Model reduction and neural networks for parametric PDEs (Q2050400)

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scientific article

Language	Label	Description	Also known as
English	Model reduction and neural networks for parametric PDEs	scientific article

Statements

scholarly article

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Model reduction and neural networks for parametric PDEs (English)

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Kaushik Bhattacharya

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Bamdad Hosseini

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Nikola B. Kovachki

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publication date

31 August 2021

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full work available at URL

https://arxiv.org/abs/2005.03180

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zbMATH Keywords

approximation theory

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deep learning

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model reduction

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neural networks

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partial differential equations

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describes a project that uses

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MaRDI profile type

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Solving ill-posed inverse problems using iterative deep neural networks

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Prediction of aerodynamic flow fields using convolutional neural networks

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Data Assimilation in Reduced Modeling

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Learning Theory

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Reduced basis techniques for stochastic problems

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Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

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Approximation of high-dimensional parametric PDEs

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Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs

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ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

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Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps

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Besov priors for Bayesian inverse problems

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

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Stable architectures for deep neural networks

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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Non-intrusive reduced order modeling of nonlinear problems using neural networks

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Reducing the Dimensionality of Data with Neural Networks

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Well-posed Bayesian geometric inverse problems arising in subsurface flow

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Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

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Data Assimilation

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An Introduction to Computational Stochastic PDEs

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A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics

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Lower bounds for approximation by MLP neural networks

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Modal representation of geometrically nonlinear behavior by the finite element method

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On the Sum of the Largest Eigenvalues of a Symmetric Matrix

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Data-driven operator inference for nonintrusive projection-based model reduction

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Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems

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Reduced Basis Methods for Partial Differential Equations

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Probabilistic Forecasting and Bayesian Data Assimilation

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Deep neural networks motivated by partial differential equations

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Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

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On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA

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Refined generalizations of the triangle inequality on Banach spaces

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Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

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A proposal on machine learning via dynamical systems

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Error bounds for approximations with deep ReLU networks

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Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification

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The SMAI journal of computational mathematics

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.5802/SMAI-JCM.74

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Sitelinks

Mathematics(1 entry)

mardi Publication:2050400

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