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2019.07.11- Differential Equations and Deep Learning

中国矿业大学(北京)理学院

报告题目:  Differential Equations and Deep Learning

报告人:  刘海亮教授   Iowa State University 

报告人简介:刘海亮教授1986-1988年在清华大学应数学系学习,获理学硕士学位,后在中科院系统所继续深造,并获理学博士学位.1997-1998年为德国洪堡学者.1999-2002年在加州大学洛杉矶分校工作. 2002 至今在Iowa State University 工作, 任终身教授和应用数学首席 (Holl Chair). 刘海亮教授多年来致力于发展新的数学工具和计算方法求解某些重要应中出现的发展型偏微分方程, 近几年的工作和成果主要集中在以下几个: (1)渐近分析和数值建模;(2)用偏微分方程中临界门槛现象及数学理论;(3)保结构的高精度计算方法.1995 年以来,刘海亮教授发表了120 余篇研究论文,引用超过2200. 

摘要Deep learning is machine learning using neural networks with many hidden layers, and it has become a primary tool in a wide variety of practical learning tasks. In this talk we begin with a simple optimization problem, and show how it can be reformulated as gradient flows, which in turn lead to different optimization solvers. We further introduce the mathematical formulation of deep residual neural networks as a PDE optimal control problem. We state and prove optimality conditions for the inverse deep learning problem, using the Hamilton-Jacobi-Bellmann equation and the Pontryagin maximum principle.

时间:2019711日(周下午4:00

地点:逸夫楼1537

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