activity
20212025
most citedA Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs

14 citations · 45 across the 6 of their papers we have counts for

collaborators

6 papers

math.NA2025

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…

math.NA2025

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…

math.NA2024★ 13 cited

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…

math.NA2024★ 6 cited

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…

math.NA2023★ 14 cited

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…

math.NA2021★ 12 cited

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…