報告題目：Error estimates of deep learning techniques for certain partial differential equations
報告人：田靜
報告時間：2023年6月13日14：00
報告地點：伟德bvA302
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.
專家簡介：田靜，美國馬裡蘭州立大學陶森分校副教授。2016年美國德州農工大學博士畢業，2017年美國南佛羅裡達大學博士後出站。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 Eguations，Numerische Mathematik等雜志上發表。