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.

翻译：本文的目的是探讨如何利用深层次学习解决非线性过滤问题,这是通过一种深层分离法解决Zakai方程式实现的,这种方法以前是为(随机的)部分差异方程式的近似解决办法而开发的,与一个深神经网络功能近似的基于能源的模式相结合,结果产生了一种计算快捷的过滤法,该过滤法将观测作为输入,在收到新的观测时不需要再培训。该方法在四个例子中进行了测试,一个一和二十维中的两个线性,一个层面中的两个非线性。该方法显示,与Kalman过滤器和靴子粒子过滤器相比,其业绩是大有希望的。