Uniform error estimates for artificial neural network approximations for heat equations

DOI10.1093/imanum/drab027zbMath1502.65171arXiv1911.09647OpenAlexW2991444716MaRDI QIDQ5093099

Lukas Gonon, Arnulf Jentzen, David Šiška, David Kofler, Philipp Grohs

Publication date: 26 July 2022

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.09647

zbMATH Keywords

curse of dimensionalitydeep neural networkinformation based complexityhigh-dimensional PDEstractability of multivariate problems

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Probabilistic models, generic numerical methods in probability and statistics (65C20) Heat equation (35K05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Complexity and performance of numerical algorithms (65Y20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

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