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

Analysis and applications, 2019-01, Vol.17 (1), p.19-55

2019

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Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs

1st Edition 2023, 2023

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Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case

Constructive approximation, 2022-06, Vol.55 (3), p.987-1036

2022

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Neural and spectral operator surrogates: unified construction and expression rate bounds

Advances in computational mathematics, 2024-08, Vol.50 (4), Article 72

2024

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Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case

Constructive approximation, 2022-06, Vol.55 (3), p.919-986

2022

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Convergence rates of high dimensional Smolyak quadrature

ESAIM: Mathematical Modelling and Numerical Analysis, 2020-07, Vol.54 (4), p.1259-1307

2020

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Deep neural network expression of posterior expectations in Bayesian PDE inversion

Inverse problems, 2020-12, Vol.36 (12), p.125011

2020

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Shape Holomorphy of the Stationary Navier--Stokes Equations

SIAM journal on mathematical analysis, 2018-01, Vol.50 (2), p.1720-1752

2018

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Electromagnetic wave scattering by random surfaces: Shape holomorphy

Mathematical models & methods in applied sciences, 2017-11, Vol.27 (12), p.2229-2259

2017

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Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)

SIAM/ASA journal on uncertainty quantification, 2023-03, Vol.11 (1), p.199-234

2023

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Deep neural network expression of posterior expectations in Bayesian PDE inversionThe main part of the paper was written while LH was at the Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland, and during the postdoctoral stay of JZ to the Department of Aeronautics and Astronautics, MIT, 02139 Cambridge, MA, USA. JZ is supported by the Swiss National Science Foundation under Early Postdoc.Mobility Fellowship 184530. CS acknowledges stimulating discussions at

Inverse problems, 2020-12, Vol.36 (12)

2020

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Multilevel approximation of parametric and stochastic PDES

Mathematical models & methods in applied sciences, 2019-08, Vol.29 (9), p.1753-1817

2019

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De Rham compatible Deep Neural Network FEM

Neural networks, 2023-08, Vol.165, p.721-739

2023

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Multilevel domain uncertainty quantification in computational electromagnetics

Mathematical models & methods in applied sciences, 2023-04, Vol.33 (4), p.877-921

2023

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Domain Uncertainty Quantification in Computational Electromagnetics

SIAM/ASA journal on uncertainty quantification, 2020-01, Vol.8 (1), p.301-341

2020

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Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions

SIAM/ASA journal on uncertainty quantification, 2019-01, Vol.7 (3), p.913-947

2019

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Multilevel Smolyak Sparse-Grid Interpolation and Quadrature

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, Vol.2334, p.145-195

2023

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Smolyak Sparse-Grid Interpolation and Quadrature

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, Vol.2334, p.123-143

2023

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Parametric Posterior Analyticity and Sparsity in BIPs

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, Vol.2334, p.115-121

2023

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Elliptic Divergence-Form PDEs with Log-Gaussian Coefficient

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, Vol.2334, p.39-78

2023

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Sparsity for Holomorphic Functions

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, Vol.2334, p.79-113

2023

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Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization

1, 2022

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Conclusions

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, p.197-198

2023

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Preliminaries

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, p.11-38

2023

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Introduction

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs, 2023, p.1-10

2023

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

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs

Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case

Neural and spectral operator surrogates: unified construction and expression rate bounds

Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case

Convergence rates of high dimensional Smolyak quadrature

Deep neural network expression of posterior expectations in Bayesian PDE inversion

Shape Holomorphy of the Stationary Navier--Stokes Equations

Electromagnetic wave scattering by random surfaces: Shape holomorphy

Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)

Multilevel approximation of parametric and stochastic PDES

De Rham compatible Deep Neural Network FEM

Multilevel domain uncertainty quantification in computational electromagnetics

Domain Uncertainty Quantification in Computational Electromagnetics

Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions

Multilevel Smolyak Sparse-Grid Interpolation and Quadrature

Smolyak Sparse-Grid Interpolation and Quadrature

Parametric Posterior Analyticity and Sparsity in BIPs

Elliptic Divergence-Form PDEs with Log-Gaussian Coefficient

Sparsity for Holomorphic Functions

Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization

Conclusions

Preliminaries

Introduction

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