Related papers: A Modified Hermite Radial Basis Function for Accur…

The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis functions (RBF-FD). For certain classes of PDEs this…

Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in…

A major obstacle to the application of the standard Radial Basis Function-generated Finite Difference (RBF-FD) meshless method is constituted by its inability to accurately and consistently solve boundary value problems involving Neumann…

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…

In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…

A grouping-circular-based (GCB) greedy algorithm is proposed to promote the efficiency of mesh deformation. By incorporating the multigrid concept that the computational errors on the fine mesh can be approximated with those on the coarse…

We propose a differential radial basis function (RBF) network termed RBF-DiffNet -- whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF -- to make the baseline RBF network robust to noise in…

Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for…

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…

The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a theoretical framework for this problem by leveraging a…

We study the problem of selecting the shape parameter in Radial Basis function (RBF) interpolation using leave-one-out-cross-validation (LOOCV). Since the classical LOOCV formula requires repeated solves with a dense $N \times N$ kernel…

We introduce a polyanalytic extension of the Gaussian radial basis function (RBF) kernel by computing the action of the convolution operator on normalized Hermite functions. In particular, using the Zaremba-Bergman formula we derive an…

Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for…

Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite…

The purpose of this study is to apply some new RBF collocation schemes and recently-developed kernel RBFs to various types of partial differential equation systems. By analogy with the Fasshauer's Hermite interpolation, we recently…

Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the convergence theories in the literature, when applied to nonuniform…

We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is on practical accuracy, robustness and efficiency. To address…

We present a computational method for solving the coupled problem of chemical transport in a fluid (blood) with binding/unbinding of the chemical to/from cellular (platelet) surfaces in contact with the fluid, and with transport of the…