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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
v1v2 (latest)

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
Arnulf Jentzen
Diyora Salimova
Timo Welti
    AI4CE
ArXiv (abs)PDFHTML

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"

50 / 59 papers shown
A deep solver for backward stochastic Volterra integral equations
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A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han
Arnulf Jentzen
Weinan E
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321
7
0
07 May 2025
Universal Approximation Theorem of Deep Q-Networks
Universal Approximation Theorem of Deep Q-Networks
Qian Qi
310
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04 May 2025
FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning
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FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations
Zaijun Ye
Wansheng Wang
299
3
0
15 Dec 2024
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$-sense
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in LpL^pLp-sense
Ariel Neufeld
Tuan Anh Nguyen
387
1
0
30 Sep 2024
Dimension-independent learning rates for high-dimensional classification
  problems
Dimension-independent learning rates for high-dimensional classification problems
Andrés Felipe Lerma Pineda
P. Petersen
Simon Frieder
Thomas Lukasiewicz
213
1
0
26 Sep 2024
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
Madison Cooley
Shandian Zhe
Robert M. Kirby
Varun Shankar
479
1
0
04 Jun 2024
Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow
Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow
Pablo Arratia
Matthias Ehrhardt
Lisa Kreusser
400
0
0
03 Jun 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEsCommunications in nonlinear science & numerical simulation (CNSNS), 2024
Ariel Neufeld
Philipp Schmocker
Sizhou Wu
638
13
0
08 May 2024
Approximating Langevin Monte Carlo with ResNet-like Neural Network
  architectures
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures
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Janina Enrica Schutte
David Sommer
Martin Eigel
287
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06 Nov 2023
Residual Multi-Fidelity Neural Network Computing
Residual Multi-Fidelity Neural Network ComputingBIT Numerical Mathematics (BIT), 2023
Owen Davis
Mohammad Motamed
Raúl Tempone
283
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An Extreme Learning Machine-Based Method for Computational PDEs in
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An Extreme Learning Machine-Based Method for Computational PDEs in Higher DimensionsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Yiran Wang
Suchuan Dong
383
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0
13 Sep 2023
Deep Learning Methods for Partial Differential Equations and Related
  Parameter Identification Problems
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification ProblemsInverse Problems (IP), 2022
Derick Nganyu Tanyu
Jianfeng Ning
Tom Freudenberg
Nick Heilenkötter
A. Rademacher
U. Iben
Peter Maass
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365
65
0
06 Dec 2022
Neural Network Approximations of PDEs Beyond Linearity: A
  Representational Perspective
Neural Network Approximations of PDEs Beyond Linearity: A Representational PerspectiveInternational Conference on Machine Learning (ICML), 2022
Tanya Marwah
Zachary Chase Lipton
Jianfeng Lu
Andrej Risteski
333
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0
21 Oct 2022
Deep neural network expressivity for optimal stopping problems
Deep neural network expressivity for optimal stopping problemsFinance and Stochastics (Fin. Stoch.), 2022
Lukas Gonon
314
13
0
19 Oct 2022
From Monte Carlo to neural networks approximations of boundary value
  problems
From Monte Carlo to neural networks approximations of boundary value problems
L. Beznea
Iulian Cîmpean
Oana Lupascu-Stamate
Ionel Popescu
A. Zarnescu
178
5
0
03 Sep 2022
The Deep Ritz Method for Parametric $p$-Dirichlet Problems
The Deep Ritz Method for Parametric ppp-Dirichlet Problems
A. Kaltenbach
Marius Zeinhofer
140
4
0
05 Jul 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via
  Deep Learning
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep LearningInternational Conference on Machine Learning (ICML), 2022
Lorenz Richter
Julius Berner
317
20
0
21 Jun 2022
Generic bounds on the approximation error for physics-informed (and)
  operator learning
Generic bounds on the approximation error for physics-informed (and) operator learningNeural Information Processing Systems (NeurIPS), 2022
Tim De Ryck
Siddhartha Mishra
PINN
386
79
0
23 May 2022
Convergence of a robust deep FBSDE method for stochastic control
Convergence of a robust deep FBSDE method for stochastic controlSIAM Journal on Scientific Computing (SISC), 2022
Kristoffer Andersson
Adam Andersson
C. Oosterlee
504
26
0
18 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and
  parabolic boundary value problems
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
Nikolas Nusken
Lorenz Richter
PINNDiffM
369
38
0
07 Dec 2021
Physics-enhanced deep surrogates for partial differential equations
Physics-enhanced deep surrogates for partial differential equations
R. Pestourie
Youssef Mroueh
Chris Rackauckas
Payel Das
Steven G. Johnson
PINNAI4CE
379
40
0
10 Nov 2021
Approximation properties of Residual Neural Networks for Kolmogorov PDEs
Approximation properties of Residual Neural Networks for Kolmogorov PDEs
Jonas Baggenstos
Diyora Salimova
246
4
0
30 Oct 2021
Wasserstein Generative Adversarial Uncertainty Quantification in
  Physics-Informed Neural Networks
