Studien-, Bachelor- oder Master-Arbeiten

Im Folgenden finden Sie eine Auswahl offener studentischer Abschlussarbeiten bei uns im Fachgebiet EMFT. Weitere Arbeiten in den genannten Themenbereichen sind auf Anfrage möglich. Kontaktieren Sie uns gerne!

Der Leitfaden enthält Hinweise zum Schreiben von Abschluss- und Hausarbeiten. Außerdem stehen LaTeX-Vorlagen für Arbeiten und Vorträge bereit.

  • Architecture Optimization in Physics-Informed Neural Networks

    03.09.2020

    Bachelorarbeit, Masterarbeit, Projektseminar, Arbeitstyp nach Absprache, Hiwi Stelle

    Artificial Neural Networks (NNs) have provided transformative results in numerous and diverse engineering domains, e.g. image processing or pattern recognition. In recent years, NNs have also been utilized for solving Partial Differential Equations (PDEs). Therein, one of the most popular approaches are Physics-Informed Neural Networks (PINNs). The procedure in PINNs is the following: First, an NN is employed to approximate the solution of the PDE. Next, an optimization algorithm is used to calibrate the NN’s intrinsic parameters such that the NN satisfies the PDE and the initial/boundary conditions.

    A key factor which determines the performance and expressive capabilities of an NN is its architecture, i.e. number of layers, neurons per layer, connectivity, activation functions, etc. Nevertheless, investigations regarding efficient PINN architectures are virtually non-existent in the related literature. In an attempt to fill that gap, the task of this thesis will be the implementation of various NN architectures in the context of PINNs and their evaluation in terms of PDE solution quality. Possibilities include Long-Term/Short-Term Memory (LSTM) NNs, adaptive activation functions, Deep Jointly-Informed NNs (DJINNs), and others.

    Betreuer/innen: Dr.-Ing. Dimitrios Loukrezis, Moritz von Tresckow, M.Sc.

    Ausschreibung als PDF

  • Parareal Physics-Informed Neural Networks for Transient Electromagnetic Field Problems

    03.09.2020

    Bachelorarbeit, Masterarbeit, Projektseminar, Arbeitstyp nach Absprache, Hiwi Stelle

    Artificial Neural Networks (NNs) have provided transformative results in numerous and diverse engineering domains, e.g. image processing or pattern recognition. In recent years, NNs have also been utilized for solving Partial Differential Equations (PDEs). Therein, one of the most popular approaches are Physics-Informed Neural Networks (PINNs).

    A major drawback of PINNs is the computational cost arising due to the use of large datasets and NNs with many degrees of freedom. As a remedy, a recent work has proposed a combination of the Parareal and PINN algorithms, resulting in a method referred as PPINN. The PPINN algorithm splits long-time problems into many independent short-time problems, supervised by an inexpensive and fast coarse-grained conjugatebgradient solver. The benefit of PPINN is that it decreases the computational cost of training a DNN by reducing the size of the training set and the number of d.o.f.s per network.

    The task of the thesis is to implement the PPINN algorithm to a suitable, transient electromagnetics problem, a test case that has not appeared in the literature so far. A comparison against standard PINNs will complement this work.

    Betreuer/innen: Dr.-Ing. Dimitrios Loukrezis, Moritz von Tresckow, M.Sc.

    Ausschreibung als PDF

  • p-Type algebraic multigrid for high order hierarchical FEM for Maxwell's equations

    15.02.2020

    Bachelorarbeit, Masterarbeit, Projektseminar

    In this work, a novel p-type AMG formulation for the solution of Maxwell’s equations will be developed. The method will be based on the high order hierarchic approximation space of Zaglmayer in order to derive appropriate smoothing, restriction and interpolation operators. The method is to be implemented in parallel the platform, PETSC. Furthermore, the numerical performance of the method will be analyzed for relevant applications in a HPC environment.

    Betreuer/in: PD Dr. rer. nat. Erion Gjonaj

    Ausschreibung als PDF

  • Elastodynamic Wave Propagation in Rail Tracks

    30.10.2019

    Bachelorarbeit, Masterarbeit, Projektseminar

    A train excites elastodynamic waves in the rail track. The track consists of rails, fasteners, railroad ties (or sleepers) and ballast. The system can be decomposed in waveguide parts and connections. The former are represented by waveguides with corresponding wave numbers and impedances. The latter are represented by additional impedances. In this respect, the track system has many similarities with a waveguide system for electromagnetic waves. This suggests exploiting well known techniques for electromagnetic waveguide systems to model rail tracks.

    Betreuer/in: Prof. Dr.-Ing. Herbert De Gersem

    Ausschreibung als PDF