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MA50250: Inverse problems, data assimilation and filtering

[Page last updated: 15 October 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 70%, OR 30%
Further information on unit assessment Assessment Detail:
  • Coursework 1 (CW 35%)
  • Coursework 2 (CW 35%)
  • Oral presentation (Viva) (OR 30%)
Further information on supplementary assessment Supplementary Assessment:
MA50250 - Coursework / Oral presentation (where allowed by programme regulations)
Further information on requisites 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.
Further information on programme availabilityProgramme availability:

MA50250 is Optional on the following programmes:

Department of Mathematical Sciences

Notes: