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We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces.
LIII. On lines and planes of closest fit to systems of points in space
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An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
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On the eigenspectrum of the Gram matrix and the generalization error of kernel-PCA
J. Shawe-Taylor, C. K. I. Williams, N. Cristianini, and J. Kandola · 2005
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Gilles Blanchard, Olivier Bousquet, and Laurent Zwald · 2007
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Convergence rates of best n-term Galerkin approximations for a class of elliptic SPDEs
Albert Cohen, Ronald DeVore, and Christoph Schwab · 2010
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Sin-Ei Takahasi, John M Rassias, Saburou Saitoh, and Yasuji Takahashi · 2010
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Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs
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A discussion on solving partial differential equations using neural networks
Tim Dockhorn · 2019
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Field inversion and machine learning with embedded neural networks: Physics-consistent neural network training
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Learning neural PDE solvers with convergence guarantees
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A theoretical analysis of deep neural networks and parametric PDEs
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