Uncertainty Quantification and Data Assimilation

Course manual 2020/2021

Course content

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.

Study materials

Literature

• 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 cover a selection from chapters 2-4 .

• 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.

Objectives

• Students are familiar with the key questions and topics in uncertainty quantification and data assimilation.
• Students have gained understanding of a variety of methods to tackle these topics.
• Students  are able to apply the methods on prototype model problems and implement them on a computer.

Teaching methods

• Presentation/symposium
• Lecture
• Exercises

Students work in small teams on the homework exercises. Part of the exercises count towards the final grade, for these a brief report must be handed in (one per team). Each team is expected to give once a short joint presentation on its results for an exercise.

Learning activities

Attendance

This programme does not have requirements concerning attendance (TER-B).

Assessment

The final exam consists of a take-home exam assignment for which students hand in a report that will be assessed and discussed individually. The final grade for the course is determined for 75% by the final exam grade and for 25% by the average of 4 submitted homework exercises. For the homework exercises, a single grade per team is given. Each team gives a (joint) presentation once, this is assessed with a pass/fail grade for the team. Without a pass grade for the presentation, no final grade for the course will be given.

In case a resit of the final exam is needed, the grades for the homework exercises and the presentation will still count towards the final grade, in the same manner as described above (i.e., 75% resit final exam grade, 25% homework, pass grade for presentation). A resit will be a take-home exam assignment with discussion of the submitted report, similar to the regular final exam.

Fraud and plagiarism

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

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• prof. dr. D.T. Crommelin