14 citations · 45 across the 6 of their papers we have counts for
6 papers
Deep Learning Accelerated Algebraic Multigrid Methods for Polytopal Discretizations of Second-Order Differential Problems
Paola F. Antonietti, Matteo Caldana, Lorenzo Gentile +1
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable param…
MAGNET: an open-source library for mesh agglomeration by Graph Neural Networks
Paola F. Antonietti, Matteo Caldana, Ilario Mazzieri +1
We introduce MAGNET, an open-source Python library designed for mesh agglomeration in both two- and three-dimensions, based on employing Graph Neural Networks (GNN). MAGNET serves…
Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
Matteo Caldana, Jan S. Hesthaven
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog t…
Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning
Matteo Caldana, Paola F. Antonietti, Luca Dede'
Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon. Artificial viscosity is a po…
A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs
Matteo Caldana, Paola F. Antonietti, Luca Dede'
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discr…
Accelerating Algebraic Multigrid Methods via Artificial Neural Networks
Paola F. Antonietti, Matteo Caldana, Luca Dede'
We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the…