46 citations · 101 across the 35 of their papers we have counts for
38 papers
Adaptive Non-Linear Partition of Unity Methods for Scattered Data Interpolation with Discontinuities
Adeeba Haider, Roberto Cavoretto, Juan Ruiz-Álvarez +1
Scattered data approximation with discontinuities is challenging due to the Gibbs phenomenon, which significantly reduces accuracy near interfaces. The recently introduced Non-Line…
Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks
Roberto Cavoretto, Alessandra De Rossi, Adeeba Haider +1
Kolmogorov-Arnold Networks (KANs) approximate multivariate functions using learnable univariate edge functions, typically parameterized by B-spline bases. Although effective, splin…
Graph Neural Networks for Community Detection in Graph Signal Analysis
Roberto Cavoretto, Alessandra De Rossi, Enrico Montini
Community detection is a central problem in graph analysis, with applications ranging from network science to graph signal processing. In recent years, Graph Neural Networks (GNNs)…
Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning
A. Noorizadegan, R. Cavoretto, D. L. Young +1
Background: Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equa…
Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
R. Cavoretto, F. Dell'Accio, A. De Rossi +2
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet prob…
Node-Bound Communities for Partition of Unity Interpolation on Graphs
Roberto Cavoretto, Alessandra De Rossi, Sandro Lancellotti +1
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach…
Bayesian Approach for Radial Kernel Parameter Tuning
Roberto Cavoretto, Alessandra De Rossi, Sandro Lancellotti
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively fi…
Node-Binded Communities for Interpolation on Graphs
Roberto Cavoretto, Alessandra De Rossi, Sandro Lancellotti +1
Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic…
Parameter Tuning in the Radial Kernel-Based Partition of Unity Method by Bayesian Optimization
Roberto Cavoretto, Alessandra De Rossi, Sandro Lancellotti +1
In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using…
A Bayesian Approach for Simultaneously Radial Kernel Parameter Tuning in the Partition of Unity Method
Roberto Cavoretto, Alessandra De Rossi, Sandro Lancellotti +1
In this paper, Bayesian optimisation is used to simultaneously search the optimal values of the shape parameter and the radius in radial basis function partition of unity interpola…
Numerical cubature on scattered data by adaptive interpolation
R. Cavoretto, F. Dell'Accio, A. De Rossi +4
We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, P…
Adaptive LOOCV-based kernel methods for solving time-dependent BVPs
Roberto Cavoretto
In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based met…
An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations
R. Cavoretto A. De Rossi
In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introd…
Partition of Unity Methods for Signal Processing on Graphs
Roberto Cavoretto, Alessandra De Rossi, Wolfgang Erb
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation sc…
Anisotropic weights for RBF-PU interpolation with subdomains of variable shapes
R. Cavoretto, A. De Rossi, G. E. Fasshauer +2
The partition of unity (PU) method, performed with local radial basis function (RBF) approximants, has already been proved to be an effective tool for solving interpolation or coll…
Adaptive meshless refinement schemes for RBF-PUM collocation
R. Cavoretto, A. De Rossi
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method.…
A RBF partition of unity collocation method based on finite difference for initial-boundary value problems
G. Garmanjani, R. Cavoretto, M. Esmaeilbeigi
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect t…
Numerical Methods for Pulmonary Image Registration
Roberto Cavoretto, Alessandra De Rossi, Roberta Freda +2
Due to complexity and invisibility of human organs, diagnosticians need to analyze medical images to determine where the lesion region is, and which kind of disease is, in order to…
Hermite-Birkhoff interpolation on scattered data on the sphere and other manifolds
Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expre…
Optimal selection of local approximants in RBF-PU interpolation
Roberto Cavoretto, Alessandra De Rossi, Emma Perracchione
The Partition of Unity (PU) method, performed with local Radial Basis Function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpol…
On the topology preservation of Gneiting's functions in image registration
Chiara Bosica, Roberto Cavoretto, Alessandra De Rossi +1
The purpose of image registration is to determine a transformation such that the transformed version of the source image is similar to the target one. In this paper we focus on lan…
RBF-PU Interpolation with Variable Subdomain Sizes and Shape Parameters
Roberto Cavoretto, Alessandra De Rossi, Emma Perracchione
In this paper, we deal with the challenging computational issue of interpolating large data sets, with eventually non-homogeneous densities. To such scope, the Radial Basis Functio…
Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds
Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi
We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolan…
Partition of unity interpolation using stable kernel-based techniques
R. Cavoretto, S. De Marchi, A. De Rossi +2
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) met…