Mathematician Kang-Li Xu conducts research in Magdeburg supported by an Alexander von Humboldt Fellowship
Humboldt Fellow from China visits the Max Planck Institute Magdeburg // Close collaboration on Riemannian optimization model order reduction methods for nonlinear systems
The Chinese mathematician and systems science expert Dr. Kang-Li Xu is conducting research at the Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg for one year supported by an Alexander von Humboldt Fellowship. She is a visiting research fellow in the research group Computational Methods in Systems and Control Theory, where she is devoting herself to her special field of Riemannian optimization.
The Alexander von Humboldt Foundation has awarded Dr. Kang-Li Xu a research fellowship for doctoral researchers. The scientist has been working at the Max Planck Institute Magdeburg since December 1, 2023. In her research stay, she will work on Riemannian optimization model order reduction methods for nonlinear systems with polynomial or rational nonlinearities with her host, Prof. Peter Benner.
"We are very pleased to host Dr. Xu as a Humboldt Fellow at the MPI Magdeburg and to be able to cooperate with her scientifically," says Prof. Dr. Peter Benner, Director at the Max Planck Institute Magdeburg and Head of the Department of Computational Methods in Systems and Control Theory. "The selection process for the Humboldt research fellowships is highly competitive, so being awarded the fellowship is a special honor. We are looking forward to a fruitful collaboration."
Riemannian optimization: special mathematical method
In many research and application fields, modeling and simulation are necessary. The accurate description of the behavior of complex physical systems often yields large-scale systems. Very often, the direct simulation of these systems will lead to unacceptable time consumption. Model order reduction is an efficient tool to achieve fast simulation, optimization and control of large-scale systems. Approximating a large-scale system by a much smaller model (known as reduced-order model or “surrogate”) and meanwhile preserving the essential physical properties are the goal of model order reduction.
Since 2015, Kang-Li Xu has been devoted to exploring model order reduction methods for dynamical systems, and was focusing on establishing globally convergent Riemannian optimization model order reduction methods by taking advantage of certain geometric properties on Riemannian manifolds.
The Riemannian optimization is applied to solve the mean-squared optimal model order reduction problem whose constraints can be characterized as a Riemannian manifold. Making full use of the Riemannian geometry of Riemannian manifolds, the minimization solution is guaranteed to exist over the compact subset and the proposed methods can yield good global convergence behavior.
Many scientists in the research group Computational Methods in Systems and Control Theory at the Max Planck Institute Magdeburg are working on model order reduction with many excellent results. “I have studied many articles of Prof. Benner and his group, which were very helpful for my previous work. More importantly, as an internationally renowned professor in the field of model order reduction, Prof. Benner is doing a lot of cutting-edge research and has deep insights into many model order reduction methods. Thus, I hope to communicate and cooperate with Prof. Benner and his group, and carry out my future research work with his guidance and help.” says Kang-Li Xu about her motivation and her expectations regarding the collaboration.
About Dr. Kang-Li Xu
Kang-Li Xu was born in 1990 in Qingdao, China. From 2015 to 2018, she conducted research at the College of Mathematics and Systems Science at Xinjiang University, where she successfully completed her PhD in 2018. From 2018 to 2020, she was a postdoctoral research fellow at the School of Mathematics and Statistics at Xi'an Jiaotong University. From 2020 to 2022, she worked there as an Assistant Professor and since 2022 as an Associate Professor. Kang-Li Xu has already been awarded with several research prizes.
Together with her husband, she prepared intensively for her time in Magdeburg and attended a two-month German course at the Goethe-Institut in Göttingen, which was offered to her as part of her fellowship.
Every year, the Alexander von Humboldt Foundation enables over 2,000 researchers from all over the world to spend an academic residency in Germany.
English text: Dr. Kang-Li Xu and Gabriele Ebel