Nonlinear filtering is a fundamental problem in signal processing, information theory, communication, control and optimization, and systems theory. In the 1960s, celebrated results on nonlinear filtering were obtained. Nevertheless, the computational issues for nonlinear filtering remained to be a long-standing and challenging problem. In this talk, in lieu of treating the stochastic partial differential equations for obtaining the conditional distribution or conditional measure, we construct finite-dimensional approximations using deep neural networks for the optimal weights. Two recursions are used in the algorithm. One of them is the approximation of the optimal weight and the other is for approximating the optimal learning rate.

This is a joint work with Hongjiang Qian (Cornell University) and Qing Zhang (University of Georgia).