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural NetworksJournal of Computational Physics (JCP), 2021
Yihang Gao
Michael K. Ng
291
40
0
30 Aug 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks
Parametric Complexity Bounds for Approximating PDEs with Neural NetworksNeural Information Processing Systems (NeurIPS), 2021
Tanya Marwah
Zachary Chase Lipton
Andrej Risteski
248
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0
03 Mar 2021
Error Estimates for the Deep Ritz Method with Boundary Penalty
Error Estimates for the Deep Ritz Method with Boundary PenaltyMathematical and Scientific Machine Learning (MSML), 2021
Johannes Müller
Marius Zeinhofer
609
29
0
01 Mar 2021
Solving high-dimensional parabolic PDEs using the tensor train format
Solving high-dimensional parabolic PDEs using the tensor train formatInternational Conference on Machine Learning (ICML), 2021
Lorenz Richter
Leon Sallandt
Nikolas Nusken
295
62
0
23 Feb 2021
Deep neural network surrogates for non-smooth quantities of interest in
  shape uncertainty quantification
Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification
L. Scarabosio
359
9
0
18 Jan 2021
An overview on deep learning-based approximation methods for partial
  differential equations
An overview on deep learning-based approximation methods for partial differential equations
C. Beck
Martin Hutzenthaler
Arnulf Jentzen
Benno Kuckuck
692
175
0
22 Dec 2020
Some observations on high-dimensional partial differential equations
  with Barron data
Some observations on high-dimensional partial differential equations with Barron dataMathematical and Scientific Machine Learning (MSML), 2020
E. Weinan
Stephan Wojtowytsch
AI4CE
403
24
0
02 Dec 2020
Neural network approximation and estimation of classifiers with
  classification boundary in a Barron class
Neural network approximation and estimation of classifiers with classification boundary in a Barron classThe Annals of Applied Probability (Ann. Appl. Probab.), 2020
A. Caragea
P. Petersen
F. Voigtlaender
269
41
0
18 Nov 2020
Numerically Solving Parametric Families of High-Dimensional Kolmogorov
  Partial Differential Equations via Deep Learning
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
Julius Berner
Markus Dablander
Philipp Grohs
301
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0
09 Nov 2020
Exponential ReLU Neural Network Approximation Rates for Point and Edge
  Singularities
Exponential ReLU Neural Network Approximation Rates for Point and Edge SingularitiesFoundations of Computational Mathematics (FoCM), 2020
C. Marcati
J. Opschoor
P. Petersen
Christoph Schwab
226
36
0
23 Oct 2020
Deep neural network approximation for high-dimensional elliptic PDEs
  with boundary conditions
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditionsIMA Journal of Numerical Analysis (IMA J. Numer. Anal.), 2020
Philipp Grohs
L. Herrmann
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Expressivity of Deep Neural Networks
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Gitta Kutyniok
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Space-time deep neural network approximations for high-dimensional
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Space-time deep neural network approximations for high-dimensional partial differential equations
F. Hornung
Arnulf Jentzen
Diyora Salimova
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272
21
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
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Nikolas Nusken
Lorenz Richter
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341
149
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Neural Network Solutions to Differential Equations in Non-Convex
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Andrew M. Nagel
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196
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25 Apr 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural
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Overall error analysis for the training of deep neural networks via
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Uniform error estimates for artificial neural network approximations for
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20 Nov 2019
Review: Ordinary Differential Equations For Deep Learning
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On the space-time expressivity of ResNets
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309
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A deep surrogate approach to efficient Bayesian inversion in PDE and
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Peter Du
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Full error analysis for the training of deep neural networks
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C. Beck
Arnulf Jentzen
Benno Kuckuck
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30 Sep 2019
Deep neural network approximations for Monte Carlo algorithms
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Philipp Grohs
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Space-time error estimates for deep neural network approximations for
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Philipp Grohs
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Arnulf Jentzen
Philipp Zimmermann
240
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11 Aug 2019
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C. Beck
S. Becker
Patrick Cheridito
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Ariel Neufeld
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The Barron Space and the Flow-induced Function Spaces for Neural Network
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