Project Grant 2204795

This $281,964 National Science Foundation project grant supports research at the University of Texas at Dallas to investigate mean field games and mean field control in the context of supervised and deep learning. Specifically, the three-year award under the NSF's Mathematical and Physical Sciences program (CFDA 47.049) will examine applying mean field control theory to replace empirical data distributions with joint probability distributions between inputs and outputs in machine learning models. It will also analyze replacing large numbers of layers in deep networks with an infinite number and using control of partial differential equations instead of ordinary differential equations for data with spatial elements. The university aims to develop novel Hilbert space control methods and algorithms to more efficiently handle gradients and replace stochastic gradient algorithms with mean field solutions. Project results could provide new applications of machine learning in data-intensive situations and enhance privacy, fairness, and interpretability.