  The purpose of this paper is to explore the use of deep learning for the
solution of the nonlinear filtering problem. This is achieved by solving the
Zakai equation by a deep splitting method, previously developed for approximate
solution of (stochastic) partial differential equations. This is combined with
an energy-based model for the approximation of functions by a deep neural
network. This results in a computationally fast filter that takes observations
as input and that does not require re-training when new observations are
received. The method is tested on four examples, two linear in one and twenty
dimensions and two nonlinear in one dimension. The method shows promising
performance when benchmarked against the Kalman filter and the bootstrap
particle filter.
