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Space-time error estimates for deep neural network approximations for
  differential equations

Space-time error estimates for deep neural network approximations for differential equations

Advances in Computational Mathematics (Adv. Comput. Math.), 2019
11 August 2019
Philipp Grohs
F. Hornung
Arnulf Jentzen
Philipp Zimmermann
ArXiv (abs)PDFHTML

Papers citing "Space-time error estimates for deep neural network approximations for differential equations"

11 / 11 papers shown
Sampling Complexity of Deep Approximation Spaces
Sampling Complexity of Deep Approximation Spaces
Ahmed Abdeljawad
Philipp Grohs
199
3
0
20 Dec 2023
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
341
75
0
23 May 2022
Deep neural network approximation for high-dimensional parabolic
  Hamilton-Jacobi-Bellman equations
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations
Philipp Grohs
L. Herrmann
244
9
0
09 Mar 2021
Strong overall error analysis for the training of artificial neural
  networks via random initializations
Strong overall error analysis for the training of artificial neural networks via random initializationsCommunications in Mathematics and Statistics (Commun. Math. Stat.), 2020
Arnulf Jentzen
Adrian Riekert
242
3
0
15 Dec 2020
Error Estimation and Correction from within Neural Network Differential
  Equation Solvers
Error Estimation and Correction from within Neural Network Differential Equation Solvers
Akshunna S. Dogra
179
1
0
09 Jul 2020
Overall error analysis for the training of deep neural networks via
  stochastic gradient descent with random initialisation
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisationApplied Mathematics and Computation (Appl. Math. Comput.), 2020
Arnulf Jentzen
Timo Welti
201
20
0
03 Mar 2020
Uniform error estimates for artificial neural network approximations for
  heat equations
Uniform error estimates for artificial neural network approximations for heat equationsIMA Journal of Numerical Analysis (IMA J. Numer. Anal.), 2019
Lukas Gonon
Philipp Grohs
Arnulf Jentzen
David Kofler
David Siska
323
37
0
20 Nov 2019
Full error analysis for the training of deep neural networks
Full error analysis for the training of deep neural networksInfinite Dimensional Analysis Quantum Probability and Related Topics (IDAQP), 2019
C. Beck
Arnulf Jentzen
Benno Kuckuck
305
56
0
30 Sep 2019
Deep neural network approximations for Monte Carlo algorithms
Deep neural network approximations for Monte Carlo algorithms
Philipp Grohs
Arnulf Jentzen
Diyora Salimova
200
33
0
28 Aug 2019
A proof that artificial neural networks overcome the curse of
  dimensionality in the numerical approximation of Black-Scholes partial
  differential equations
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
379
185
0
07 Sep 2018
Solving the Kolmogorov PDE by means of deep learning
Solving the Kolmogorov PDE by means of deep learning
C. Beck
S. Becker
Philipp Grohs
Nor Jaafari
Arnulf Jentzen
337
110
0
01 Jun 2018
1
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