An energy-based deep splitting method for the nonlinear filtering problem

Kasper Bågmark (), Adam Andersson () and Stig Larsson ()
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Kasper Bågmark: Chalmers University of Technology and University of Gothenburg
Adam Andersson: Chalmers University of Technology and University of Gothenburg
Stig Larsson: Chalmers University of Technology and University of Gothenburg

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-27

Abstract: Abstract 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.

Keywords: Filtering problem; Zakai equation; Stochastic partial differential equation; Splitting scheme; Deep learning; Energy-based method; 60G35; 62F15; 62G07; 62M20; 65C30; 65M75; 68T07 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00231-5

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