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Theses
We are always looking for talented and motivated students who want to write a thesis or carry out a term project in Uncertainty Quantification, Scientific Computing or Numerical Analysis. As prerequisite you should have completed a course (e.g. MA5348, MA9804, MA9803) or seminar (Bachelor, Master) offered by the group (see teaching page). Please contact Prof. Ullmann by email for an appointment to discuss possible topics.
PhD Theses
- Multilevel Estimators for Rare Events with Selective Refinement Strategy, Winter 2024/25
- Efficient Risk Estimation via Multilevel Monte Carlo Nested Sequential Simulation, Winter 2024/25
- Uncertainty Quantification of PDEs with Random Parameters on Random Domains, Winter 2024/25
- Galerkin Neural Networks for Numerically Solving Partial Differential Equations - Improvements, Comparison and Goal-Oriented Error Estimation, Summer 2022
- Consensus Based Rare Event Estimation, Summer 2022
- Reconstruction and Optimal Experimental Design for Multispectral Optoacoustic Tomography - A Bayesian Approach, Summer 2022
- Analysis of KL truncation error for rare event estimation, Winter 2021/22
- Physics-informed Neural Networks in Bayesian Inversion, Winter 2021/22
- Physics-informed neural networks and finite differences augmented with neural networks for solving differential equations, Winter 2021/22
- Gaussian process surrogates for Bayesian parameter identification in computational oncology, Summer 2018
- Particle methods for Deep Learning, Summer 2018
- Parameterized solution of Karhunen-Loève Eigenproblems with Reduced Basis Methods in Uncertainty Quantification, Summer 2017
- Iterative Solution of Time-Stepping Schemes and Preconditioned All-at-Once Systems – A Numerical Benchmark for the Heat Equation, Winter 2024/25
- Multigrid Computation of Poisson Seamless Cloning, Winter 2024/25
- Iterative methods and preconditioners for discretized partial differential equations, Summer 2024
- Chladni Plate - Eigenvalue Problem of the Biharmonic Operator, Summer 2022
- Network-based inference for the prediction of the COVID-19 spread, Summer 2022
- Multigrid Methods for the Approximate Solution of Partial Differential Equations, Summer 2021
- Stein Variational Gradient Descent for Rare Event Estimation, Summer 2020
- Hierarchical Neural Networks for Rare Event Estimation, Summer 2020
- Efficient Implementation of the Ising Model and Image Denoising, Summer 2019
- Adaptive Metropolis for Bayesian Inference in Crystallography, Summer 2019
- Visual SLAM using artificial visual markers, Summer 2019
- Approximation of Dynamical Systems with Neural Networks, Summer 2019
- Iterative Solvers for Discretized PDEs, Summer 2019
- Sequential Monte Carlo for time-dependent Bayesian Inverse Problems, Summer 2018
- On multilevel algorithms for the estimation of failure probabilities and rare event simulation, Summer 2018
- Neural Networks as a Method for Solving ODEs, Summer 2018