报告人：Bastian Harrach教授

报告题目： Inverse Problems in Partial Differential Equations (I)

报告摘要：

Inverse problems appear in a broad class of applications where the aim is to deduce unknown information (typically related to physical properties) from observed data. The behavior of the underlying physical system is often governed by partial differential equations (PDEs). Solving the PDEs allows to simulate the system numerically (in the sense of a digital twin). Hence, a natural approach for solving inverse problems is to fit the unknown parameters (e.g., the coefficients of a PDE) so that the system’s simulated behavior complies with the real observations. The practical solution of such inverse coefficient problems highly suffers from ill-posedness and non-linearity effects. In the first part of this talk, we will give a general introduction to inverse problems, demonstrate the problem of ill-posedness, and explain the general idea of overcoming ill-posedness by regularization.

报告题目： Inverse Problems in Partial Differential Equations (II)

报告摘要：We will then turn to the more specific problem of reconstructing the coefficient of an elliptic PDE from knowledge of the boundary values of its solutions (the famous Calderón problem). We will present recent results on how to overcome the problem of non-linearity by utilizing a special monotonicity and convexity structure of such problems with respect to the semi-definite (Loewner) order. We also derive a new connection to semidefinite convex optimization that allows globally convergent reconstruction algorithms.

报告时间：2025年3月10日  13：00~16：00

报告地点：理学楼609

报告人简介：Professor Bastian Harrach studied mathematics with a minor in physics at the University of Mainz and received his doctorate in 2006. After postdoc stays in Austria and Mainz, he became associate professor at the TU Munich and the University of Würzburg. In 2013, he was appointed full professor and chair (W3) of Optimization and Inverse Problems at the University of Stuttgart. He followed the call for a W3-professorship for Numerics of Partial Differential Equations at Goethe University Frankfurt in 2015. He rejected a further W3-offer to TU Berlin in 2023 in favor of the competing offer to stay at Goethe University. Since January 1, 2024, he is the Dean of the Department of Computer Science and Mathematics at Goethe University.