115 citations · 257 across the 10 of their papers we have counts for
10 papers
On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon
Ferdinando Auricchio, Maria Roberta Belardo, Gianluca Fabiani +2
In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by t…
The effect of time discretization on the solution of parabolic PDEs with ANNs
Francesco Calabrò, Salvatore Cuomo, Daniela di Serafino +2
We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational c…
Deep Learning for the Approximation of a Shape Functional
F. Calabrò, S. Cuomo, F. Giampaolo +4
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep…
Numerical Solution and Bifurcation Analysis of Nonlinear Partial Differential Equations with Extreme Learning Machines
Gianluca Fabiani, Francesco Calabrò, Lucia Russo +1
We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the comp…
Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
Francesco Calabrò, Gianluca Fabiani, Constantinos Siettos
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal funct…
Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
G. Radenković, A. Borković, B. Marussig
The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the…
Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
A. Aimi, F. Calabrò, M. Diligenti +3
This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometr…
How to get high order without loosing efficiency for the resolution of systems of nonlinear equations: A short review of Shamanskii's m method
Francesco Calabrò, Andrea Polsinelli
We present relations between some recently proposed methods for the solution of a nonlinear system of equations. In particular, we review the Shamanskii's m method, that is an iter…
Fast formation of isogeometric Galerkin matrices by weighted quadrature
Francesco Calabrò, Giancarlo Sangalli, Mattia Tani
In this paper we propose an algorithm for the formation of matrices of isogeometric Galerkin methods. The algorithm is based on three ideas. The first is that we perform the extern…
Quadrature With Respect to Binomial Measures
Francesco Calabró, Antonio Corbo Esposito
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for…