At 4pm on Monday, April 19, Professor Sedar Ngoma from SUNY-Geneseo will provide an overview of inverse problems. Zoom link: ithaca.zoom.us/j/91482691861
Everyone is invited! Please join us for our Math Colloquium series this semester on Mondays at 4pm: ithaca.zoom.us/j/91482691861. If you have any questions, please contact Prof. Ted Galanthay at tgalanthay@ithaca.edu.
On Monday, April 19, we are hosting Professor Sedar Ngoma from SUNY-Geneseo who will be delivering a presentation entitled "An Overview of Inverse Problems."
Abstract: In order to find approximate solutions to problems emanating from science, engineering, mathematics, and many other fields, a process called model is described in detail and an appropriate input called a cause is supplied. One is then required to find the unique output (or approximate solution) called effect. This is known as direct or forward problems, in which the media properties of a given model described by equations (for example, equation coefficients) are assumed to be known. However, media properties are often not readily observable. This lack of specification in the model leads to inverse problems, in which one is required to find the cause of the effect given the effect. For example, one can try to determine the equation coefficients (which usually represent important media properties) from the information about solutions of the direct problem.
One of the downsides of inverse problems is that their approximate solutions are almost always ill-posed in the sense that they may not be unique or stable. In this talk we introduce inverse problems, investigate some examples, and describe analytically and numerically a regularization technique used to combat instability in the solutions. We conclude the talk with a time-dependent inverse source problem for a parabolic partial differential equation.
https://www.ithaca.edu/intercom/article.php/20210414130725335