Benno Kuckuck

activity

20112026

most citedAn overview on deep learning-based approximation methods for partial differential equations

88 citations · 204 across the 14 of their papers we have counts for

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Showing 2023Show all

2 papers · 1 filter

cs.LG2023★ 7 cited

Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including…

math.NA2023★ 1 cited

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^{p}$ -sense

Julia Ackermann, Arnulf Jentzen, Thomas Kruse +2

Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have gener…

Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^{p}$ -sense