Uncertainty Quantification of Partial and Ordinary Differential Equations with random coefficients
Teacher: Lorenzo Tamellini, CNR-IMATI, Pavia
Teaching assistant: Chiara Piazzola, CNR-IMATI, Pavia
Dates: April 12 - May 31
Class: Mondays, 11am/1pm
Lab sessions: Thursdays, 9:30am/11:30am
Syllabus: here
Registration: send an email to tamellini <at> imati <dot> cnr <dot> it
Room: Classes and lab sessions will be held online via zoom (send me an email if you didn't receive the link by email - recordings will be made available to registered students), even if Pavia is back to covid classifcation "yellow zone"
Language: Classes and teaching/lab material will be in English
Access to material: we're happy to share our slides ! Just send an email to address above to get access (even after the end of the course)
All material on this website is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license.
News
June 1: uploaded zoom recording and slides of yesterday's class. The slides include also a short biblio for the course. The course is finished, thanks for participating. Get in touch with us for any questions
Final program
Part 1 (week 1, April 12 and 15): motivations & examples, recap on probability, random fields
Part 2 (week 2, April 19 and 22): Monte Carlo and other sampling methods (Latin Hypercube Sampling, Quasi-Monte Carlo)
Part 3 (weeks 3 and 4, April 26 to May 6): Polynomial Chaos Expansion for forward UQ: Stochastic Galerkin and Least squares methods
Part 4 (weeks 4 and 5, May 3 to May 13): Sparse Grids Stochastic Collocation Method for forward UQ
Part 5 (week 6, May 17 and 20): Multi-level methods for forward UQ: Multi-Level Monte Carlo, Multi-Index Stochastic Collocation. Stochastic Radial Basis functions and application of forward UQ techniques to a naval engineering problem. No exercise session this week
Part 6 (weeks 7 and 8, May 24 to May 31): Inverse UQ: Bayesian inversion, structural and Practical Identifiability, and application to SIR-like dynamical systems
Teaching material and links to zoom recordings
Part 1 (introduction, recap on probability, random fields)
Part 2 (Monte Carlo, Quasi Monte Carlo)
Part 3 (Polynomial Chaos Expansion)
Part 4 (Sparse grids)
Part 5 (multi-fidelity methods)
slides:
slides with annotations
Multi-Level Monte Carlo, Multi-Index stochastic Collocation: here
zoom recordings:
Part 6 (Inverse UQ)
Lab session material
We'll use Matlab and the sparse grids matlab kit. Download the most recent version of the sparse grids matlab kit (18.10, "Esperanza") here. The package is compatible with any reasonably recent version of Matlab. Compatibility with Octave has never been tested