Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs

DOI10.1016/j.jcp.2022.110969OpenAlexW4226106627WikidataQ114013977 ScholiaQ114013977MaRDI QIDQ2133772

Nathaniel Trask, Andy Huang, Xiaozhe Hu

Publication date: 5 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.11799

zbMATH Keywords

de Rham complexPDE-constrained optimizationdiscrete exterior calculusdata driven modelinggraph neural networksscientific machine learning

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx) General theory of differentiable manifolds (58Axx)

Related Items (5)

Learning finite element convergence with the multi-fidelity graph neural network ⋮ De Rham compatible deep neural network FEM ⋮ A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations ⋮ NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators ⋮ Data-driven Whitney forms for structure-preserving control volume analysis

Uses Software

• METIS
• Xyce
• redbKIT
• Adam
• PINNsNTK

Cites Work

• Statistical ranking and combinatorial Hodge theory
• Networks beyond pairwise interactions: structure and dynamics
• Mixed finite elements in \(\mathbb{R}^3\)
• Conservative polytopal mimetic discretization of the incompressible Navier-Stokes equations
• Inferring solutions of differential equations using noisy multi-fidelity data
• Discrete Poincaré lemma
• Quasilinear hyperbolic systems with involutions
• On the mathematical foundations of electrical circuit theory
• Geometric deep learning for computational mechanics. I: Anisotropic hyperelasticity
• DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
• On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Harmonic functions and boundary value problems on a chain complex
• A Conservative Spectral Element Method for Curvilinear Domains
• Finite element exterior calculus, homological techniques, and applications
• Finite element exterior calculus: from Hodge theory to numerical stability
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• The Dirichlet to Neumann Map for a Resistor Network
• Direct Discretization of Planar Div-Curl Problems
• Elliptic Partial Differential Equations of Second Order
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• Topological Signal Processing Over Simplicial Complexes
• Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
• Hodge Laplacians on Graphs
• An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations
• Synthesis of mechanical networks: the inerter
• Reduced Basis Methods for Partial Differential Equations
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