Error bounds for approximations with deep ReLU neural networks in \(W^{s,p}\) norms

We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms. First, we construct, based on a calculus of ReLU networks, artificial neural networks with ReLU activation functions that achieve certain approximation rates. Second, we es...

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Veröffentlicht in:	arXiv.org 2019-02
Hauptverfasser:	Gühring, Ingo, Kutyniok, Gitta, Petersen, Philipp
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Artificial neural networks Lower bounds Mathematical analysis Neural networks Norms Numerical analysis Partial differential equations
Online-Zugang:	Volltext
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