Learning operators for identifying weak solutions to the Navier-Stokes equations

We employ a combination of deep learning methods and compactness argument to derive learning operators for weak solutions of Navier-Stokes equations for any large initial data 2D, and for low dimensional initial data in 3D. Additionally, we utilize the universal approximation theorem to derive the lower bound on the number of sensors required to achieve accurate identification of weak solutions in 3D. Our results demonstrate the potential of using deep learning techniques to address challenges in the study of fluid mechanics, particularly in identifying weak solutions to the Navier-Stokes equations. This is a joint work with Dr. Cheng Yu.