Strong overall error analysis for the training of artificial neural networks via random initializations

Jentzen A, Riekert A (2023)

In: Communications in Mathematics and Statistics, 0. doi:10.1007/s40304-022-00292-9

Research article (journal) | Peer reviewed | accepted / in press (not yet published)

Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation

Jentzen A, Riekert A (2023)

In: Journal of Mathematical Analysis and Applications, 517(2), 126601. doi:10.1016/j.jmaa.2022.126601

Research article (journal) | Peer reviewed | Published

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

Grohs P, Ibragimov S, Jentzen A, Koppensteiner S (2023)

In: Journal of Complexity, 0, 101746. doi:10.1016/j.jco.2023.101746

Research article (journal) | Peer reviewed | accepted / in press (not yet published)

Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen--Cahn equations

In: , -.

| Peer reviewed

The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality

In:

| Preprint

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Strong overall error analysis for the training of artificial neural networks via random initializations Jentzen A, Riekert A (2023) In: Communications in Mathematics and Statistics, 0. doi:10.1007/s40304-022-00292-9 Research article (journal) \| Peer reviewed \| accepted / in press (not yet published)
An overview on deep learning-based approximation methods for partial differential equations Beck C, Hutzenthaler M, Jentzen A, Kuckuck B (2023) In: Discrete and Continuous Dynamical Systems - Series B, 28(6), 3697-3746. doi:10.3934/dcdsb.2022238 Research article (journal) \| Peer reviewed \| Published
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation Jentzen A, Riekert A (2023) In: Journal of Mathematical Analysis and Applications, 517(2), 126601. doi:10.1016/j.jmaa.2022.126601 Research article (journal) \| Peer reviewed \| Published
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations Hutzenthaler M, Jentzen A, Kruse T, Nguyen TA (2023) In: Journal of Numerical Mathematics, 31(2), 1-28. doi:10.1515/jnma-2021-0111 Research article (journal) \| Peer reviewed \| Published
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality Grohs P, Ibragimov S, Jentzen A, Koppensteiner S (2023) In: Journal of Complexity, 0, 101746. doi:10.1016/j.jco.2023.101746 Research article (journal) \| Peer reviewed \| accepted / in press (not yet published)
Space-time error estimates for deep neural network approximations for differential equations In: , . \| Peer reviewed
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen--Cahn equations In: , -. \| Peer reviewed
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions In: , . \| Peer reviewed
The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality In: \| Preprint
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations In: \| Preprint