【讲座题目】Error Estimates for Deep Learning Methods in Fluid Dynamics
【主 讲 人】田静副教授
【讲座时间】2023/06/08星期四上午10:30-11:30
【讲座地点】主C636， 腾讯会议ID：918-4651-0003
【主讲人简介】田静，美国马里兰州立大学陶森分校副教授。2016年美国德州农工大学博士毕业。2017年美国南佛罗里达大学博士后出站。长期从事非线性偏微分方程、计算流体力学的研究，研究成果在Journal of Differential Equations, NumerischeMathematik等杂志上发表。
【讲座内容简介】
Machine Learning, which has been at the forefront of the data science and artificial intelligence revolution in the last twenty years, has a wide range of applications in natural language processing, computer vision, speech and image recognition, among others. Recently, its use has proliferated in computational sciences and physical modeling such as the modeling of turbulence. Moreover, machine learning methods (physics informed neural networks which are mesh-free) have gained wide applicability in obtaining numerical solutions of various types of partial differential equations.
In this talk, we provide error estimates and stability analysis of machine learning techniques (deep learning, in particular) for certain partial differential equations including the incompressibleNavier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.
