Computational Science: Uncertainty Quantification & Data-driven Modelling

<p>The course is an elective course in the second cycle for a degree of Master of Science in Computational Science, Applied Computational Science, or Mathematics with specialisation in Numerical Analysis. The course can also be given as an independent course. The overarching goal of the course is that the students acquire 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 multi- query simulations, and observational data integration into dynamical models.</p><p>The course treats:</p> <ul> <li>Important concepts in uncertainty quantification (UQ), such as verification vs. validation, intrusive vs. non-intrusive, and forward vs. inverse UQ</li> <li>Numerical discretisation for PDEs with random parameters: stochastic Galerkin and stochastic collocation</li> <li>Bayesian inference and its applications to parameter estimation</li> <li>Sampling techniques: Monte Carlo and importance sampling</li> <li>Gaussian processes for surrogate modeling</li> <li>Basics of projection-based and data-driven model reduction</li> <li>Data assimilation with Kalman filter</li> </ul>