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)
Type of Publication: Research article (journal)

Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at…

Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L (2022)
In: Discrete and Continuous Dynamical Systems - Series B, 27(7)
Type of Publication: Research article (journal)

Strong error analysis for stochastic gradient descent optimization algorithms

Jentzen A, Kuckuck B, Neufeld A, von Wurstemberger P (2021)
In: IMA Journal of Numerical Analysis, 41(1)
Type of Publication: Research article (journal)

Deep neural network approximation theory for high-dimensional functions

Beneventano P, Cheridito P, Graeber R, Jentzen A, Kuckuck B (2021)
In: Sampling Theory in Signal and Image Processing, 0
Type of Publication: Research article (journal)

Monotonicity, Duplication Monotonicity, and Pareto Optimality in the Scoring-Based Allocation of Indivisible Goods

Kuckuck, Benno; Rothe, Jörg (2019)
In: Lujak, Marin (eds.), Agreement Technologies, 6th International Conference, AT 2018, Bergen, Norway, December 6-7, 2018, Revised Selected Papers. Cham, Switzerland: .
Type of Publication: Research article in edited proceedings (conference)

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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) Type of Publication: Research article (journal)
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 Type of Publication: Research article (journal)
Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at… Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L (2022) In: Discrete and Continuous Dynamical Systems - Series B, 27(7) Type of Publication: Research article (journal)
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) Type of Publication: Research article (journal)
Strong error analysis for stochastic gradient descent optimization algorithms Jentzen A, Kuckuck B, Neufeld A, von Wurstemberger P (2021) In: IMA Journal of Numerical Analysis, 41(1) Type of Publication: Research article (journal)
Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations Hutzenthaler M, Jentzen A, Kuckuck B, Padgett JL (2021) In: arXiv, 0 Type of Publication: Research article (journal)
Deep neural network approximation theory for high-dimensional functions Beneventano P, Cheridito P, Graeber R, Jentzen A, Kuckuck B (2021) In: Sampling Theory in Signal and Image Processing, 0 Type of Publication: Research article (journal)
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L (2021) In: Journal of Mathematical Analysis and Applications, 502(2) Type of Publication: Research article (journal)
Monotonicity, Duplication Monotonicity, and Pareto Optimality in the Scoring-Based Allocation of Indivisible Goods Kuckuck, Benno; Rothe, Jörg (2019) In: Lujak, Marin (eds.), Agreement Technologies, 6th International Conference, AT 2018, Bergen, Norway, December 6-7, 2018, Revised Selected Papers. Cham, Switzerland: . Type of Publication: Research article in edited proceedings (conference)
Refugee allocation in the setting of hedonic games Kuckuck, Benno; Rothe, Jörg; Weißenfeld, Anke (2019) In: Pekeč, Saša; Venable, Kristen Brent (eds.), Algorithmic Decision Theory, 6th International Conference, ADT 2019, Durham, NC, USA, October 25–27, 2019, Proceedings. Cham, Switzerland: . Type of Publication: Research article in edited proceedings (conference)