Arnulf Jentzen
发表
Arnulf Jentzen,
Philippe von Wurstemberger,
Arnulf Jentzen,
2018,
J. Complex..
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2019
.
Arnulf Jentzen,
Benjamin J. Fehrman,
Benjamin Gess,
2019,
J. Mach. Learn. Res..
Arnulf Jentzen,
Philipp Grohs,
Julius Berner,
2018,
SIAM J. Math. Data Sci..
Arnulf Jentzen,
Philipp Grohs,
Fabian Hornung,
2019,
Advances in Computational Mathematics.
Arnulf Jentzen,
Weinan E,
Jiequn Han,
2017,
Proceedings of the National Academy of Sciences.
Peter E. Kloeden,
Arnulf Jentzen,
Martin Hutzenthaler,
2011
.
Arnulf Jentzen,
Benno Kuckuck,
Christan Beck,
2019,
ArXiv.
Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities
pdf
Arnulf Jentzen,
Thomas Kruse,
Martin Hutzenthaler,
2019,
Foundations of Computational Mathematics.
Arnulf Jentzen,
Felix Lindner,
Primoz Pusnik,
2018,
Numerical Algorithms.
Arnulf Jentzen,
Patrick Cheridito,
Sebastian Becker,
2019,
Journal of Risk and Financial Management.
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
pdf
Arnulf Jentzen,
Philippe von Wurstemberger,
Philipp Grohs,
2018,
Memoirs of the American Mathematical Society.
E Weinan,
Arnulf Jentzen,
Christian Beck,
2017,
J. Nonlinear Sci..
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
pdf
Arnulf Jentzen,
Philippe von Wurstemberger,
Martin Hutzenthaler,
2020,
ArXiv.
Arnulf Jentzen,
Thomas Kruse,
Christian Beck,
2019,
J. Num. Math..
Space-time deep neural network approximations for high-dimensional partial differential equations
pdf
Arnulf Jentzen,
Fabian Hornung,
Diyora Salimova,
2020,
ArXiv.
Arnulf Jentzen,
Philipp Grohs,
Diyora Salimova,
2019,
ArXiv.
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2019,
ArXiv.
Peter E. Kloeden,
Arnulf Jentzen,
Andreas Neuenkirch,
2009,
Numerische Mathematik.
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
pdf
Arnulf Jentzen,
Philippe von Wurstemberger,
Patrick Cheridito,
2020,
ArXiv.
Peter E. Kloeden,
Arnulf Jentzen,
Andreas Neuenkirch,
2009
.
Arnulf Jentzen,
Michael B. Giles,
Timo Welti,
2019,
ArXiv.
Arnulf Jentzen,
Arnulf Jentzen,
2011,
SIAM J. Numer. Anal..
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
pdf
Tuan Anh Nguyen,
Arnulf Jentzen,
Martin Hutzenthaler,
2020,
ArXiv.
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
pdf
Arnulf Jentzen,
Patrick Cheridito,
Ariel Neufeld,
2020,
ArXiv.
Arnulf Jentzen,
Michael Röckner,
Arnulf Jentzen,
2010,
Found. Comput. Math..
Arnulf Jentzen,
Mario Hefter,
Arnulf Jentzen,
2017,
Finance Stochastics.
Arnulf Jentzen,
2018
.
E Weinan,
Arnulf Jentzen,
Thomas Kruse,
2017,
Journal of Scientific Computing.
Tuan Anh Nguyen,
Arnulf Jentzen,
Thomas Kruse,
2019,
SN Partial Differential Equations and Applications.
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2020,
ArXiv.
Arnulf Jentzen,
Martin Hutzenthaler,
M. Hutzenthaler,
2009,
Found. Comput. Math..
Sebastian Becker,
Arnulf Jentzen,
Philipp Grohs,
2018,
ArXiv.
Arnulf Jentzen,
Philipp Grohs,
Julius Berner,
2019,
2019 13th International conference on Sampling Theory and Applications (SampTA).
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
pdf
Arnulf Jentzen,
Diyora Salimova,
Timo Welti,
2018,
Communications in Mathematical Sciences.
E Weinan,
Arnulf Jentzen,
Jiequn Han,
2017,
Communications in Mathematics and Statistics.
Christian Beck,
Arnulf Jentzen,
Benno Kuckuck,
2020,
ArXiv.
Arnulf Jentzen,
2018
.
Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning
pdf
E Weinan,
Arnulf Jentzen,
Jiequn Han,
2017,
ArXiv.
Arnulf Jentzen,
Dirk Blömker,
Arnulf Jentzen,
2013,
SIAM J. Numer. Anal..
Stefan Siegmund,
Arnulf Jentzen,
Arno Berger,
2010,
IEEE Transactions on Automatic Control.
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
pdf
Arnulf Jentzen,
Lukas Gonon,
Christian Beck,
2020,
ArXiv.
Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
pdf
Arnulf Jentzen,
Felix Lindner,
Martin Hutzenthaler,
2019,
ArXiv.
Strong overall error analysis for the training of artificial neural networks via random initializations
pdf
Arnulf Jentzen,
Adrian Riekert,
Arnulf Jentzen,
2020,
ArXiv.
Arnulf Jentzen,
Lukas Gonon,
Diyora Salimova,
2020,
ArXiv.
Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations
pdf
Arnulf Jentzen,
Thomas Kruse,
Christian Beck,
2020,
ArXiv.
Sebastian Becker,
Peter E. Kloeden,
Arnulf Jentzen,
2018,
BIT Numerical Mathematics.
