走向现代数学学术报告 - 张娟教授（No. 701）

题目：Data-Driven Optimal Iterative Parameter Prediction and its Applications

报告人：张娟 教授（湘潭大学）

时间：2024年4月29日 10:00

地点：东海岸校区-D实209

摘要：Matrix splitting iterative methods with parameters play a crucial role in solving linear systems. How to choose optimal splitting parameters is a key problem. In this talk, we propose a data-driven approach for predicting optimal iterative parameters: multi-task kernel learning Gaussian regression prediction (GPR) method. We develop the generalized alternating direction implicit (GADI) framework with optimal parameters, successfully integrating it as a smoother in algebraic multigrid methods to solve linear systems. Moreover, we accelerate GPR using mixed precision strategy and evaluate the predicted results with statistical indicators. Further, we have successfully applied GPR to (time-dependent) linear algebraic systems (elliptic equations, Poisson equations, convection-diffusion equations, Helmholtz equations) and linear matrix equations (Sylvester equations). Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. When the system size exceeds hundreds of thousands, the acceleration ratio of the GADI framework can reach hundreds to thousands of times.

报告人简介：张娟，教授，博士生导师，湘潭大学数学与计算科学学院副院长，“智能计算与信息处理”教育部重点实验室常务副主任。2021年、2015年赴澳门大学访问。2023年、2018年赴新加坡国立大学访问。主持国自科面上、青年项目，博士后基金面上项目一等资助，湖南省教育厅重点、优秀青年项目，湖南省自科基金青年项目等国家级和省部级项目10余项。作为核心成员参与国家重点研发计划、军科委GF项目、工业软件内核研发及应用验证产业基础共性技术中心项目多项。主要从事数值代数、控制理论、矩阵计算等方面的研究。在国内外重要学术期刊 SIAM J. Sci. Comput.、Automatica、J. Comput. Phys.等发表和接收发表SCI论文50余篇。