報(bào) 告 人：田靜 副教授

報(bào)告題目：Error estimates of deep learning techniques for certain partial differential equations

報(bào)告時(shí)間：2023年06月13日（周二）下午4：00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

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

報(bào)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.