Error estimates of deep learning techniques for certain partial differential equations

田静

（马里兰州立大学陶森分校）

报告时间：15：00-16：00，2023-6-8（星期四）

报告地点：沙河校区E404

内容简介：Machine Learning, which has been at the forefront of the data science and artificial intelligence revolution in recent decades, 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 a rigorous error analysis of deep learning methods employed in certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution.

报告人简介：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, Numerische Mathematik等杂志上发表。

邀请人：彭临平