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 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.

Automated summary

We propose a gradient-enhanced, partition-of-unity surrogate model and adaptive sampling procedure for functions with low regularity or rapid variation. This method reconstructs local quadratic models using function and gradient data from neighboring points and blends them with partition-of-unity basis functions. It is shown to be competitive with Kriging models and outperforms Kriging for functions with slowly decaying spectra, without the need for hyperparameter training.