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An Energy-based Deep Splitting Method for the Nonlinear Filtering Problem by Kasper Bågmark; Adam Andersson; Stig Larsson is a Mathematics article available to read on EtoBox.

What is An Energy-based Deep Splitting Method for the Nonlinear Filtering Problem about?

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.

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Author

Kasper Bågmark; Adam Andersson; Stig Larsson

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)