In this paper we consider numerical integration over the sphere by radial basis functions (RBF). After a brief introduction on RBF and spherical radial basis functions (SRBF), we show how to compute integrals of functions whose values are known at scattered data points. Numerical examples are given.

In this paper, a novel hybrid Radial Basis Function Neural Network (RBF–NN) ensemble model is proposed for rainfall forecasting based on Kernel Partial Least Squares Regression (K–PLSR). In the process of ensemble modeling, the first stage the initial data set is divided into different training sets by used Bagging and Boosting technology. In the second stage, these training sets are input to t...

In this paper we propose a strategy to shape adaptive radial basis functions through potential functions. DYPOF (DYnamic POtential Functions) neural network (NN) is designed based on radial basis functions (RBF) NN with a two-stage training procedure. Static (fixed number of RBF) and dynamic (ability to add or delete one or more RBF) versions of our learning algorithm are introduced. We investi...

Radial Basis Function Networks (RBFNs) have been successfully employed in several function approximation and pattern recognition problems. In RBFNs, radial basis functions are used to compute the activation of artificial neurons. The use of different radial basis functions in RBFN has been reported in the literature. Here, the use of the q-Gaussian function as a radial basis function in RBFNs i...

Radial Basis Functions (RBF) interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues. The RBF interpolation is convenient for un-ordered data sets in n-dimensional space, in general. This approach is convenient especially for a higher dimension N 2 conversion to ordered data set, e.g. using tessellation, is computationally v...

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the ...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson’s equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomoge...

We introduce a master–worker framework for parallel global optimization of computationally expensive functions using response surface models. In particular, we parallelize two radial basis function (RBF) methods for global optimization, namely, the RBF method by Gutmann [Gutmann, H.M., 2001a. A radial basis function method for global optimization. Journal of Global Optimization 19(3), 201–227] ...