题目: Reduced order models

报告时间：2019.10.17 上午10:00-11:00  

报告地点：数学学院E404（沙河校区）

摘要:Models of reduced computational complexity is used extensively throughout science and engineering to enable the fast/real-time/subscale modeling of complex systems for control, design, multi-scale analysis, uncertainty quantification etc While of undisputed value these reduced models are, however, often heuristic in nature and the accuracy of the output is often unknown, hence limiting the predictive value.We discuss the development of reduced methods for parameterized partial differential equations. We outline the basic ideas behind certified reduced basis methods, discuss an offline-online approach to ensure computational efficiency, and emphasize how the error estimator can be exploited to construct an efficient basis at minimal computational off-line cost. The discussion will draw on a number of different examples, including also the use of neural networks to enable the efficient modeling of complex nonlinear problems

个人简介：Jan Hesthaven教授是瑞士洛桑联邦理工学院（EPFL）的基础科学部部长，并担任计算数学与科学模拟中心主任、科学信息技术应用支持（SCITAS）中心院长等职务。作为计算数学领域的国际知名教授，Hesthaven教授是美国工业与应用数学学会会士，也是SIAM Journal of Scientific Computing、Journal of Computational Physics和Journal of Scientific Computing等多个国际著名期刊的主编。他曾就职于美国布朗大学应用数学系16年，并获得Philip J. Bray最佳自然科学教学奖（布朗大学的最高荣誉教学奖）。Jan S Hesthaven教授主要研究如何利用计算数学与科学计算方法解决自然与工程领域中复杂系统的多尺度问题，包含偏微分方程高阶精确数值方法的拓展分析、不确定性量化、降维、波问题及数据驱动的计算模拟，并将这些数值方法广泛应用于流体科学、电磁等离子物理等方面，并关注它们在大尺度平台上的布署。

邀请人：王 鹏