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).

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 most polynomially growing derivatives

Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L (2022)

In: Discrete and Continuous Dynamical Systems - Series B, 27(7).

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).

Research article (journal)

Deep neural network approximation theory for high-dimensional functions

In: .

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

In: (eds.), .

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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). 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, 51. 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 most polynomially growing derivatives Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L (2022) In: Discrete and Continuous Dynamical Systems - Series B, 27(7). 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), 2150020. 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). 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: ((Bitte Journal prüfen)), 0. Research article (journal)
Deep neural network approximation theory for high-dimensional functions In: .
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values In: .
Monotonicity, Duplication Monotonicity, and Pareto Optimality in the Scoring-Based Allocation of Indivisible Goods In: (eds.), .
Refugee allocation in the setting of hedonic games In: (eds.), .