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This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W.
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Ivar Fredholm · 1903
Earlier work this paper cites.
Ground state of liquid he 4
William Lauchlin McMillan · 1965
Earlier work this paper cites.
Remarques sur un résultat non publié de B. Maurey
Gilles Pisier · 1981
Earlier work this paper cites.
A course in functional analysis
John B. Conway · 1990
Earlier work this paper cites.
Probability in Banach Spaces: Isoperimetry and Processes
Michel Ledoux and Michel Talagrand · 1991
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
Andrew R Barron · 1993
Earlier work this paper cites.
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Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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