Discontinuous Galerkin

Discontinuous Galerkin (DG) methods are high-order numerical techniques for solving partial differential equations, particularly useful for problems with discontinuities like shocks. Current research focuses on improving DG's efficiency and accuracy, particularly through the integration of machine learning (ML) techniques such as neural networks and reinforcement learning. These ML approaches are used to develop adaptive mesh refinement strategies, optimize artificial viscosity models for improved shock capturing, and even learn subgrid-scale models for computationally efficient simulations of complex fluid flows. The resulting advancements promise significant improvements in the accuracy and speed of simulations across various scientific and engineering disciplines.

Papers

September 27, 2024

A model-constrained Discontinuous Galerkin Network (DGNet) for Compressible Euler Equations with Out-of-Distribution Generalization
Hai Van Nguyen (1), Jau-Uei Chen (1), William Cole Nockolds (2), Wesley Lao (2), Tan Bui-Thanh (1 and 2) ((1) Department of Aerospace Engineering and Engineering Mechanics, the University of Texas at Austin, Texas (2) The Oden Institute for Computational Engineering and Sciences, the University of Texas at Austin, Texas)
Large Scale Distribution Generalization Compressible Flow Discontinuous Galerkin

February 26, 2024

Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning
Matteo Caldana, Paola F. Antonietti, Luca Dede'
Physic Informed Machine Learning Conservation Law Discontinuous Galerkin Artificial Viscosity

October 29, 2023

Enhancing Low-Order Discontinuous Galerkin Methods with Neural Ordinary Differential Equations for Compressible Navier--Stokes Equations
Shinhoo Kang, Emil M. Constantinescu
Neural Ordinary Differential Equation Subgrid Scale Compressible Flow Discontinuous Galerkin

September 12, 2023

Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning
Andrea Beck, Marius Kurz
Large Eddy Simulation Discretization Method Discontinuous Galerkin Eddy Viscosity

July 9, 2023

A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I
Rajat Arora
Partial Differential Equation Deep Learning Framework Numerical Experiment Different PaRT Data Discretization Hyperbolic Partial Differential Equation Discontinuous Galerkin

October 31, 2022

Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers
P. F. Antonietti, N. Farenga, E. Manuzzi, G. Martinelli, L. Saverio
Graph Neural Network Financial Application Multigrid Method Kernel Multigrid Discontinuous Galerkin Polygonal Mapping Algebraic Multigrid

February 25, 2022

Machine Learning based refinement strategies for polyhedral grids with applications to Virtual Element and polyhedral Discontinuous Galerkin methods
P. F. Antonietti, F. Dassi, E. Manuzzi
Machine Learning Iterative Refinement Voronoi Tessellation Polygonal Mapping Discontinuous Galerkin

Discontinuous Galerkin

Papers

A model-constrained Discontinuous Galerkin Network (DGNet) for Compressible Euler Equations with Out-of-Distribution Generalization

Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning

Enhancing Low-Order Discontinuous Galerkin Methods with Neural Ordinary Differential Equations for Compressible Navier--Stokes Equations

Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning

A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I

Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers

Machine Learning based refinement strategies for polyhedral grids with applications to Virtual Element and polyhedral Discontinuous Galerkin methods