MAGIC079: Inverse Problems

Course details

A core MAGIC course


Spring 2020
Monday, January 20th to Friday, March 27th


Live lecture hours
Recorded lecture hours
Total advised study hours


11:05 - 11:55 (UK)


When it is possible to input the governing equation(s), shape(s) and size(s) of the domain(s), boundary and initial conditions, material properties of the media contained in the field, and forces or sources, then the analysis determining the unknown field is considered mathematically well-posed, i.e. the solution exists, is unique and it depends continuously on the data. If any of these elements are unknown or unavailable, then the field problem becomes improperly defined (ill-posed) and is of an indirect (or inverse) type. The course will give an introduction to Inverse Problems. Various mathematical and numerical techniques for solving inverse problems will be described.


There is a background level of linear algebra, partial differential equations, numerical and functional analysis for which there are general courses. Also just enough physics to understand the phenomena of heat conduction, fluid flow, acoustics, optics and electromagnetism used to formulate the forward problems.

Related courses


* Basic linear inverse problems - enough linear algebra and functional analysis to understand ill-conditioning and regularization of inverse problems.
* Basic techniques for linear inverse problems - truncated singular value decomposition, Tikhonov's regularization, parameter choice methods, etc.
* PDE theory for inverse problems - enough to read the main existence, uniqueness and stability papers, e.g. Isakov's book. Some mathematical techniques and concepts, e.g. Schauder fixed point theorem, contraction principle, Fredholm alternative, etc.
* Numerical methods for inverse problems including FEM and BEM for forward problem solution and iterative regularization methods. Level set method. Constrained minimization gradient based methods.


  • DL

    Professor Daniel Lesnic

    University of Leeds
    Main contact
  • SH

    Dr Sean Holman

    University of Manchester


Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

  • Inverse Heat Conduction (Beck et al., )
  • The Boundary Element Method for Solving Improperly Posed Problems (Ingham and Yuan, )
  • The Mollification Method and the Numerical Solution of Ill-Posed Problems (Murio, )
  • Inverse Problems for Partial Differential Equations (Isakov, )


The assessment for this course will be released on Monday 20th April 2020 at 00:00 and is due in before Monday 4th May 2020 at 11:00.

"The assessment for this course will be via a single take-home paper with 2 weeks to complete, scan (pdf) and submit online. You will need the equivalent of 50

Please note that you are not registered for assessment on this course.


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