The overarching theme of this work is the efficient computation of large-scale systems. Here we deal with two types of mathematical challenges, which are quite different at first glance but offer similar opportunities and challenges upon closer examination.

Physical descriptions of phenomena and their mathematical modeling are performed on diverse scales, ranging from nano-scale interactions of single atoms to the macroscopic dynamics of the earth's atmosphere. We consider such systems of interacting particles and explore methods to simulate them efficiently and accurately, with a focus on the kinetic and macroscopic description of interacting particle systems.

Macroscopic governing equations describe the time evolution of a system in time and space, whereas the more fine-grained kinetic description additionally takes the particle velocity into account.

The study of discretizing kinetic equations that depend on space, time, and velocity variables is a challenge due to the need to preserve physical solution bounds, e.g. positivity, avoiding spurious artifacts and computational efficiency.

In the pursuit of overcoming the challenge of computability in both kinetic and multi-scale modeling, a wide variety of approximative methods have been established in the realm of reduced order and surrogate modeling, and model compression. ... mehr

Physical descriptions of phenomena and their mathematical modeling are performed on diverse scales, ranging from nano-scale interactions of single atoms to the macroscopic dynamics of the earth's atmosphere. We consider such systems of interacting particles and explore methods to simulate them efficiently and accurately, with a focus on the kinetic and macroscopic description of interacting particle systems.

Macroscopic governing equations describe the time evolution of a system in time and space, whereas the more fine-grained kinetic description additionally takes the particle velocity into account.

The study of discretizing kinetic equations that depend on space, time, and velocity variables is a challenge due to the need to preserve physical solution bounds, e.g. positivity, avoiding spurious artifacts and computational efficiency.

In the pursuit of overcoming the challenge of computability in both kinetic and multi-scale modeling, a wide variety of approximative methods have been established in the realm of reduced order and surrogate modeling, and model compression. ... mehr

Zugehörige Institution(en) am KIT |
Institut für Angewandte und Numerische Mathematik (IANM) Institut für Informationssicherheit und Verlässlichkeit (KASTEL) Scientific Computing Center (SCC) |

Publikationstyp |
Hochschulschrift |

Publikationsdatum |
05.06.2023 |

Sprache |
Englisch |

Identifikator |
KITopen-ID: 1000158838 |

HGF-Programm |
46.21.02 (POF IV, LK 01) Cross-Domain ATMLs and Research Groups |

Verlag |
Karlsruher Institut für Technologie (KIT) |

Umfang |
xvii, 198 S. |

Art der Arbeit |
Dissertation |

Fakultät |
Fakultät für Mathematik (MATH) |

Institut |
Institut für Angewandte und Numerische Mathematik (IANM) |

Prüfungsdatum |
03.05.2023 |

Projektinformation |
SPP 2298 (DFG, DFG KOORD, FR 2841/9-1) |

Schlagwörter |
Kinetic Models, Numerical Methods, Machine Learning, Neural Networks, Optimization, Low-Rank Compression |

Referent/Betreuer |
Frank, Martin Platzer, André Hauck, Cory D. |

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