9 papers
A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training
Andrea Angino, Bindi Çapriqi, Shega Likaj +2
Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region me…
Protect the Brain When Treating the Heart: Feasibility of 2.5D U-Net for Real-Time Gaseous Microemboli Detection
Andrea Angino, Ken Trotti, Diego Ulisse Pizzagalli +3
Gaseous microemboli (GME) represent a common complication of cardiac structural interventions across both surgical and transcatheter approaches. Intraoperative transesophageal echo…
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…
Data-Parallel Neural Network Training via Nonlinearly Preconditioned Trust-Region Method
Samuel A. Cruz Alegría, Ken Trotti, Alena Kopaničáková +1
Parallel training methods are increasingly relevant in machine learning (ML) due to the continuing growth in model and dataset sizes. We propose a variant of the Additively Precond…
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…