報 告 人：田靜 副教授

報告題目：Error estimates of deep learning techniques for certain partial differential equations

報告時間：2023年06月13日（周二）下午4：00

報告地點：靜遠樓1508會議室

主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術(shù)研究院

報告人簡介：

      田靜，美國馬里蘭州立大學陶森分校副教授。2016年美國德州農(nóng)工大學博士畢業(yè)。2017年美國南佛羅里達大學博士后出站。長期從事非線性偏微分方程，計算流體力學的研究，研究成果在Journal of Differential Equations, Numerische Mathematik等雜志上發(fā)表。

報告摘要：

      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.