Physics-informed \textsc{MeshGraphNets} (PI-MGNs): neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes
DOI10.1016/j.cma.2024.117102MaRDI QIDQ6588258
Clemens Zimmerling, Gerhard Neumann, Tobias Würth, Niklas Freymuth, Luise Kärger
Publication date: 15 August 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
partial differential equationsmachine learningsurrogate modelgraph neural networkphysics-based simulation
Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10) Basic methods in thermodynamics and heat transfer (80M99) Diffusive and convective heat and mass transfer, heat flow (80A19)
Cites Work
- DGM: a deep learning algorithm for solving partial differential equations
- PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
- Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems
- PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
- Physics-informed PointNet: a deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries
- Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
- Physics-informed neural network for modelling the thermochemical curing process of composite-tool systems during manufacture
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Prediction of aerodynamic flow fields using convolutional neural networks
- The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab
- Isogeometric analysis-based physics-informed graph neural network for studying traffic jam in neurons
- The Finite Element Method: Theory, Implementation, and Applications
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