Rectified deep neural networks overcome the curse of dimensionality for
nonsmooth value functions in zero-sum games of nonlinear stiff systems

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Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

15 March 2019

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Papers citing "Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems"

16 / 16 papers shown

Title
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 71 7 0 08 May 2024
Neural networks-based backward scheme for fully nonlinear PDEs H. Pham X. Warin Maximilien Germain 44 86 0 31 Jul 2019
A neural network based policy iteration algorithm with global $H^2$ -superlinear convergence for stochastic games on domains Kazufumi Ito C. Reisinger Yufei Zhang 62 27 0 05 Jun 2019
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 86 200 0 21 Feb 2019
Deep backward schemes for high-dimensional nonlinear PDEs Côme Huré H. Pham X. Warin AI4CE 57 99 0 05 Feb 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 65 210 0 08 Jan 2019
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients Arnulf Jentzen Diyora Salimova Timo Welti AI4CE 44 119 0 19 Sep 2018
Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions Weinan E Qingcan Wang 59 102 0 01 Jul 2018
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations C. Beck Weinan E Arnulf Jentzen 56 331 0 18 Sep 2017
Optimal approximation of piecewise smooth functions using deep ReLU neural networks P. Petersen Felix Voigtländer 223 475 0 15 Sep 2017
Optimal Approximation with Sparsely Connected Deep Neural Networks Helmut Bölcskei Philipp Grohs Gitta Kutyniok P. Petersen 197 256 0 04 May 2017
Understanding Deep Neural Networks with Rectified Linear Units R. Arora A. Basu Poorya Mianjy Anirbit Mukherjee PINN 154 643 0 04 Nov 2016
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review T. Poggio H. Mhaskar Lorenzo Rosasco Brando Miranda Q. Liao 124 576 0 02 Nov 2016
Deep Learning Approximation for Stochastic Control Problems Jiequn Han E. Weinan BDL 55 196 0 02 Nov 2016
Error bounds for approximations with deep ReLU networks Dmitry Yarotsky 198 1,232 0 03 Oct 2016
Deep vs. shallow networks : An approximation theory perspective H. Mhaskar T. Poggio 165 341 0 10 Aug 2016

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