A fast surrogate cross validation algorithm for meshfree RBF collocation approaches

2023/07/14 by Francesco Marchetti, Marchetti, Francesco · 2 citations
Engineering · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Fatigue and fracture mechanics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2307.07632

openalex publication_date 2023/07/14 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28

Abstract

Cross validation is an important tool in the RBF collocation setting, especially for the crucial tuning of the shape parameter related to the radial basis function. In this paper, we define a new efficient surrogate cross validation algorithm, which computes an accurate approximation of the true validation error with much less computational effort with respect to a standard implementation. The proposed scheme is first analyzed and described in details, and then tested in various numerical experiments that confirm its efficiency and effectiveness.

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