BERN07 Uncertainty Quantification & Data-Driven Modelling is an elective course in the second cycle for a degree of Master of Science in Computational Science, Applied Computational Science, or Mathematics. The course can also be given as an independent course.

Course content

This course introduces basic knowledge regarding numerical methods for uncertainty quantification and relevant data-driven modeling in computational science. This includes forward uncertainty propagation from inputs to responses, inverse parameter estimation through Bayesian approaches, surrogate modeling for accelerating multiquery simulations, and observational data integration into dynamical models. Specifically, the course treats:

Important concepts in uncertainty quantification (UQ), such as verification vs. validation, intrusive vs. non-intrusive, and forward vs. inverse UQ
Numerical discretisation for PDEs with random parameters: stochastic Galerkin and stochastic collocation
Bayesian inference and its applications to parameter estimation
Sampling techniques: Monte Carlo and importance sampling
Gaussian processes for surrogate modeling
Basics of projection-based and data-driven model reduction
Data assimilation with Kalman filters

Teaching

The teaching consists of lectures and assignment tasks. The tasks are not compulsory but preparatory for the oral exam.

Assessment

The examination consists of a written project report and an oral examination at the end of the course.

Course literature

Handouts, available digitally
Smith, Ralph C. Uncertainty Quantification: Theory, Implementation, and Applications. SIAM, 2023. ISBN 9781611973211
Rasmussen, Carl E., and Williams, Christopher KI. Gaussian Processes for Machine Learning. MIT Press, 2006. ISBN 9780262182539
Quarteroni, Alfio, Manzoni, Andrea, and Negri, Federico. Reduced Basis Methods for Partial Differential Equations: An Introduction. Springer, 2015. ISBN 9783319154305

Official course description

Course Evaluation

Link to course evaluations on the department's website:

Course Evaluations, Numerical Analysis at Faculty of Science