【讲座主题】A scalable deep learning approach for solving high-dimensional dynamic optimal transport
【讲座时间】2023年6月21日（周三）下午4:00---5:00
【讲座地点】D601
【主讲人】史作强 教授（清华大学）
【主讲人简介】史作强教授博士毕业于清华大学周培源应用数学研究中心，后赴美国加州理工学院应用与计算数学系做博士后，并曾作为访问学者在美国加州大学洛杉矶分校数学系访问。2012年全职加入清华大学，现任丘成桐数学科学中心副主任、教授、博士生导师。主要从事偏微分方程数值解法、图像处理、机器学习等研究。特别是在点云上偏微分方程的数值方法，高维数据的偏微分方程模型，数据驱动的稀疏时频分析等研究领域中取得了一系列创新研究成果，已发表学术论文60余篇。
【报告内容简介】The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization based approaches suffer from the curse of dimensionality. In this talk, I will present a deep learning based method to solve the dynamic optimal transport in high dimensional space. This method contains three main ingredients: a carefully designed representation of the velocity field, the discretization of the PDE constraint along the characteristics, and the computation of high dimensional integral by Monte Carlo method in each time step. Extensive numerical examples have been conducted to test the proposed method. Compared to other solvers of optimal transport, our method could give more accurate results in high dimensional cases and has very good scalability with respect to dimension.
