Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation ef...
The accurate representation of frontal zones—characterized by sharp scalar gradients—remains a critical challenge in regional objective analysis and data assimilation, particularly when utilizing sparse or stochastically distributed obser...
The spatial distribution of strata under nappe tectonic conditions is highly complex. Conventional approaches, such as dense borehole exploration or intensive in situ investigation, are often costly and difficult to implement for revealing detailed s...
Segmentation is one of the most important parts of medical image analysis. Manual segmentation is very cumbersome, time-consuming, and prone to inter-observer variability. Fully automatic segmentation approaches require a large amount of labeled trai...
This study introduces methods for generating fused precipitation data by applying radial basis function (RBF) interpolation, which integrates radar reflectivity-based data with ground-based precipitation gauge measurements. Rain gauges provide direct...
In multiquadratic radial basis function (MQ-RBF) interpolation, shape parameters have a direct effect on the interpolation accuracy. The paper presents an MQ-RBF interpolation technique with optimized shape parameters for estimating the parameters of...
Basis functions are key in constructing interpolation equations in hull surface modification based on radial basis functions (RBF) interpolation. However, few have studied the selection of basis functions in depth. By comparing several typical basis...
In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radia...
The study develops the displacement error recovery method in a mesh free environment for the finite element solution employing the radial point interpolation (RPI) technique. The RPI technique uses the radial basis functions (RBF), along with polynom...
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,...
Radial basis function (RBF) is gaining popularity in function interpolation as well as in solving partial differential equations thanks to its accuracy and simplicity. Besides, RBF methods have almost a spectral accuracy. Furthermore, the implementat...
To overcome the huge volume problem of light detection and ranging (LiDAR) data for the derivation of digital terrain models (DTMs), a least squares compactly supported radial basis function (CSRBF) interpolation method is proposed in this paper. The...
Accurately generating high-resolution surface grid datasets often involves merging multiple weather observation networks and addressing the challenge of network heterogeneity. This study aims to tackle the problem of accurately interpolating temperat...
Finite element data form an important basis for engineers to undertake analysis and research. In most cases, it is difficult to generate the internal sections of finite element data and professional operations are required. To display the internal da...
Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernel...
Error estimation and adaptive applications help to control the discretization errors in finite element analysis. The study implements the radial point interpolation (RPI)-based error-recovery approaches in finite element analysis. The displacement/pr...
Owing to its high accuracy, the radial basis function (RBF) is gaining popularity in function interpolation and for solving partial differential equations (PDEs). The implementation of RBF methods is independent of the locations of the points and the...
Ionospheric delay errors significantly reduce the positioning accuracy of global navigation satellite systems (GNSSs), whereas precise ionospheric modeling can effectively mitigate this issue. The ionosphere exhibits large-scale symmetry, and spheric...
In this contribution, a scattered data approximation problem, chosen from the literature and using the Radial Basis Function (RBF) approach, is considered for the application of point cloud modelling. Three solutions are investigated for the approxim...
This study focuses on the demand for rapid prediction of the flow field of aero-engine inlet free jet tests and explores the application of radial basis function interpolation (RBF) and backpropagation neural network (BPNN) methods. The proper orthog...
Spatial interpolation is a crucial aspect of soil toxic element pollution research, serving as a vital foundation for pollution assessment, treatment, and sustainability efforts. The selection and adjustment of interpolation methods directly influenc...
Interpolating and approximating scattered scalar and vector data is fundamental in resolving numerous engineering challenges. These methodologies predominantly rely on establishing a triangulated structure within the data domain, typically constraine...
In urban engineering construction, ensuring the stability and safety of subsurface geological structures is as crucial as surface planning and aesthetics. This study proposes a novel multivariate radial basis function (MRBF) interpolant for the three...
The goal of this work was to optimize the combination of natural dyes producing panchromatic absorption matched to the AM1.5 solar spectrum for use in dye sensitized solar cells (DSSCs). Six classes of dyes (Anthocyanins, Betalins, Chlorophyll, Xanth...
Orthogonally splitting imaging pose sensor is a new sensor with two orthogonal line array charge coupled devices (CCDs). Owing to its special structure, there are distortion correction and imaging model problems during the calibration procedure. This...
