### 2022　Inverse Problems and Data Assimilation

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Graduate major in Systems and Control Engineering
Instructor(s)
Amaya Kenji
Class Format
Lecture    (Blended)
Media-enhanced courses
Day/Period(Room No.)
Thr1-2(W641)
Group
-
Course number
SCE.A405
Credits
1
2022
Offered quarter
3Q
Syllabus updated
2022/5/11
Lecture notes updated
-
Language used
English
Access Index

### 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.

### Keywords

inverse problems, ill posed problems, regularization methods, singular value, decomposition, Tikhonov regularization, data assimilation, maximum likelihood 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

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

Parameter Estimation and Inverse Problems
Richard C. Aster, Brian Borchers, Clifford H. Thurber
Elsevier, 2018/10/16

### 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.