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DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

Constructive approximation, 2022-02, Vol.55 (1), p.3-71

2022

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On Foundational Discretization Barriers in STFT Phase Retrieval

The Journal of fourier analysis and applications, 2022-04, Vol.28 (2), Article 39

2022

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Towards a transferable fermionic neural wavefunction for molecules

Nature communications, 2024-01, Vol.15 (1), p.120-12, Article 120

2024

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Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces

Foundations of computational mathematics, 2024-08, Vol.24 (4), p.1085-1143

2024

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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

SIAM journal on mathematics of data science, 2020-01, Vol.2 (3), p.631-657

2020

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Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality

Constructive approximation, 2024-02, Vol.59 (1), p.61-111

2024

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Space-time error estimates for deep neural network approximations for differential equations

Advances in computational mathematics, 2023-02, Vol.49 (1), Article 4

2023

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Phase Transitions in Rate Distortion Theory and Deep Learning

Foundations of computational mathematics, 2023-02, Vol.23 (1), p.329-392

2023

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Sobolev-Type Embeddings for Neural Network Approximation Spaces

Constructive approximation, 2023-04, Vol.57 (2), p.579-599

2023

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Uniform error estimates for artificial neural network approximations for heat equations

IMA journal of numerical analysis, 2022-07, Vol.42 (3), p.1991-2054

2022

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Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data

PloS one, 2023-05, Vol.18 (5), p.e0286012

2023

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CA Special Issue on Neural Network Approximation

Constructive approximation, 2022-02, Vol.55 (1), p.1-2

2022

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Anisotropic multiscale systems on bounded domains

Advances in computational mathematics, 2020-04, Vol.46 (2), Article 39

2020

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Handbook of Variational Methods for Nonlinear Geometric Data

1st ed. 2020., 2020

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Stable Gabor Phase Retrieval and Spectral Clustering

Communications on pure and applied mathematics, 2019-05, Vol.72 (5), p.981-1043

2019

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Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies

Frontiers in public health, 2021-08, Vol.9, p.583377

2021

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Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces

SIAM journal on mathematical analysis, 2017-01, Vol.49 (3), p.1895-1911

2017

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Injectivity of Gabor phase retrieval from lattice measurements

Applied and computational harmonic analysis, 2023-01, Vol.62, p.173-193

2023

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Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder

Frontiers in computational neuroscience, 2022-03, Vol.16, p.729556

2022

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Integral representations of shallow neural network with rectified power unit activation function

Neural networks, 2022-11, Vol.155, p.536-550

2022

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Deep Neural Network Approximation Theory

IEEE transactions on information theory, 2021-05, Vol.67 (5), p.2581-2623

2021

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Gabor phase retrieval is severely ill-posed

Applied and computational harmonic analysis, 2021-01, Vol.50, p.401-419

2021

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Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

IMA journal of numerical analysis, 2022-07, Vol.42 (3), p.2055-2082

2022

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Phase Retrieval: Uniqueness and Stability

SIAM review, 2020, Vol.62 (2), p.301-350

2020

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Laguerre minimal surfaces, isotropic geometry and linear elasticity

Advances in computational mathematics, 2009-11, Vol.31 (4), p.391-419

2009

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DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

On Foundational Discretization Barriers in STFT Phase Retrieval

Towards a transferable fermionic neural wavefunction for molecules

Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality

Space-time error estimates for deep neural network approximations for differential equations

Phase Transitions in Rate Distortion Theory and Deep Learning

Sobolev-Type Embeddings for Neural Network Approximation Spaces

Uniform error estimates for artificial neural network approximations for heat equations

Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data

CA Special Issue on Neural Network Approximation

Anisotropic multiscale systems on bounded domains

Handbook of Variational Methods for Nonlinear Geometric Data

Stable Gabor Phase Retrieval and Spectral Clustering

Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies

Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces

Injectivity of Gabor phase retrieval from lattice measurements

Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder

Integral representations of shallow neural network with rectified power unit activation function

Deep Neural Network Approximation Theory

Gabor phase retrieval is severely ill-posed

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

Phase Retrieval: Uniqueness and Stability

Laguerre minimal surfaces, isotropic geometry and linear elasticity

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