Project Grant 2207449

Southern Methodist University was awarded a $348,805 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) to develop machine learning technology with deep neural networks to study oscillatory Navier-Stokes flows, nonlinear operators, and high dimensional Fokker-Planck equations. The university will research and develop multiscale deep neural network algorithms as a meshless method for solving oscillatory fluid flows, represent nonlinear operators in oscillatory function spaces, and address the curse of dimensionality in solving high-dimensional PDEs such as Fokker-Planck equations. The research aims to improve scientific computing capabilities in areas like fluid dynamics, seismic wave prediction, and transition path sampling of complex chemical and biological systems. The three-year award period began August 1, 2022.