The Random Feature Model for Input-Output Maps between Banach Spaces (Q3382802)

scientific article; zbMATH DE number 7398767

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English	The Random Feature Model for Input-Output Maps between Banach Spaces	scientific article; zbMATH DE number 7398767

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instance of

scholarly article

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title

The Random Feature Model for Input-Output Maps between Banach Spaces (English)

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SIAM Journal on Scientific Computing

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publication date

22 September 2021

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full work available at URL

https://arxiv.org/abs/2005.10224

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zbMATH Keywords

random feature

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surrogate model

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emulator

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solution map

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high-dimensional approximation

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model reduction

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parametric PDE

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supervised learning

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data-driven computing

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describes a project that uses

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Theory of Reproducing Kernels

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On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions

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Learning data-driven discretizations for partial differential equations

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An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations

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Universal approximation bounds for superpositions of a sigmoidal function

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Reconciling modern machine-learning practice and the classical bias–variance trade-off

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Model Reduction and Approximation

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Q5488485

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Adaptive finite element methods for elliptic equations with non-smooth coefficients

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Algorithms for Numerical Analysis in High Dimensions

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Model reduction and neural networks for parametric PDEs

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Data-driven forward discretizations for Bayesian inversion

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Optimal rates for the regularized least-squares algorithm

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VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM

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A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients

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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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Optimal weighted least-squares methods

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MCMC methods for functions: modifying old algorithms to make them faster

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On the mathematical foundations of learning

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A least-squares approximation of partial differential equations with high-dimensional random inputs

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Hierarchical Bayesian level set inversion

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Q5189317

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Solving electrical impedance tomography with deep learning

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Meta-learning pseudo-differential operators with deep neural networks

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Q4231113

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Numerical solution of the parametric diffusion equation by deep neural networks

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Elliptic partial differential equations of second order

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Reproducing Kernel Hilbert Spaces for Parametric Partial Differential Equations

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Stable architectures for deep neural networks

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

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Optimization with PDE Constraints

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Operator-valued kernels for learning from functional response data

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Fourth-Order Time-Stepping for Stiff PDEs

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Kernel-based reconstructions for parametric PDEs

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Blow up and regularity for fractal Burgers equation

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Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

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Variational training of neural network approximations of solution maps for physical models

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Machine learning from a continuous viewpoint. I

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Spatial variation. 2nd ed

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On Learning Vector-Valued Functions

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Bayesian learning for neural networks

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A physics-informed operator regression framework for extracting data-driven continuum models

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Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

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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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Functional multi-layer perceptron: A nonlinear tool for functional data analysis

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Deep neural networks motivated by partial differential equations

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Data driven approximation of parametrized PDEs by reduced basis and neural networks

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

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DGM: a deep learning algorithm for solving partial differential equations

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Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification

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A proposal on machine learning via dynamical systems

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A mean-field optimal control formulation of deep learning

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

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Scattered Data Approximation

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Q3394879

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ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

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Data-driven deep learning of partial differential equations in modal space

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

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Identifiers

DOI

10.1137/20M133957X

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:3382802