Related papers: Stable Mesh-Free Variational Radial Basis Function…
This work proposes a first extensive analysis of the Vehicle Routing Problem with Fractional Objective Function (vrpfof). We investigate how the principal techniques used either in the context of fractional programming or in the context of…
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate derivatives of functions from values at scattered nodes…
We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…
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…
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…
For boundary value problem of an elliptic equation with variable coefficients describing the physical field distribution in inhomogeneous media, the Levi function can represent the solution in terms of volume and surface potentials, with…
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
It is well understood that boundary conditions (BCs) may cause global radial basis function (RBF) methods to become unstable for hyperbolic conservation laws (CLs). Here we investigate this phenomenon and identify the strong enforcement of…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic…
We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
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…
In this paper we present a refined Radial Basis Function-generated Finite Difference (RBF-FD) solution for a non-Newtonian fluid in a closed differentially heated cavity. The non-Newtonian behaviour is modelled with the Ostwald-de Waele…
This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on…
In safety-critical control, managing safety constraints with high relative degrees and uncertain obstacle dynamics pose significant challenges in guaranteeing safety performance. Robust Control Barrier Functions (RCBFs) offer a potential…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…