Title: | Mathematical Frameworks for Understanding Biological Shape Formation: From Brain Organoids to Skin Wrinkles |
Speaker: | Dr. Xiaoyi Chen, Applied Mathematics, Beijing Normal University & Hong Kong Baptist University United International College |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In recent years, we studied how biological tissues generate complex morphologies through different mechanisms during growth mathematically and mechanically. Specifically, our work is concentrated in two main areas: 1. We have established a stress-free growth model to analytically study the morphological development of different biological tissues. This model provides a significant complement to the currently popular instability mechanisms. 2. We have derived asymptotically consistent morphoelastic plate/shell models that can effectively describe the large deformations of thin/slender tissues commonly found in nature. Using these models, we have explained several biological growth phenomena, including the formation of brain organic and the inversion of the Volvox embryo as well as the wrinkling of human skin. Looking ahead, we plan to develop related numerical algorithms based on the morphoelastic plate/shell theory, including the recently popular Physics-Informed Neural Networks (PINN) method. |
Title: | Composite Algorithms of Data-driven and Model-driven Methods in Banach Spaces |
Speaker: | Prof. Qi YE, School of Mathematical Sciences, South China Normal University |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this presentation, we introduce a novel mathematical framework for machine learning that integrates data-driven and model-driven methods. Typically, data-driven methods are employed to implement black-box algorithms, while model-driven methods are utilized for white-box algorithms. The primary concept involves leveraging the local information from multimodal data and multiscale models to develop global approximate solutions through learning algorithms. The utilization of composite algorithms offers an alternative approach to exploring the mathematical theory of machine learning. This includes investigating interpretability through approximation theory, nonconvexity and nonsmoothness through optimization theory, and generalization and overfitting through regularization theory. For our computational medicine project focusing on pancreatic cancer, we investigate the composite algorithm involving image processing and modeling simulation. |
Title: | Non-splitting Eulerian-Lagrangian WENO schemes for two-dimensional nonlinear convection-diffusion equations |
Speaker: | Dr. Xiaofeng Cai, Research Center for Mathematics, Beijing Normal University and UIC |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this talk, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed EL-RK-FV-WENO scheme defines modified characteristic lines and evolves the solution along them, significantly relaxing the time-step constraint for the convection term.The main algorithm design challenge arises from the complexity of constructing accurate and robust reconstructions on dynamically varying Lagrangian meshes. This reconstruction process is needed for flux evaluations on time-dependent upstream quadrilaterals and time integrations along moving characteristics.To address this, we propose a strategy that utilizes a WENO reconstruction on a fixed Eulerian mesh for spatial reconstruction, and updates intermediate solutions on the Eulerian background mesh for implicit-explicit RK temporal integration. This strategy leverages efficient reconstruction and remapping algorithms to manage the complexities of polynomial reconstructions on time-dependent quadrilaterals, while ensuring local mass conservation. The proposed scheme ensures mass conservation due to the flux-form semi-discretization and the mass-conservative reconstruction on both background and upstream cells. Extensive numerical tests have been performed to verify the effectiveness of the proposed scheme. |
We organize conferences and workshops every year. Hope we can see you in future.
Learn MoreProf. M. Cheng, Dr. Y. S. Hon, Dr. K. F. Lam, Prof. L. Ling, Dr. T. Tong and Prof. L. Zhu have been awarded research grants by Hong Kong Research Grant Council (RGC) — congratulations!
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