School Colloquium——A Complete Error Analysis for Deep Ritz Method
报告人：杨志坚 (武汉大学)
时间：2025-12-05 14:00-15:00
地点：智华楼四元厅
报告摘要: It is widely known that the error analysis for deep learning involves approximation, statistical, and optimization errors. However, it is challenging to combine them together due to overparameterization. In this presentation, we address this gap by providing a comprehensive error analysis of the Deep Ritz Method (DRM). Specifically, we investigate a foundational question in the theoretical analysis of DRM under the overparameterized regime: given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision.
报告人简介：
杨志坚，武汉大学弘毅特聘教授，湖北国家应用数学中心主任、武汉数学与智能研究院副院长。杨教授于伊人直播
获本科及硕士学位、普林斯顿大学获博士学位、加州理工伊人直播
完成博士后研究、罗彻斯特理工伊人直播
担任助理教授后，2010年加入武汉大学。
杨教授现为第八届教育部科技委委员、湖北省数学学会理事长、中国工业与应用数学学会副理事长、计算科学湖北省重点实验室主任，曾任东亚工业与应用数学学会主席、湖北省工业与应用数学学会理事长。主持国家杰出青年科学基金、科技部重点研发计划、基金委重大研究计划集成项目、重点项目、湖北省创新研究群体、卓越研究群体等科研项目。现为EAJAM、CiCP、CSIAM-AM等杂志编委。曾获CSIAM应用数学落地成果认证、王选应用数学奖等奖励。主要从事多尺度建模与计算，人工智能的数学理论、算法及应用研究。
