MATH-616 / 3 crédits

Enseignant(s): Nobile Fabio, Vanzan Tommaso, Invited lecturers (see below)

Langue: Anglais


Frequency

Only this year

Summary

The course focuses on mathematical models based on PDEs with random parameters, and presents numerical techniques for forward uncertainty propagation, inverse uncertainty analysis in a Bayesian framework and optimal control under uncertainty.

Content

Keywords

Random PDEs, Forward Uncertainty Propagation, Bayesian Inverse Problems, Optimization Under uncertainty; Monte Carlo, Multi Level Monte Carlo, Polynomial Chaos, Sparse grids, rational approximations

Learning Prerequisites

Required courses

The students are expected to have basic knowledge on probability theory, approximation theory, Partial Differential Equations, numerical analysis in general and finite element analysis in particular.

Resources

Bibliography

A. Cohen, R. DeVore “Approximation of high-dimensional parametric PDEs”. Acta Numer. 24 (2015).
A. Stuart, “Inverse problems: a Bayesian perspective”. Acta Numer, 19 (2010).
D. Kouri, A. Shapiro, “Optimization of PDEs with uncertain inputs.” in Frontiers in PDE-constrained optimization, 41–81, IMA Vol. Mat. Appl., 163, Springer, 2018.

Ressources en bibliothèque

Dans les plans d'études

  • Nombre de places: 20
  • Forme de l'examen: Exposé (session libre)
  • Matière examinée: Numerical methods for random PDEs and uncertainty
  • Cours: 24 Heure(s)
  • Projet: 28 Heure(s)

Semaine de référence