2018 Inverse Problems and Data Assimilation

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Graduate major in Systems and Control Engineering
Amaya Kenji 
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Course description and aims

This course focuses on the inverse problems and data assimilation.
Lectures will include the topics about: inverse problems, ill posed problems, regularization methods, singular value, decomposition, Tikhonov regularization, data assimilation, maximum likelihood estimation, Basian estimation.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand how to set the inverse problems.
2) Understand well posed problems and ill posed problems.
3) Understand various regularization methods and how to choose the regularization parameters.
4) Acquire knowledge to perform the practical numerical inverse problems.


inverse problems, iIll posed problems, regularization methods, singular value, decomposition, Tikhonov regularization, data assimilation, maximum liklihood estimation, Basian estimation.

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Students will get the experience of performing the computational exercises about practical inverse problem.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction to Inverse Problems Intoroduce various inverse problems in real world, and understand the basics of inverse problems
Class 2 Problem setting for inverse problems, well-posed problem, ill-posed problem Understanding of problem setting of inverse problems, well-posed problem, ill posed problem.
Class 3 Regularization method1 TSVD
Class 4 Regularization method2 Tikhonov regularization Understanding of Tikhonov regularization
Class 5 Tunning of regularization parameters Understanding of choosing methods of regularization parameters
Class 6 Data assimilation, Maximum likelihood estimathon, Basian estimation Understanding of Data assimilation, Maximum likelihood estimathon, Basian estimation
Class 7 Solving "Real" Problems Learn the practical inverse problems in engineering
Class 8 Summary of the lectures Summerizes whole series of lectures and perform computational exercises.



Reference books, course materials, etc.

Discrete Inverse Problems: Insight and Algorithms (Fundamentals of Algorithms
Per Christian Hansen SIAM

Assessment criteria and methods

Students' knowledge about inverse problem, data assimilation and their ability to apply them to problems will be assessed.
report problems 60%, exercise problems 40%.

Related courses

  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II
  • SCE.A403 : Programming workshop

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed linear algebra, basics of mathematics for engineering, computer programming.

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