6 papers · 1 filter
An Additively Preconditioned Trust Region Strategy for Machine Learning
Samuel Cruz Alegría, Bindi Çapriqi, Shega Likaj +2
Modern machine learning, especially the training of deep neural networks, depends on solving large-scale, highly nonconvex optimization problems, whose objective function exhibit a…
A note on the convergence of multigrid methods for the Riesz-space equation and an application to image deblurring
Danyal Ahmad, Marco Donatelli, Mariarosa Mazza +2
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional diffe…
Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods
Ken Trotti, Samuel A. Cruz Alegría, Alena Kopaničáková +1
We propose to train neural networks (NNs) using a novel variant of the ``Additively Preconditioned Trust-region Strategy'' (APTS). The proposed method is based on a parallelizable…
A domain splitting strategy for solving PDEs
Ken Trotti
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the -dimensional advection-…
A smoothing analysis for multigrid methods applied to tempered fractional problems
D. Ahmad, M. Donatelli, M. Mazza +2
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted…
Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes
Marco Donatelli, Rolf Krause, Mariarosa Mazza +1
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due t…