We provide error estimates and stability analysis of deep learning techniques 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. This is a joint work with A. Biswas and J. Tian.
Prof. Suleyman Ulusoy earned both his Ph.D in Mathematics in 2007 and his Master of Science in Applied Mathematics in 2003 from Georgia Institute of Technology in Atlanta, Georgia, USA. He earned both of his bachelor's degrees in mathematics and mathematics education from the Middle East Technical University in Ankara, Turkey in 2000. He did postdocs at the University of Oslo and the University of Maryland. He is currently a faculty member at the American University of Ras Al Khaimah.