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It is a crucial basis to improve the performance of neural network by constructing an appropriate activation function. This paper proposes a novel modulation window radial basis function neural network (MW-RBFNN) with an adjustable activation function. In this MW-RBFNN, a raised cosine radial basis function (RC-RBF) is adaptively modulated by an exponential function, and served as a shape-tunable activation function of MW-RBFNN. Compared with the basic RC-RBF neural network, the approximating ability of MW-RBFNN is improved due to its shape-tunable activation function. Besides, the computation of MW-RBFNN is far less than that of Gaussian radial basis function neural network (GRBFNN) because the MW-RBFNN is compactly supported. The training algorithm of MW-RBFNN is provided and its approximating ability is proved. Moreover, the regulation mechanism of the modulation index for the NN’s performance is proved and the regulating algorithm of the modulation index in MW-RBFNN is given. The computational complexity of MW-RBFNN is also analyzed. Five typical application cases are presented to illustrate the effectiveness of this proposed MW-RBFNN.

Deep neural networks (DNNs) can face limitations during training for recognition, motivating this study to improve recognition capabilities by optimizing deep learning features for hand gesture image recognition. We propose a novel approach that enhances features from well-trained DNNs using an improved radial basis function (RBF) neural network, targeting recognition within individual gesture categories. We achieve this by clustering images with a self-organizing map (SOM) network to identify optimal centers for RBF training. Our enhanced SOM, employing the Hassanat distance metric, outperforms the traditional K-Means method across a comparative analysis of various distance functions and the expanded number of cluster centers, accurately identifying hand gestures in images. Our training pipeline learns from hand gesture videos and static images, addressing the growing need for machines to interact with gestures. Despite challenges posed by gesture videos, such as sensitivity to hand pose sequences within a single gesture category and overlapping hand poses due to the high similarities and repetitions, our pipeline achieved significant enhancement without requiring time-related training data. We also improve the recognition of static hand pose images within the same category. Our work advances DNNs by integrating deep learning features and incorporating SOM for RBF training.

The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016 Stud. Appl. Math. 137, 174–188. (doi:10.1111/sapm.12106)). The method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set. This article generalizes this method to arbitrary smooth closed surfaces.

The hardware implementation of signal microprocessors based on superconducting technologies seems relevant for a number of niche tasks where performance and energy efficiency are critically important. In this paper, we consider the basic elements for superconducting neural networks on radial basis functions. We examine the static and dynamic activation functions of the proposed neuron. Special attention is paid to tuning the activation functions to a Gaussian form with relatively large amplitude. For the practical implementation of the required tunability, we proposed and investigated heterostructures designed for the implementation of adjustable inductors that consist of superconducting, ferromagnetic, and normal layers.

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R2, and a comparison with another work is analyzed.

Wind power industry plays an important role in promoting the development of low-carbon economic and energy transformation in the world. However, the randomness and volatility of wind speed series restrict the healthy development of the wind power industry. Accurate wind speed prediction is the key to realize the stability of wind power integration and to guarantee the safe operation of the power system. In this paper, combined with the Empirical Mode Decomposition (EMD), the Radial Basis Function Neural Network (RBF) and the Least Square Support Vector Machine (SVM), an improved wind speed prediction model based on Empirical Mode Decomposition (EMD-RBF-LS-SVM) is proposed. The prediction result indicates that compared with the traditional prediction model (RBF, LS-SVM), the EMDRBF-LS-SVM model can weaken the random fluctuation to a certain extent and improve the short-term accuracy of wind speed prediction significantly. In a word, this research will significantly reduce the impact of wind power instability on the power grid, ensure the power grid supply and demand balance, reduce the operating costs in the grid-connected systems, and enhance the market competitiveness of the wind power.

Purpose This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains. Design/methodology/approach The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space. Findings First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders O(τ1+γ) and O(τ2−γ) for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique. Originality/value The proposed numerical technique is flexible for different computational domains.

Classical radial basis function network (RBFN) is widely used to process the non-linear separable data sets with the introduction of activation functions. However, the setting of parameters for activation functions is random and the distribution of patterns is not taken into account. To process this issue, some scholars introduce the kernel clustering into the RBFN so that the clustering results are related to the parameters about activation functions. On the base of the original kernel clustering, this study further discusses the influence of kernel clustering on an RBFN when the setting of kernel clustering is changing. The changing involves different kernel-clustering ways [bubble sort (BS) and escape nearest outlier (ENO)], multiple kernel-clustering criteria (static and dynamic) etc. Experimental results validate that with the consideration of distribution of patterns and the changes of setting of kernel clustering, the performance of an RBFN is improved and is more feasible for corresponding data sets. Moreover, though BS always costs more time than ENO, it still brings more feasible clustering results. Furthermore, dynamic criterion always cost much more time than static one, but kernel number derived from dynamic criterion is fewer than the one from static.