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

15 March 2019

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

18 / 18 papers shown

Title
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 47 7 0 08 May 2024
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 28 34 0 06 Dec 2022
Deep neural network expressivity for optimal stopping problems Lukas Gonon 34 6 0 19 Oct 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 37 19 0 21 Jun 2022
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems Tingwei Meng Zhen Zhang Jérome Darbon George Karniadakis 37 15 0 14 Jan 2022
Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality Lukas Gonon 30 35 0 14 Jun 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 19 22 0 07 May 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 40 146 0 22 Dec 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 25 51 0 09 Jul 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 36 19 0 03 Jun 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 29 15 0 03 Mar 2020
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 39 34 0 20 Nov 2019
Full error analysis for the training of deep neural networks C. Beck Arnulf Jentzen Benno Kuckuck 24 47 0 30 Sep 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 39 33 0 11 Aug 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 36 197 0 31 Mar 2019
Unbiased deep solvers for linear parametric PDEs Marc Sabate Vidales David Siska Lukasz Szpruch OOD 34 7 0 11 Oct 2018
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations Julius Berner Philipp Grohs Arnulf Jentzen 16 181 0 09 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 21 167 0 07 Sep 2018