Overcoming the curse of dimensionality through nonlinear stochastic algorithms

Project Information

MONTECARLO

Grant agreement ID: 101045811

DOI

10.3030/101045811

Project terminated on 31 August 2025

EC signature date 29 November 2022

Start date 1 July 2023

End date 30 June 2028

Funded under

• European Research Council (ERC)

Total cost

€ 1 351 528,00

EU contribution

€ 1 351 528,00

Coordinated by

UNIVERSITAET MUENSTER
Germany

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (8)

Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations

Author(s): Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen
Published in: Memoirs of the American Mathematical Society, Issue 296, 2024, ISSN 0065-9266
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/MEMO/1481

Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations

Author(s): Christian Beck, Lukas Gonon, Arnulf Jentzen
Published in: Partial Differential Equations and Applications, Issue 5, 2024, ISSN 2662-2963
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S42985-024-00272-4

On the Existence of Minimizers in Shallow Residual ReLU Neural Network Optimization Landscapes

Author(s): Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, ISSN 0036-1429
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1556241

Nonlinear Monte Carlo Methods with Polynomial Runtime for Bellman Equations of Discrete Time High-Dimensional Stochastic Optimal Control Problems

Author(s): Christian Beck, Arnulf Jentzen, Konrad Kleinberg, Thomas Kruse
Published in: Applied Mathematics & Optimization, Issue 91, 2025, ISSN 0095-4616
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00245-024-10213-7

Space-Time Deep Neural Network Approximations for High-Dimensional Partial Differential Equations

Author(s): Fabian Hornung, Arnulf Jentzen and Diyora Salimova
Published in: Journal of Computational Mathematics, 2024, ISSN 0254-9409
Publisher: Global Science Press
DOI: 10.4208/JCM.2308-M2021-0266

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

Author(s): Steffen Dereich, Arnulf Jentzen, Adrian Riekert
Published in: Communications in Computational Physics, Issue to appear, 2024, ISSN 1815-2406
Publisher: Global Science Press
DOI: 10.48550/ARXIV.2406.14340

Non-convergence to Global Minimizers for Adam and Stochastic Gradient Descent Optimization and Constructions of Local Minimizers in the Training of Artificial Neural Networks

Author(s): Arnulf Jentzen, Adrian Riekert
Published in: SIAM/ASA Journal on Uncertainty Quantification, Issue 13, 2025, ISSN 2166-2525
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1639464

Gradient Descent Provably Escapes Saddle Points in the Training of Shallow ReLU Networks

Author(s): Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
Published in: Journal of Optimization Theory and Applications, Issue 203, 2024, ISSN 0022-3239
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10957-024-02513-3