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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Uncertainty Quantification (MATH11243)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryParameters 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 Outline of suggested topics:
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.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Probability (MATH08066) AND Numerical Ordinary Differential Equations and Applications (MATH10060)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) 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 )
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)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Use the methods presented in the course on example applications; and choose an appropriate method for a given problem.
  2. Analyse the computational complexity of methods for prediction under uncertainty, including Monte Carlo and its variants presented in the course.
  3. Formulate a data assimilation procedure in a Bayesian framework and discuss its behaviour.
  4. Perform scientific investigation of an algorithm by implementing it and performing experiments in Python.
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
Course organiserDr Aretha Teckentrup
Tel: (0131 6)50 5776
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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