mlsanityData to 14 Oct 2026

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

arXiv 2203.17153 ↗First posted 31 Mar 2022stat.CO cs.NA math.NAcited by 7

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Abstract (arXiv)

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.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 17 of its 50 references that are in the map. First posted on arXiv 31 Mar 2022.

Builds on

17 of 50 references.

References · 17

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5 more
  1. 2020Deep learning based numerical approximation algorithms for stochastic partial differential equationscited by 11
  2. 2020Deep Energy-Based NARX Modelscited by 7
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 2.

7 papers.

  1. 2024Conditional sampling within generative diffusion modelscited by 19
  2. 2024Solving stochastic partial differential equations using neural networks in the Wiener chaos expansioncited by 6
  3. 2024A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splittingcited by 2
  4. 2025Nonlinear filtering based on density approximation and deep BSDE predictioncited by 1
  5. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  6. 2025High-dimensional Bayesian filtering through deep density approximationcited by 0
  7. 2026Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecastingcited by 0