題  目：Efficient Interacting Particle Methods for Computing Near Singular Solutions of Keller-Segel Chemotaxis Systems and High-Dimensional Eigenvalue Problems

内容簡介：Mesh-based methods like finite element methods and spectral methods face challenges when solving PDEs with near singular solutions or in high-dimensional spaces. In this talk, we introduce a particle-based method to compute aggregation patterns and near singular solutions of the Keller-Segel chemotaxis system in three-dimensional space and an interacting particle method to calculate the principal eigenvalues of high-dimensional elliptic operators. We also present numerical experiments to demonstrate their performance. Furthermore, we introduce the DeepParticle method for learning and generating the distributions of solutions under variations of physical parameters.

報告人：Zhiwen Zhang（張智文）

報告人簡介：Zhiwen Zhang（張智文）received his B.S. degree and Ph.D. Degree in mathematics from Tsinghua University, Beijing, P. R. China, in 2006 and 2011, respectively. After his graduation, he was a postdoctoral scholar at California Institute of Technology from 2011 to 2015. He joined the University of Hong Kong as an Assistant Professor since 2015. Dr. Zhang’s research interests are scientific computation. Research topics include uncertainty quantification and numerical methods for PDEs arising from quantum chemistry, wave propagation, multiscale porous media, nonlinear filtering, and stochastic fluid dynamics.

時  間：2024年7月6日（周六）下午14：00開始

地  點：騰訊會議号59157539380

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