MATH 6397 Applied Inverse Problems (Fall 2020)
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Important information for the course Applied Inverse Problems (MATH 6397 — 21337) will be posted on this page. Please visit it on a regular basis. Check the syllabus regularly for any important updates. It is the students responsibility to be aware of additional course policies presented by the instructor during class.Course Description
Inverse problems are paramount importance and can be found in virtually all scientific disciplines with applications ranging from medicine, geophysics, to engineering. In many of these applications the forward or simulation problem, i.e., the solution of an underlying mathematical model to yield outputs given some inputs, is already a challenging task. Many applications require us to go beyond evaluating forward operators; we have to address what is often the ultimate goal: prediction and decision-making. This requires us to tackle mathematical challenges that comprise, and, therefore, are more difficult than the forward problem. One example is the solution of inverse problems. Here, we seek model inputs (or parameters) so that the output of the forward model matches observational data.This course will introduce the theoretical foundations of inverse problems and strategies to their numerical solution. We will consider applications in data and physical sciences. Starting from first principles we will discuss how to design and analyze direct and iterative methods for efficiently solving different classes of inverse problems. Students will get to explore the design of computational strategies to solve these problems. Examples studied in the class will be selected from different areas of computational sciences and engineering, including deblurring, imaging, and continuum mechanics.