6 EC
Semester 1, period 1, 2
5334UQDA6Y
Uncertainty Quantification and Data Assimilation (UQ and DA) are concerned with two closely related questions. In UQ, the central question is how to deal with uncertainties in mathematical models for simulation and prediction of complex phenomena. For DA, the main question is how to incorporate data (e.g. from physical measurements) in models in a suitable way, in order to improve model predictions and quantify prediction uncertainty.
The focus of this course will be on the mathematical techniques and methodologies developed for UQ and DA. We will cover a selection of the following topics: Stochastic Galerkin method, polynomial chaos expansion, stochastic collocation, sparse grids and quadrature, surrogate modeling, sensitivity analysis, Sobol indices, Kalman filter, variational data assimilation, ensemble Kalman filter.
D. Xiu, Numerical Methods for Stochastic Computations. A Spectral Method Approach. Princeton University Press, 2010.
This is the primary book for the course. We read chapters 3-7 .
K. Law, A. Stuart, K. Zygalakis, Data Assimilation. A Mathematical Introduction. Springer, 2015.
We read chapter 2 and a selection from chapters 3-4 .
T.J. Sullivan, Introduction to Uncertainty Quantification. Springer, 2015.
This book is background literature and provides more in-depth analysis of the topics treated in the book by Xiu.
R.C. Smith, Uncertainty Quantification. Theory, Implementation, and Applications. SIAM, 2014.
We read part of chapter 15 on global sensitivity analysis.
All students are expected to read the assigned chapters for each course meeting, and participate actively in the meetings. The students take turns presenting the reading material for each meeting, with self-prepared slides to summarize the material and highlight some topics. Furthermore, the students work individually on two (partly numerical) home assignments throughout the semester, in which they apply some of the methods and techniques that have been discussed on simple examples. Students hand in written reports on the assignments which will be discussed in oral exams.
|
Activity |
Hours |
|
|
Course meetings |
28 |
|
|
Self study |
140 |
|
|
Total |
168 |
(6 EC x 28 uur) |
The programme does not have requirements concerning attendance (OER-B).
Additional requirements for this course:
The student may be absent in max. 2 course meetings.
| Item and weight | Details |
|
Final grade | |
|
0.4 (40%) Presentations | |
|
0.2 (20%) Assignment reports | |
|
0.3 (30%) Oral exams | |
|
0.1 (10%) Class participation |
The grade will be based on presentations (including slides) (40%), assignment written reports (20%), oral exams about assignment reports (30%) and active class participation (10%).
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
During the first half of the course we read chapters 3-7 from the book by Xiu. At the end of this half the first assignment will be handed out. The second half of the course is devoted to the material from the books by Smith and by Law et al., and concludes with the second assignment.
The schedule for this course is published on DataNose.