An energy-based deep splitting method for the nonlinear filtering problem
Journal article, 2023

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.

stochastic partial differential equation

energy-based method

splitting scheme

deep learning

Zakai equation

Filtering problem

Author

Kasper Bågmark

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Adam Andersson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Partial Differential Equations and Applications

26622963 (ISSN) 26622971 (eISSN)

Vol. 4 2 14

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Computer Vision and Robotics (Autonomous Systems)

Mathematical Analysis

Other Electrical Engineering, Electronic Engineering, Information Engineering

DOI

10.1007/s42985-023-00231-5

More information

Latest update

7/24/2023