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)

• slides: here

• slides with annotations: here

• zoom recording: here

Part 2 (Monte Carlo, Quasi Monte Carlo)

• slides: here

• slides with annotations: here

• zoom recording: here

Part 3 (Polynomial Chaos Expansion)

• slides: here

• slides with annotations: here

• zoom recordings:

  • class of April 26: here

  • class of May 3: here (first 45 minutes)

Part 4 (Sparse grids)

• slides: here

• slides with annotation:

  • up to adaptive sparse grids example: here

  • remaining part: here

• zoom recordings:

  • class of May 3: here (from minute 45);

  • class of May 10: here

• Sparse grids / PCE cheat sheet: here

Part 5 (multi-fidelity methods)

• slides:

  • Multi-Level Monte Carlo, Multi-Index stochastic Collocation: here

  • Stochastic Radial Basis Functions: here

  • Naval UQ (MISC and SRBF): here

• slides with annotations

  • Multi-Level Monte Carlo, Multi-Index stochastic Collocation: here

• zoom recordings:

  • class of May 17: here

  • seminar of May 20, radial basis functions: here

  • seminar of May 20, naval UQ (MISC and SBRF): here

Part 6 (Inverse UQ)

• slides:

  • Bayesian inversion: here

  • SIR-like models and identifiability + biblio for course: here

• slides with annotations:

  • Bayesian inversion: here

  • SIR-like models and identifiability: here

• zoom recordings:

  • class of May 24: here

  • class of May 31: here

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

• Lab 1: exercise text: here

• Lab 1: zoom recording: here

• Lab 1: codes: here

• Lab 2: exercise text: here

• Lab 2: codes: here

• Lab 2: zoom recording: here

• Lab 3: exercise text: here

• Lab 3: codes: here

• Lab 3: zoom recording: here

• Lab 4: exercise text: here

• Lab 4: codes: here

• Lab 4: zoom recording: here

• Lab 5: exercise text: here

• Lab 5: codes: here

• Lab 6: exercise text: here

• Lab 6: codes: here

• Lab 6: zoom recording: here