报告题目：Positivity-preserving finite element methods for the chemotaxis(-fluid) equations
报告人：王坤 副教授（重庆大学）
邀请人：黄启华
报告时间：2026年11月11日（星期三）15:30-16:30
报告地点：数学大楼912
参加人员：教师、研究生、本科生
报告摘要：In this talk, we consider two kinds of positivity-preserving finite element methods for solving the chemotaxis(-fluid) equations. In the first part, based on the flux-corrected transport technique, we develop a fully decoupled, linear, positivity-preserving and stable finite element scheme for solving the chemotaxis–fluid equations, in which we only need to solve several linearized sub-problems at each time step. The stability and error estimate of the scheme are proved. In the second part, based on the function transformation, we study a mass conservation and positivity-preserving finite element method for the chemotaxis equations. The stability and error estimate of the method are also proved. A series of numerical examples are shown to verify the theoretical predictions.
报告人简介：王坤，重庆大学数学与统计学院副教授，主要研究方向为偏微分方程数值解，具体包括复杂流体力学方程及其耦合问题、趋化方程的数值分析与模拟等，结果曾在 SIAM Journal on Numerical Analysis、Mathematics of Computation 等杂志上发表。
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报告题目：Identification of the governing equation from stimulus-response data at both individual and population level
报告人：唐敏 教授（上海交通大学）
邀请人：黄启华
报告时间：2026年11月11日（星期三）16:30-17:30
报告地点：数学大楼912
参加人员：教师、研究生、本科生
报告摘要：Microscopic organisms like bacteria and algae often adjust their movement in response to changing environments, such as light or chemical signals. They do this using a behavior called run-and-tumble, alternating between straight swimming and reorientation. Understanding how internal cell processes drive this behavior is difficult, especially when we can't directly observe the biochemical pathways involved. In this study, we present a machine learning approach that discovers the governing rules behind these behaviors using only observable input-output data. Our model, based on neural networks, learns from how cells respond to simple stimuli and can predict how they behave under more complex, realistic conditions, both at individual and population level, without needing to know the details of internal reactions. We validated the method using simulations of bacterial chemotaxis and real experimental data from Euglena gracilis, a microorganism that responds to light. Our model accurately predicted cell responses and revealed insights into possible internal signaling structures. This approach provides a powerful tool for studying biological behavior and could help uncover how other organisms process environmental information.
报告人简介：唐敏，上海交通大学数学学院/自然科学研究院教授，从事与多尺度现象相关的生物数学建模分析和多尺度算法设计研究，建立生物系统中不同尺度现象的关联，设计物理、工程问题数值模拟中的多尺度、可并行算法。主持基金委 NSAF 联合（重点）基金、面上等项目，部分工作被作为合作者国际数学家一小时报告主要内容。入选国家级青年人才；受邀出任 SIAM Multiscale Modeling & Simulations、Journal of Mathematical Biology、Kinetic and Related Models、PLoS Computational Biology、Communications in Mathematical Sciences 等应用数学重要期刊编委。
