Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization
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Publication:6066782
DOI10.1137/22m1524278zbMath1527.68206arXiv2209.02624MaRDI QIDQ6066782
Roland Maier, Daniel Peterseim, Unnamed Author
Publication date: 13 December 2023
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.02624
Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order elliptic equations (35J15) Theoretical approximation in context of PDEs (35A35)
Cites Work
- Multiscale finite element methods for high-contrast problems using local spectral basis functions
- Multiscale techniques for parabolic equations
- A machine learning approach for efficient uncertainty quantification using multiscale methods
- Explicit computational wave propagation in micro-heterogeneous media
- A multi-stage deep learning based algorithm for multiscale model reduction
- A Bayesian multiscale deep learning framework for flows in random media
- NH-PINN: neural homogenization-based physics-informed neural network for multiscale problems
- DNN expression rate analysis of high-dimensional PDEs: application to option pricing
- A theoretical analysis of deep neural networks and parametric PDEs
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Reconstruction of quasi-local numerical effective models from low-resolution measurements
- Data-driven reduced homogenization for transient diffusion problems with emergent history effects
- Relaxing the CFL condition for the wave equation on adaptive meshes
- Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices
- Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Localized orthogonal decomposition method for the wave equation with a continuum of scales
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors
- Eliminating the pollution effect in Helmholtz problems by local subscale correction
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- Localization of elliptic multiscale problems
- Numerical Homogenization of H(curl)-Problems
- Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization
- Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix
- A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients
- Superconvergence of time invariants for the Gross–Pitaevskii equation
- A generalized finite element method for the strongly damped wave equation with rapidly varying data
- Multiscale scattering in nonlinear Kerr-type media
- Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems
- A Space-Time Multiscale Method for Parabolic Problems
- Deep ReLU networks and high-order finite element methods
- Numerical Homogenization by Localized Orthogonal Decomposition
- Finite element quasi-interpolation and best approximation
- Oversampling for the Multiscale Finite Element Method
- Super-localization of elliptic multiscale problems
- Fast mass lumped multiscale wave propagation modelling
- Expressivity of Deep Neural Networks
- Numerical homogenization beyond scale separation
- Regularity results for Laplace interface problems in two dimensions
- Prediction of numerical homogenization using deep learning for the Richards equation
