Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs

DOI10.1016/j.jcp.2023.112242arXiv2112.06660MaRDI QIDQ6162913

Publication date: 16 June 2023

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

Full work available at URL: https://arxiv.org/abs/2112.06660

zbMATH Keywords

Fourier multi-scale activation function DNN subspace-decomposed

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

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Generalized multiscale finite element methods (GMsFEM)
Numerical homogenization of the acoustic wave equations with a continuum of scales
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast
Weak adversarial networks for high-dimensional partial differential equations
The heterogeneous multiscale methods
Machine learning from a continuous viewpoint. I
Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
The variational multiscale method -- a paradigm for computational mechanics
A multiscale finite element method for elliptic problems in composite materials and porous media
Anomalous slow diffusion from perpetual homogenization.
Inferring solutions of differential equations using noisy multi-fidelity data
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
DGM: a deep learning algorithm for solving partial differential equations
Kernel flows: from learning kernels from data into the abyss
Adaptive activation functions accelerate convergence in deep and physics-informed 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
A proposal on machine learning via dynamical systems
Adaptivity and variational stabilization for convection-diffusion equations
Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
A localized orthogonal decomposition method for semi-linear elliptic problems
Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
Analysis of the heterogeneous multiscale method for elliptic homogenization problems
Localization of elliptic multiscale problems
Multiscale Finite Element Methods
Homogenization of Parabolic Equations with a Continuum of Space and Time Scales
Iterative Methods by Space Decomposition and Subspace Correction
An Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems
A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
Deep Potential: A General Representation of a Many-Body Potential Energy Surface
Machine Learning and Computational Mathematics
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction
Bayesian Numerical Homogenization
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients

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