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Programme & Unit Catalogues

## MA50250: Inverse problems, data assimilation and filtering

[Page last updated: 15 October 2020]

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: CW 70%, OR 30%
Assessment Detail:
• Coursework 1 (CW 35%)
• Coursework 2 (CW 35%)
• Oral presentation (Viva) (OR 30%)
Supplementary Assessment:
MA50250 - Coursework / Oral presentation (where allowed by programme regulations)
Requisites: Before taking this module you must take MA40198 AND ( take MA50174 OR take MA50178 )
Description: Aims:
Students should know why inverse problems are important in many areas of mathematics and its applications. They should be able to demonstrate theoretical and practical understanding of data assimilation, filtering and regularisation methods for solving inverse problems.

Learning Outcomes:
Students should be able to: Formulate inverse problems, regularise ill-posed problems, and analyse their structure; Construct, analyse, and interpret solutions to inverse problems using regularisation and statistical data assimilation techniques; Apply statistical filtering methods and interpret their solutions; Communicate problem descriptions, model formulations, and problem solutions.

Skills:
Problem solving (T, F&A), computing (T, F&A), written and oral communication (F&A).

Content:
Inverse problems; ill-posedness and regularisation methods, Tikhonov regularisation and truncated singular value decomposition.
Statistical data assimilation and filtering; variational methods (3DVar/4DVar); Kalman filters and extensions, particle filters.
Applications, for example, in medical imaging, meteorology and oceanography.
Programme availability:

#### MA50250 is Optional on the following programmes:

Department of Mathematical Sciences

 Notes: This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here for 2020/21. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.