In recent years, geographically weighted regression (GWR) models have been widely used to address the spatial heterogeneity and spatial autocorrelation of PM2.5, but these studies have not fully considered the effects of all potential variables on PM...
Accurate spatial interpolation of environmental data requires utilizing flexible models that can capture complex spatial patterns. In this paper, we present two improved dual kriging (DK) models comprising a nonlinear trend function that combines Gau...
This study focuses on delineating the spatial boundaries of heavy metal soil contamination in populated areas. Fieldwork was conducted to collect soil samples using various sampling techniques from the Massiv 52, Novy Svet settlement and the Severnay...
Function interpolation and approximation are classical problems of vital importance in many science/engineering areas and communities. In this paper, we propose a powerful methodology for the optimal placement of centers, when approximating or interp...
In this paper we improve an efficient implicit surface reconstruction method based on the surface following method for the radial basis functions interpolant. The method balances the reconstruction efficiency and the evaluation efficiency in the proc...
Fluid structure interaction (FSI) is a complex phenomenon that in several applications cannot be neglected. Given its complexity and multi-disciplinarity the solution of FSI problems is difficult and time consuming, requiring not only the solution of...
Accurate and spatially consistent rainfall estimation is essential for hydrological modeling and flood risk mitigation, especially in mountainous tropical regions with sparse observational networks and highly heterogeneous rainfall. This study presen...
Learning in neural networks with locally-tuned neuron models such as radial Basis Function (RBF) networks is often seen as instable, in particular when multi-layered architectures are used. Furthermore, universal approximation theorems for single-lay...
This paper proposes a localized Hermite method of approximate particular solutions (LHMAPS) for solving the 2D inhomogeneous Helmholtz-type equations. Building on the local scheme of the localized method of approximate particular solutions (LMAPS) fo...
In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are...
This is a continuation of our previous study on the shape parameter contained in the shifted surface spline. We insist that the data points be purely scattered without meshes and the domain can be of any shape when conducting function interpolation b...
This paper presents a new means to control the processes involving energy conversion. Electric machines fed by electronic converters provide a useful power defined by the inner product of two generalized energetic variables: effort and flow. The nove...
In this paper, we present an easily accessible approach to finding a suitable shape parameter in the shifted surface spline for function interpolation. We aim at helping more readers, including mathematicians and non-mathematicians, to use our method...
The distributed measured data in large regions and remote locations, along with a need to estimate climatic data for point sites where no data have been recorded, has encouraged the implementation of spatial interpolation techniques. Recently, the in...
This paper presents the construction of a family of radial functions aimed at emulating the behavior of the radial basis function known as thin plate spline (TPS). Additionally, a method is proposed for applying fractional derivatives, both partially...
This paper offers an approach to computing Radial Basis Function–Finite Difference (RBF-FD) weights by integrating a kernel-based function. We derive new weight sets that effectively approximate both the first and second differentiations of a f...
The traditional radial basis function collocation method (RBFCM) has poor stability when solving two-dimensional elastic problems, and the numerical results are very sensitive to shape parameters, especially in solving elastic problems. In this paper...
An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the co...
The flow dynamics of low-yield horizontal wells demonstrate considerable complexity and unpredictability, chiefly attributable to the structural attributes of the wellbore and the interplay of gas–water two-phase flow. In horizontal wellbores,...
The electromagnetic radiation (EMR) data collected along a road have a largely empty region overall, while they have a linear distribution locally. Moreover, the traditional spatial interpolation method is not suitable for the electromagnetic radiati...
The characterization of rotating aeroacoustic sources using microphone array methods has been proven to be a useful tool. One technique to identify rotating sources is the virtual rotating array method. The method interpolates the pressure time data...
Precipitation is a significant input variable required in hydrological models such as the Soil & Water Assessment Tool (SWAT). The utilization of inaccurate precipitation data can result in the poor representation of the true hydrologic condition...
The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, eff...
This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent varia...
Coal seam thickness prediction is crucial in coal mine design and coal mining. In order to improve the prediction accuracy, an improved Kriging interpolation method on the basis of efficient data and Radial Basis Function (RBF-Kriging) is firstly pro...
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