Sebastian Becker,
Arnulf Jentzen,
Patrick Cheridito,
2019,
European Journal of Applied Mathematics.
Sebastian Becker,
Peter E. Kloeden,
Arnulf Jentzen,
2013,
SIAM J. Numer. Anal..
Sebastian Becker,
Arnulf Jentzen,
Patrick Cheridito,
2018,
J. Mach. Learn. Res..
E Weinan,
Arnulf Jentzen,
Jiequn Han,
2020,
Nonlinearity.
Arnulf Jentzen,
Philipp Grohs,
David Siska,
2019,
ArXiv.
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation
pdf
Arnulf Jentzen,
Timo Welti,
Arnulf Jentzen,
2020,
Appl. Math. Comput..
Arnulf Jentzen,
Patrick Cheridito,
Christian Beck,
2019,
SIAM J. Sci. Comput..
Xiaojie Wang,
Arnulf Jentzen,
Martin Hutzenthaler,
2013,
Math. Comput..
Arnulf Jentzen,
Thomas Kruse,
Martin Hutzenthaler,
2018,
Proceedings of the Royal Society A.
Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
pdf
Arnulf Jentzen,
Benno Kuckuck,
Martin Hutzenthaler,
2021,
ArXiv.
Arnulf Jentzen,
Patrick Cheridito,
Benno Kuckuck,
2021,
ArXiv.
A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions
pdf
Arnulf Jentzen,
Adrian Riekert,
2021,
ArXiv.
Arnulf Jentzen,
Ryan Kurniawan,
Arnulf Jentzen,
2015,
Found. Comput. Math..
Arnulf Jentzen,
Benno Kuckuck,
Martin Hutzenthaler,
2021
.
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality
pdf
Arnulf Jentzen,
Philipp Grohs,
Shokhrukh Ibragimov,
2021,
ArXiv.
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
pdf
Arnulf Jentzen,
Thomas Kruse,
Martin Hutzenthaler,
2021,
J. Num. Math..
Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases
pdf
Arnulf Jentzen,
Timo Kröger,
Arnulf Jentzen,
2021,
ArXiv.
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2019,
IEEE Transactions on Neural Networks and Learning Systems.
On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
pdf
Arnulf Jentzen,
Adrian Riekert,
Arnulf Jentzen,
2021,
ArXiv.
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2020,
J. Complex..
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation
pdf
Arnulf Jentzen,
Georg S. Weiss,
Adrian Riekert,
2021,
ArXiv.
Arnulf Jentzen,
Timo Welti,
Ladislas Jacobe de Naurois,
2015,
Applied Mathematics & Optimization.
Arnulf Jentzen,
Philipp Grohs,
Nor Jaafari,
2018,
Journal of Scientific Computing.
Arnulf Jentzen,
Weinan E,
Jiequn Han,
2020,
Nonlinearity.
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation
pdf
Arnulf Jentzen,
Adrian Riekert,
2021,
ArXiv.
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
pdf
Luca Scarpa,
Arnulf Jentzen,
Martin Hutzenthaler,
2021,
ArXiv.
Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions
pdf
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2021,
ArXiv.
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
pdf
Arnulf Jentzen,
Patrick Cheridito,
Florian Rossmannek,
2021,
J. Complex..
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions
pdf
Arnulf Jentzen,
Adrian Riekert,
2021,
ArXiv.
Full history recursive multilevel Picard approximations for ordinary differential equations with expectations
pdf
Arnulf Jentzen,
Martin Hutzenthaler,
Christian Beck,
2021,
ArXiv.
Arnulf Jentzen,
Thomas Kruse,
Weinan E,
2021,
Partial Differential Equations and Applications.
Arnulf Jentzen,
Martin Hutzenthaler,
Christian Beck,
2020,
Stochastics and Dynamics.
E Weinan,
Arnulf Jentzen,
Thomas Kruse,
2016
.
Arnulf Jentzen,
Philipp Grohs,
Christoph Schwab,
2018,
Constructive Approximation.
Peter E. Kloeden,
Arnulf Jentzen,
Martin Hutzenthaler,
2011,
1105.0226.
Arnulf Jentzen,
Arnulf Jentzen,
Primovz Puvsnik,
2015,
IMA Journal of Numerical Analysis.
Arnulf Jentzen,
Lukas Gonon,
Martin Hutzenthaler,
2019,
Discrete & Continuous Dynamical Systems - B.
Arnulf Jentzen,
Máté Gerencsér,
Diyora Salimova,
2017,
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
Arnulf Jentzen,
Martin Hutzenthaler,
2020
.
Arnulf Jentzen,
Jan van Neerven,
Sonja Cox,
2020,
IMA Journal of Numerical Analysis.
Arnulf Jentzen,
Martin Hutzenthaler,
Diyora Salimova,
2016,
1604.02053.
Martin Hairer,
Arnulf Jentzen,
Martin Hutzenthaler,
2012,
1209.6035.
Arnulf Jentzen,
Arnulf Jentzen,
2015
.
Arnulf Jentzen,
Daniel Conus,
Ryan Kurniawan,
2014,
The Annals of Applied Probability.
Arnulf Jentzen,
Sonja Cox,
Ryan Kurniawan,
2016,
1612.03210.
Arnulf Jentzen,
Peter Kloeden,
P. Kloeden,
2011,
1210.8320.
Peter E. Kloeden,
Arnulf Jentzen,
P. Kloeden,
2009
.
Arnulf Jentzen,
Ryan Kurniawan,
Adam Andersson,
2014,
Journal of Mathematical Analysis and Applications.