Undergraduate Course: Numerical Methods for Uncertainty Quantification (MATH11246)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Parameters in mathematical models of real-world systems are often impossible to measure fully or accurately and are hence subject to uncertainty. This uncertainty propagates through the model, and to mitigate risk and make informed decisions, it is then crucial to quantify the uncertainty in predictions made by the model. In this course, we will focus on mathematical models given by ordinary differential equations, which are prototypical for many applications.
In the first part of the course, we will consider efficient methods for prediction and risk assessment under various forms of uncertainty. In the second part of the course, we will further consider incorporating observational data in the framework of data assimilation.
The focus of the course will be on algorithms and the mathematics behind them. There is a computational component in Python |
| Course description |
1. Motivating examples, sources of uncertainty
2. Monte Carlo methods, including multilevel Monte Carlo
3. Reduced order models
4. Data assimilation
The coursework component of the course will consist of a computational assignment in Python.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Probability (MATH08066) AND
Numerical Ordinary Differential Equations and Applications (MATH10060)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2024/25, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework : 20%
Examination : 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Numerical Methods for Uncertainty Quantification (MATH11246) | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Use the methods presented in the course on example applications; and choose an appropriate method for a given problem.
- Analyse the computational complexity of methods for prediction under uncertainty, including Monte Carlo and its variants presented in the course.
- Formulate a data assimilation procedure in a Bayesian framework and discuss its behaviour.
- Perform scientific investigation of an algorithm by implementing it and performing experiments in Python.
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Reading List
1. Uncertainty Quantification: Theory, Implementation, and Applications,. Ralph Smith, SIAM, 2013.
2. An introduction to computational stochastic PDEs. Gabriel Lord, Catherine Powell and Tony Shardlow, Cambridge University Press, 2014.
3. Data assimilation: A mathematical Introduction, Andrew Stuart, Kody Law and Konstantinos Zygalakis. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | NMUQ |
Contacts
| Course organiser | Dr Aretha Teckentrup
Tel: (0131 6)50 5776
Email: A.Teckentrup@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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