4 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…