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.
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, ill posed problems, regularization methods, singular value, decomposition, Tikhonov regularization, data assimilation, maximum likelihood estimation, Basian estimation.
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||✔ Practical and/or problem-solving skills|
Students will get the experience of performing the computational exercises about practical inverse problem.
|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|
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.
Parameter Estimation and Inverse Problems
Richard C. Aster, Brian Borchers, Clifford H. Thurber
Discrete Inverse Problems: Insight and Algorithms (Fundamentals of Algorithms)
Per Christian Hansen SIAM
Students' knowledge about inverse problem, data assimilation and their ability to apply them to problems will be assessed.
report problems 60%, exercise problems 40%.
Students must have successfully completed linear algebra, basics of mathematics for engineering, computer programming.