupled aerostructural model to demonstrate its relative effectiveness. The performance of the partition-of-unity surrogate is assessed relative to Kriging and gradient-enhanced Kriging (GEK) models constructed from appropriate one-shot and adaptive sampling methods. The proposed model obtains results competitive with those of the equivalent Kriging models for the tested functions, and it notably outperforms Kriging for functions with slowly decaying spectra, such as those featuring strong jumps, non-smoothness, and low regularity. Furthermore, the model achieves its competitive accuracy without requiring hyperparameter training.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-023-03620-x