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Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising e.g.
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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On a BPX-preconditioner for P 1 {\rm P}1 elements
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Element-by-element construction of wavelets satisfying stability and moment conditions
W. Dahmen and R. Stevenson · 1999
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Complexifications of real Banach spaces, polynomials and multilinear maps
G. A. Muñoz, Y. Sarantopoulos, and A. Tonge · 1999
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Approximation theory of the MLP model in neural networks
A. Pinkus · 1999
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An introduction to frames and Riesz bases
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Hierarchical Riesz bases for H s ( Ω ) , 1 < s < 5 2 H^{s}(\Omega),\ 1<s<{5\over 2}
O. Davydov and R. Stevenson · 2005
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Multilevel frames for sparse tensor product spaces
H. Harbrecht, R. Schneider, and C. Schwab · 2008
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Function Spaces and Wavelets on Domains
H. Triebel · 2008
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Sparse tensor discretization of elliptic SPDEs
M. Bieri, R. Andreev, and C. Schwab · 2009
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Adaptive wavelet methods for solving operator equations: an overview
R. Stevenson · 2009
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Convergence rates of best N N -term Galerkin approximations for a class of elliptic sPDEs
A. Cohen, R. DeVore, and Ch. Schwab · 2010
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F. W. J. Oliver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors · 2010
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Bases in function spaces, sampling, discrepancy, numerical integration
H. Triebel · 2010
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Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE’s
A. Cohen, R. DeVore, and Ch. Schwab · 2011
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Continuous shearlet tight frames
P. Grohs · 2011
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A basis theory primer
C. Heil · 2011
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Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
Ch. Schwab and C. J. Gittelson · 2011
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Mercer’s theorem on general domains: on the interaction between measures, kernels, and RKHSs
I. Steinwart and C. Scovel · 2012
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High-dimensional adaptive sparse polynomial interpolation and applications to parametric pdes
A. Chkifa, A. Cohen, and C. Schwab · 2013
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On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
M. A. Chkifa · 2013
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Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
A. L. Teckentrup, R. Scheichl, M. B. Giles, and E. Ullmann · 2013
Fourier neural operator for parametric partial differential equations
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2021
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A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data, 2021
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Arbitrary-depth universal approximation theorems for operator neural networks, 2021
A. Yu, C. Becquey, D. Halikias, M. E. Mallory, and A. Townsend · 2021
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Metric hypertransformers are universal adapted maps, 2022
B. Acciaio, A. Kratsios, and G. Pammer · 2022
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Convergence rate of Deep ONets for learning operators arising from advection-diffusion equations
B. Deng, Y. Shin, L. Lu, Z. Zhang, and G. E. Karniadakis · 2022
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Parabolic molecules
P. Grohs and G. Kutyniok · 2014
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Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
A. Chkifa, A. Cohen, and C. Schwab · 2015
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Approximation of high-dimensional parametric pdes
A. Cohen and R. DeVore · 2015
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Solving ill-posed inverse problems using iterative deep neural networks
J. Adler and O. Öktem · 2017
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Fully discrete approximation of parametric and stochastic elliptic PDEs
M. Bachmayr, A. Cohen, D. Dung, and C. Schwab · 2017
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Electromagnetic wave scattering by random surfaces: Shape holomorphy
C. Jerez-Hanckes, C. Schwab, and J. Zech · 2017
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V. Fanaskov and I. Oseledets · 2022
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Constructive Deep ReLU Neural Network Approximation
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Error estimates for DeepONets: a deep learning framework in infinite dimensions
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Transformer for partial differential equations’ operator learning
Z. Li, K. Meidani, and A. B. Farimani · 2022
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Deep nonparametric estimation of operators between infinite dimensional spaces
H. Liu, H. Yang, M. Chen, T. Zhao, and W. Liao · 2022
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De Rham compatible Deep Neural Networks
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Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities
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Exponential ReLU DNN expression of holomorphic maps in high dimension
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Wavelet neural operator: a neural operator for parametric partial differential equations, 2022
T. Tripura and S. Chakraborty · 2022
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Analyticity and sparsity in uncertainty quantification for pdes with gaussian random field inputs
D. Dung, V. K. Nguyen, C. Schwab, and J. Zech · 2023
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Neural operator: learning maps between function spaces with applications to PDEs
N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2023
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Operator learning with PCA-Net: upper and lower complexity bounds
S. Lanthaler · 2023
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Error bounds for learning with vector-valued random features, 2023
S. Lanthaler and N. H. Nelsen · 2023
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Exponential convergence of deep operator networks for elliptic partial differential equations
C. Marcati and C. Schwab · 2023
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Deep operator network approximation rates for lipschitz operators
C. Schwab, A. Stein, and J. Zech · 2023
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Deep learning in high dimension: neural network expression rates for analytic functions in L 2 ( ℝ d , γ d ) L^{2}(\mathbb{R}^{d},\gamma_{d})
C. Schwab and J. Zech · 2023
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Measure transport via polynomial density surrogates, 2023
J. Westermann and J. Zech · 2023
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