Arnulf Jentzen
Westfälische Wilhelms-Universität Münster
H-index: 49
Europe-Germany
Top articles of Arnulf Jentzen
Numerical Analysis Seminar
2024/4/10
Arnulf Jentzen
H-Index: 33
Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks
arXiv preprint arXiv:2402.05155
2024/2/7
Arnulf Jentzen
H-Index: 33
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
Mathematical Finance
2024/1
Sebastian Becker
H-Index: 3
Arnulf Jentzen
H-Index: 33
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
Partial Differential Equations and Applications
2023/12
Sebastian Becker
H-Index: 3
Arnulf Jentzen
H-Index: 33
An efficient Monte Carlo scheme for Zakai equations
Communications in Nonlinear Science and Numerical Simulation
2023/11/1
Christian Beck
H-Index: 24
Sebastian Becker
H-Index: 3
Arnulf Jentzen
H-Index: 33
Ariel Neufeld
H-Index: 10
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
arXiv preprint arXiv:2310.20360
2023/10/31
Arnulf Jentzen
H-Index: 33
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation
Applied Mathematics and Computation
2023/10/15
Arnulf Jentzen
H-Index: 33
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz …
arXiv preprint arXiv:2309.13722
2023/9/24
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality
Journal of Complexity
2023/8/1
Philipp Grohs
H-Index: 21
Arnulf Jentzen
H-Index: 33
On the Itô-Alekseev-Gröbner formula for stochastic differential equations
2023/7/3
Martin Hutzenthaler
H-Index: 20
Arnulf Jentzen
H-Index: 33
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
2023/4
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Journal of Numerical Mathematics
2020/12/16
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems
arXiv preprint arXiv:2303.03390
2023/3/3
Strong overall error analysis for the training of artificial neural networks via random initializations
Communications in Mathematics and Statistics
2023/3/2
Arnulf Jentzen
H-Index: 33
On the existence of minimizers in shallow residual ReLU neural network optimization landscapes
arXiv preprint arXiv:2302.14690
2023/2/28
Arnulf Jentzen
H-Index: 33
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
arXiv preprint arXiv:2302.03286
2023/2/7
Arnulf Jentzen
H-Index: 33
Space-time error estimates for deep neural network approximations for differential equations
Advances in Computational Mathematics
2023/2
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation
Journal of Mathematical Analysis and Applications
2023/1/15
Arnulf Jentzen
H-Index: 33
Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global …
arXiv preprint arXiv:2212.13111
2022/12/26
Arnulf Jentzen
H-Index: 33
An overview on deep learning-based approximation methods for partial differential equations
2020/12/22
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