Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95

Machine learning in medicine: Performance calculation of dementia prediction by support vector machines (SVM)

Risk assessment and management of excavation system based on fuzzy set theory and machine learning methods

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering disciplines. Successful use of surrogate models can provide significant savings of computational cost. However, with a variety of surrogate model approaches available in literature, it is a difficult task to select an appropriate one at hand. In this paper, we present an overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation. The accuracy and efficiency of these approaches are compared with several benchmark examples. The strengths and weaknesses of these surrogate models are discussed, and the recommendations are provided for different types of applications. For ease of implementations, the packages, as well as toolboxes, of surrogate model techniques and their applications for global sensitivity analysis are collected.

Surrogate-assisted global sensitivity analysis: an overview

This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d -dimensional interpolation. The RBF methods lead to a solution of linear system of equations and computational complexity of solution is nearly independent of a dimensionality. However, the RBF methods are usually applied for small data sets with a small span geometric coordinates. This contribution explores properties of the RBF interpolation for large data sets and large span of geometric coordinates of the given data sets with regard to expectable numerical stability of computation.

RBF Interpolation with CSRBF of Large Data Sets.

Radial basis function approximations: comparison and applications

Big geo data surface approximation using radial basis functions: A comparative study

Vector field radial basis function approximation

Space subdivision to speed-up convex hull construction in E3

Many Radial Basis Functions (RBFs) contain a shape parameter which has an important role to ensure good quality of the RBF approximation. Determination of the optimal shape parameter is a difficult problem. In the majority of papers dealing with the RBF approximation, the shape parameter is set up experimentally or using some ad-hoc method. Moreover, the constant shape parameter is almost always used for the RBF approximation, but the variable shape parameter produces more accurate results. Several variable shape parameter methods, which are based on random strategy or on an evolutionary algorithm, have been developed. Another aspect which has an influence on the quality of the RBF approximation is the placement of reference points. A novel algorithm for finding an appropriate set of reference points and a variable shape parameter selection for the RBF approximation of functions y = f(x) (i.e. the case when a one-dimensional dataset is given and each point from this dataset is associated with a scalar value) is presented. Our approach has two steps and is based on exploiting features of the given dataset, such as extreme points or inflection points, and on comparison of the first curvature of a curve. The proposed algorithm can be used for the approximation of data describing a curve parameterized by one variable in multidimensional space, e.g. a robot path planning, etc.

Zuzana Majdisova

Papers

Radial basis function approximations: comparison and applications

Big geo data surface approximation using radial basis functions: A comparative study

Vector field radial basis function approximation

Space subdivision to speed-up convex hull construction in E3

Algorithm for placement of reference points and choice of an appropriate variable shape parameter for the RBF approximation