Abstract

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 incompressible Navier-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.

Short bio

Jing Tian is an Assistant Professor of Mathematics from Towson University. She got her Ph.D. in Mathematics from Texas A&M University. She was a postdoctoral scholar at the University of South Florida. Her research is in the theoretical analysis of partial differential equations and numerical analysis, including computational fluid Dynamics and machine learning.