
Dettaglio Insegnamento
Academic Year 
2022/2023 
Name 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Programme Year 
1 
ID Code 
058410 
Course Title 
AN INTRODUCTION TO FORWARD UNCERTAINTY QUANTIFICATION FOR STOCHASTIC PDES 
Course Type 
MONODISCIPLINARE 
Credits (CFU / ECTS) 
5.0 
Course Description 
Prerequisites:
The course is suitable for mathematically/physically/engineering grounded graduates, who wish to learn methodologies for incorporating uncertainty into their mathematical models and for deriving reliable numerical approximations.
We assume knowledge of undergraduatelevel mathematics, including some basics of analysis and linear algebra, but we will recall and provide background on probability theory (Part I) and standard Galerkin finite element methods for solving deterministic PDEs (Part II.III).
During the exercise sessions in laboratory, the students will have the opportunity of implementing the techniques discussed in class and solve examples that illustrate the key concepts. Matlab is a convenient software for numerical scientific computing, and it will be employed during the exercise classes. Matlab knowledge does not represent a prerequisite: when needed, an introductory class on the software will be offered to the students.
Development of the course:
The course develops incrementally: from basic UQ techniques applied to instructional examples of stochastic PDEs to the stateoftheart methodologies for UQ in geophysical applications.
The incremental growth runs along two tracks: one for mathematical models and applications, and the second for UQ methodologies. Concerning the first, the key UQ concepts will be first illustrated on toy problems, and later applied to more realistic PDEs, like the Darcy boundary value problem with stochastic permeability field, used in geophysical application for modeling the fluid flow in heterogenous media.
Concerning the second, we will start from the most straightforward approach to tackle the uncertainty quantification problem (namely the Monte Carlo method), and we will progressively move towards more advanced techniques, like the Stochastic Galerkin and Stochastic Collocation methods. 
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Bonizzoni Francesca


