Adaptive sampling with a Lipschitz criterion for accurate metamodeling

Abstract

Lipschitz Sampling, unlike standard space lling strategies (Minimax and Maximin distance, Integrated Mean Squared Error, Eadze-Eglais, etc.) for producing good metamodels, incorporates information from output evaluation in order to estimate in some sense the local complexity of the function at hand. The complexity indicator considered is a suitable denition of local Lipschitz constant. New points are proposed to be evaluated where the product of the local Lipschitz constant by the distance from the nearest already evaluated point is maximum. Benchmarks are proposed on standard test functions in comparison with standard space lling strategies. Smaller prediction errors are obtained by Lipschitz sampling when the function considered shows sudden variations in some part of the domain and varies more slowly in other regions.