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

19 September 2018

Papers citing "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"

28 / 28 papers shown

Title
Universal Approximation Theorem of Deep Q-Networks Qian Qi 45 1 0 04 May 2025
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation Madison Cooley Shandian Zhe Robert M. Kirby Varun Shankar 67 1 0 04 Jun 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 45 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 23 34 0 06 Dec 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 52 10 0 21 Oct 2022
Deep neural network expressivity for optimal stopping problems Lukas Gonon 27 6 0 19 Oct 2022
The Deep Ritz Method for Parametric $p$ -Dirichlet Problems A. Kaltenbach Marius Zeinhofer 22 3 0 05 Jul 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 27 19 0 21 Jun 2022
Convergence of a robust deep FBSDE method for stochastic control Kristoffer Andersson Adam Andersson C. Oosterlee 34 19 0 18 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
Physics-enhanced deep surrogates for partial differential equations R. Pestourie Youssef Mroueh Chris Rackauckas Payel Das Steven G. Johnson PINN AI4CE 25 15 0 10 Nov 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 38 29 0 30 Aug 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 28 19 0 03 Mar 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 30 52 0 10 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 29 19 0 03 Jun 2020
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space Nikolas Nusken Lorenz Richter AI4CE 24 104 0 11 May 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 22 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 29 34 0 20 Nov 2019
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models Teo Deveney Amelia Gosse Peter Du 23 9 0 03 Oct 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 29 33 0 11 Aug 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 23 125 0 08 Jul 2019
The Barron Space and the Flow-induced Function Spaces for Neural Network Models E. Weinan Chao Ma Lei Wu 38 109 0 18 Jun 2019
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks Kaitong Hu Zhenjie Ren David Siska Lukasz Szpruch MLT 30 104 0 19 May 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 23 197 0 31 Mar 2019
Unbiased deep solvers for linear parametric PDEs Marc Sabate Vidales David Siska Lukasz Szpruch OOD 32 7 0 11 Oct 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 16 167 0 07 Sep 2018