Advanced Topics in Uncertainty Quantification (Summer Semester 2024)
Uncertainty quantification (UQ) is crucial across modern scientific and engineering applications. Whether predicting climate patterns, optimizing financial portfolios, or designing robust engineering systems, dealing with uncertainty is an inherent part of the problem. UQ techniques combine numerous mathematical principles to tackle the applications' complex dependence on uncertainties. In this seminar, we study several modern applied mathematical methods to assess uncertainties at the interface of complex computational models, machine learning models, and data.
Students with an interest and background in applied mathematics, probability theory, statistics, and related fields will learn about selected modern UQ methods. They will understand the method's mathematical principles and thus gain a critical understanding of its applicability.
Preliminary selection of topics:
- Hierarchical approximation techniques (e.g., multi-level and multi-index methods) for forward and inverse UQ
- Ensemble Kalman Inversion
- Probabilistic Numerics
- Assessing Uncertainties in Neural Networks.
Other topics may be addressed depending on the interest in the seminar. Students will present their assigned topics in a block seminar at the end of the lecture period.
Preliminary Meeting
A preliminary information meeting will take place on Monday, February 12, 2024, at 14:00 in SR 3.068 (building 20.30).