After successful completion of the course, students are able to explain recent topics and current approaches in forward and inverse uncertainty quantification as well as machine learning methods for various applications in computational science and engineering. They also learn how to prepare and give a presentation and to write a seminar paper.

Uncertainty quantification (UQ) and machine learning (ML) have been of great interest in many applications in computational science and engineering. In recent years, UQ for PDE-based models has been developed for reliable simulation-based predictions as real-world applications in science and technology are affected significantly by uncertainties. UQ combines theory and methods from mathematics and statistics such as multilevel Monte-Carlo for solving PDEs with random input data, and Markov-chain Monte-Carlo methods for Bayesian statistical inverse problems and optimal experimental design. On the other hand, machine learning techniques and neural-networks such as physics-informed neural networks (PINNs) as surrogate methods for PDE approximation as well as for inverse modeling are growing fast.
The applications are but not limited to medical imaging, computational biology, materials science, nanotechnology, and computational fluid dynamics (CFD).

Blackboard lecture

Writing a seminar paper and presenting on the blackboard