Approximations with deep neural networks in Sobolev time-space

DOI10.1142/S0219530522500014zbMath1489.35007arXiv2101.06115WikidataQ114072421 ScholiaQ114072421MaRDI QIDQ5075578

Ahmed Abdeljawad, Philipp Grohs

Publication date: 16 May 2022

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.06115

zbMATH Keywords

function approximationdeep neural networksBochner-Sobolev spacesrectified cubic unit

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Theoretical approximation in context of PDEs (35A35) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

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SignReLU neural network and its approximation ability ⋮ Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations

Uses Software

• DGM

Cites Work

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