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Fabian Hornung
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A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black–Scholes partial differential equations
P Grohs, F Hornung, A Jentzen, P Von Wurstemberger
American Mathematical Society 284 (1410), 2023
2502023
Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard …
C Beck, F Hornung, M Hutzenthaler, A Jentzen, T Kruse
Journal of Numerical Mathematics 28 (4), 197-222, 2020
592020
Space-time error estimates for deep neural network approximations for differential equations
P Grohs, F Hornung, A Jentzen, P Zimmermann
Advances in Computational Mathematics 49 (1), 4, 2023
512023
The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates
F Hornung
Journal of Evolution Equations 18, 1085-1114, 2018
422018
Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space
Z Brzeźniak, F Hornung, L Weis
Probability Theory and Related Fields 174, 1273-1338, 2019
372019
Space-time deep neural network approximations for high-dimensional partial differential equations
F Hornung, A Jentzen, D Salimova
arXiv preprint arXiv:2006.02199, 2020
282020
Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise
Z Brzeźniak, F Hornung, U Manna
Stochastics and Partial Differential Equations: Analysis and Computations 8 …, 2020
132020
Global solutions of the nonlinear Schrodinger equation with multiplicative noise
F Hornung
Dissertation, Karlsruhe, Karlsruher Institut für Technologie (KIT), 2018, 2018
102018
Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds
Z Brzeźniak, F Hornung, L Weis
Stochastics and Partial Differential Equations: Analysis and Computations 10 …, 2022
82022
The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds
F Hornung
Nonlinear Differential Equations and Applications NoDEA 27 (4), 40, 2020
52020
The stochastic nonlinear Schr\" odinger equation in unbounded domains and manifolds
F Hornung
arXiv preprint arXiv:1906.08638, 2019
12019
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant …
P Grohs, F Hornung, A Jentzen, P von Wurstemberger
2021
MARTINGALE SOLUTIONS FOR THE STOCHASTIC NONLINEAR SCHR ODINGER EQUATION IN THE ENERGY SPACE
ZB ZNIAK, F HORNUNG, L WEIS
emu (t) 1000, 1, 2017
2017
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