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 arXiv preprint arXiv:1809.02362, 2018 | 66 | 2018 |

Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space Z Brzeźniak, F Hornung, L Weis Probability Theory and Related Fields 174 (3-4), 1273-1338, 2019 | 20 | 2019 |

The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates F Hornung Journal of Evolution Equations 18 (3), 1085-1114, 2018 | 20 | 2018 |

Space-time error estimates for deep neural network approximations for differential equations P Grohs, F Hornung, A Jentzen, P Zimmermann arXiv preprint arXiv:1908.03833, 2019 | 15 | 2019 |

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 1 (ahead-of-print), 2020 | 13 | 2020 |

Global solutions of the nonlinear Schrödinger equation with multiplicative noise F Hornung PhD thesis, Karlsruhe Institute of Technology, 2018 | 8 | 2018 |

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 | 7 | 2020 |

Uniqueness of martingale solutions for the stochastic nonlinear Schr\" odinger equation on 3d compact manifolds Z Brzezniak, F Hornung, L Weis arXiv preprint arXiv:1808.10619, 2018 | 6 | 2018 |

Space-time deep neural network approximations for high-dimensional partial differential equations F Hornung, A Jentzen, D Salimova arXiv preprint arXiv:2006.02199, 2020 | 1 | 2020 |

Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise Z Brzezniak, F Hornung, U Manna | 1 | 2018 |

The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds F Hornung Nonlinear Differential Equations and Applications NoDEA 27 (4), 1-46, 2020 | | 2020 |

The stochastic nonlinear Schr\" odinger equation in unbounded domains and manifolds F Hornung arXiv preprint arXiv:1906.08638, 2019 | | 2019 |

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 |