IDEAS home Printed from https://ideas.repec.org/a/spr/pardea/v4y2023i2d10.1007_s42985-023-00231-5.html
   My bibliography  Save this article

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

Author

Listed:
  • Kasper Bågmark

    (Chalmers University of Technology and University of Gothenburg)

  • Adam Andersson

    (Chalmers University of Technology and University of Gothenburg
    Saab AB Radar Solutions)

  • Stig Larsson

    (Chalmers University of Technology and University of Gothenburg)

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.

Suggested Citation

  • Kasper Bågmark & Adam Andersson & Stig Larsson, 2023. "An energy-based deep splitting method for the nonlinear filtering problem," Partial Differential Equations and Applications, Springer, vol. 4(2), pages 1-27, April.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:2:d:10.1007_s42985-023-00231-5
    DOI: 10.1007/s42985-023-00231-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s42985-023-00231-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s42985-023-00231-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cassola, Federico & Burlando, Massimiliano, 2012. "Wind speed and wind energy forecast through Kalman filtering of Numerical Weather Prediction model output," Applied Energy, Elsevier, vol. 99(C), pages 154-166.
    2. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rana Muhammad Adnan & Zhongmin Liang & Xiaohui Yuan & Ozgur Kisi & Muhammad Akhlaq & Binquan Li, 2019. "Comparison of LSSVR, M5RT, NF-GP, and NF-SC Models for Predictions of Hourly Wind Speed and Wind Power Based on Cross-Validation," Energies, MDPI, vol. 12(2), pages 1-22, January.
    2. Alessandrini, S. & Sperati, S. & Pinson, P., 2013. "A comparison between the ECMWF and COSMO Ensemble Prediction Systems applied to short-term wind power forecasting on real data," Applied Energy, Elsevier, vol. 107(C), pages 271-280.
    3. Zonggui Yao & Chen Wang, 2018. "A Hybrid Model Based on A Modified Optimization Algorithm and An Artificial Intelligence Algorithm for Short-Term Wind Speed Multi-Step Ahead Forecasting," Sustainability, MDPI, vol. 10(5), pages 1-33, May.
    4. Wang, Yun & Zou, Runmin & Liu, Fang & Zhang, Lingjun & Liu, Qianyi, 2021. "A review of wind speed and wind power forecasting with deep neural networks," Applied Energy, Elsevier, vol. 304(C).
    5. Koo, Junmo & Han, Gwon Deok & Choi, Hyung Jong & Shim, Joon Hyung, 2015. "Wind-speed prediction and analysis based on geological and distance variables using an artificial neural network: A case study in South Korea," Energy, Elsevier, vol. 93(P2), pages 1296-1302.
    6. Liu, Hui & Tian, Hong-qi & Pan, Di-fu & Li, Yan-fei, 2013. "Forecasting models for wind speed using wavelet, wavelet packet, time series and Artificial Neural Networks," Applied Energy, Elsevier, vol. 107(C), pages 191-208.
    7. Niu, Tong & Wang, Jianzhou & Zhang, Kequan & Du, Pei, 2018. "Multi-step-ahead wind speed forecasting based on optimal feature selection and a modified bat algorithm with the cognition strategy," Renewable Energy, Elsevier, vol. 118(C), pages 213-229.
    8. Costa, Marcelo Azevedo & Ruiz-Cárdenas, Ramiro & Mineti, Leandro Brioschi & Prates, Marcos Oliveira, 2021. "Dynamic time scan forecasting for multi-step wind speed prediction," Renewable Energy, Elsevier, vol. 177(C), pages 584-595.
    9. Tonglin Fu & Chen Wang, 2018. "A Hybrid Wind Speed Forecasting Method and Wind Energy Resource Analysis Based on a Swarm Intelligence Optimization Algorithm and an Artificial Intelligence Model," Sustainability, MDPI, vol. 10(11), pages 1-24, October.
    10. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    11. Tian, Chengshi & Hao, Yan & Hu, Jianming, 2018. "A novel wind speed forecasting system based on hybrid data preprocessing and multi-objective optimization," Applied Energy, Elsevier, vol. 231(C), pages 301-319.
    12. El-Baz, Wessam & Tzscheutschler, Peter, 2015. "Short-term smart learning electrical load prediction algorithm for home energy management systems," Applied Energy, Elsevier, vol. 147(C), pages 10-19.
    13. Xu, Lei & Hou, Lei & Zhu, Zhenyu & Li, Yu & Liu, Jiaquan & Lei, Ting & Wu, Xingguang, 2021. "Mid-term prediction of electrical energy consumption for crude oil pipelines using a hybrid algorithm of support vector machine and genetic algorithm," Energy, Elsevier, vol. 222(C).
    14. Hu, Jianming & Heng, Jiani & Wen, Jiemei & Zhao, Weigang, 2020. "Deterministic and probabilistic wind speed forecasting with de-noising-reconstruction strategy and quantile regression based algorithm," Renewable Energy, Elsevier, vol. 162(C), pages 1208-1226.
    15. Lv, Sheng-Xiang & Wang, Lin, 2022. "Deep learning combined wind speed forecasting with hybrid time series decomposition and multi-objective parameter optimization," Applied Energy, Elsevier, vol. 311(C).
    16. Vadim Manusov & Pavel Matrenin & Muso Nazarov & Svetlana Beryozkina & Murodbek Safaraliev & Inga Zicmane & Anvari Ghulomzoda, 2023. "Short-Term Prediction of the Wind Speed Based on a Learning Process Control Algorithm in Isolated Power Systems," Sustainability, MDPI, vol. 15(2), pages 1-12, January.
    17. Murthy, K.S.R. & Rahi, O.P., 2017. "A comprehensive review of wind resource assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 72(C), pages 1320-1342.
    18. Khasanzoda, Nasrullo & Zicmane, Inga & Beryozkina, Svetlana & Safaraliev, Murodbek & Sultonov, Sherkhon & Kirgizov, Alifbek, 2022. "Regression model for predicting the speed of wind flows for energy needs based on fuzzy logic," Renewable Energy, Elsevier, vol. 191(C), pages 723-731.
    19. Yuan, Renyu & Ji, Wenju & Luo, Kun & Wang, Jianwen & Zhang, Sanxia & Wang, Qiang & Fan, Jianren & Ni, MingJiang & Cen, Kefa, 2017. "Coupled wind farm parameterization with a mesoscale model for simulations of an onshore wind farm," Applied Energy, Elsevier, vol. 206(C), pages 113-125.
    20. Wang, Jianzhou & Hu, Jianming & Ma, Kailiang & Zhang, Yixin, 2015. "A self-adaptive hybrid approach for wind speed forecasting," Renewable Energy, Elsevier, vol. 78(C), pages 374-385.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:pardea:v:4:y:2023:i:2:d:10.1007_s42985-023-00231-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.