Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

Schembera, Björn; Wübbeling, Frank; Kleikamp, Hendrik; Biedinger, Christine; Fiedler, Jochen; Reidelbach, Marco; Shehu, Aurela; Schmidt, Burkhard; Koprucki, Thomas; Iglezakis, Dorothea; Göddeke, Dominik (2024)

In: Garoufallou, Emmanouel; Sartori, Fabio (eds.), Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, 161-168. Cham: .

Research article in edited proceedings (conference) | 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)

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

Gonon, L.; Graeber, R.; Jentzen, A. (2023)

In: arXiv.org:2212.13111.

Research article in digital collection | Preprint | submitted / under review

Full error analysis for the training of deep neural networks

Beck C, Jentzen A, Kuckuck B (2022)

In: Infinite Dimensional Analysis, Quantum Probability and Related Topics, 25(2), 2150020. doi:10.1142/S021902572150020X

Research article (journal) | Peer reviewed | Published

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 local minima with high probability

Ibragimov, S.; Jentzen, A.; Riekert, A. (2022)

In: arXiv.org:2212.13111.

Research article in digital collection | Preprint | submitted / under review

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Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines Schembera, Björn; Wübbeling, Frank; Kleikamp, Hendrik; Biedinger, Christine; Fiedler, Jochen; Reidelbach, Marco; Shehu, Aurela; Schmidt, Burkhard; Koprucki, Thomas; Iglezakis, Dorothea; Göddeke, Dominik (2024) In: Garoufallou, Emmanouel; Sartori, Fabio (eds.), Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, 161-168. Cham: . Research article in edited proceedings (conference) \| Peer reviewed \| 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
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)
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions Boussange, V.; Becker, S.; Jentzen, A.; Kuckuck, B.; Pellissier, L. (2023) In: SN Partial Differential Equations and Applications, 4, 51. doi:10.1007/s42985-023-00244-0 Research article (journal) \| Peer reviewed \| Published
The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality Gonon, L.; Graeber, R.; Jentzen, A. (2023) In: arXiv.org:2212.13111. Research article in digital collection \| Preprint \| submitted / under review
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation Eberle, Simon; Jentzen, Arnulf; Riekert, Adrian; Weiss, Georg S. (2023) In: Electronic Research Archive, 31(5), 2519-2554. doi:10.3934/era.2023128 Research article (journal) \| Peer reviewed \| Published
Full error analysis for the training of deep neural networks Beck C, Jentzen A, Kuckuck B (2022) In: Infinite Dimensional Analysis, Quantum Probability and Related Topics, 25(2), 2150020. doi:10.1142/S021902572150020X Research article (journal) \| Peer reviewed \| Published
An efficient Monte Carlo scheme for Zakai equations Beck, C.; Becker, S.; Cheridito, P.; Jentzen, A.; Neufeld, A. (2022) In: arXiv.org:2210.13530. Research article in digital collection \| Preprint \| submitted / under review
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 local minima with high probability Ibragimov, S.; Jentzen, A.; Riekert, A. (2022) In: arXiv.org:2212.13111. Research article in digital collection \| Preprint \| submitted / under review
On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations Beck C, Hutzenthaler M, Jentzen A (2021) In: Stochastics and Dynamics, 21(8). doi:10.1142/S0219493721500489 Research article (journal) \| Peer reviewed \| Published