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Electrostatic Field Estimation Based on a Generative Method.

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Title: Electrostatic Field Estimation Based on a Generative Method.
Authors: Zhou, Pan1 zhoupan961013@163.com, Tu, Liangping2 tuliangping@ustl.edu.cn, Wang, Xu3 wangxu@szpu.edu.cn, Kuang, Guowen3 gkuang@szpu.edu.cn, Mao, Liang3 maoliangscau@szpu.edu.cn, Wang, Fan4 wangfaneg@163.com, Zhao, Tianshuai5 kuchaboy@qq.com
Source: Engineering Letters. Jul2026, Vol. 34 Issue 7, p2982-2994. 13p.
Subjects: Electrostatic fields, Electric fields, Numerical analysis, Electromagnetic compatibility, Artificial neural networks, Deep learning, Image representation
Abstract: Accurate estimation of electrostatic fields is fun damental to the optimal design of power equipment and electromagnetic compatibility assessments. Traditional numer-ical algorithms suffer from severe computational efficiency bottlenecks, while existing deep learning methods are prone to numerical instability and gradient explosion, especially when handling geometric singularities such as sharp corners and non-smooth boundaries. To address these challenges, we propose an electrostatic field estimation framework based on the prediction of electric potential gradient direction. Specifically, by setting the prediction target as the direction of the electric potential gradient, this method inherently avoids the severe gradient oscil-lations caused by geometric singularities, ensuring stable model convergence and high-precision electrostatic field reconstruc-tion. For input data, the framework employs an efficient image based encoding scheme that directly maps complex conductor distributions and boundary conditions into dual-channel im-ages, significantly simplifying data preparation. Subsequently, a deep neural network predicts the electric potential gradient direction field, which is then used to generate equipotential lines. By accurately estimating the electric potential values associated with these lines, the electric field distribution within the entire physical domain is obtained. Notably, compared with mainstream methods such as physics-informed neural networks. (PINNs), the proposed method enables direct inference on unseen samples after training without requiring retraining for new cases. Experimental results on a dataset comprising 60,000 training samples and 5,000 test samples validate the robustness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Electrostatic Field Estimation Based on a Generative Method.
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  Data: <searchLink fieldCode="AR" term="%22Zhou%2C+Pan%22">Zhou, Pan</searchLink><relatesTo>1</relatesTo><i> zhoupan961013@163.com</i><br /><searchLink fieldCode="AR" term="%22Tu%2C+Liangping%22">Tu, Liangping</searchLink><relatesTo>2</relatesTo><i> tuliangping@ustl.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xu%22">Wang, Xu</searchLink><relatesTo>3</relatesTo><i> wangxu@szpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Kuang%2C+Guowen%22">Kuang, Guowen</searchLink><relatesTo>3</relatesTo><i> gkuang@szpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Mao%2C+Liang%22">Mao, Liang</searchLink><relatesTo>3</relatesTo><i> maoliangscau@szpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Fan%22">Wang, Fan</searchLink><relatesTo>4</relatesTo><i> wangfaneg@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Tianshuai%22">Zhao, Tianshuai</searchLink><relatesTo>5</relatesTo><i> kuchaboy@qq.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Jul2026, Vol. 34 Issue 7, p2982-2994. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Electrostatic+fields%22">Electrostatic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+fields%22">Electric fields</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Electromagnetic+compatibility%22">Electromagnetic compatibility</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Image+representation%22">Image representation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Accurate estimation of electrostatic fields is fun damental to the optimal design of power equipment and electromagnetic compatibility assessments. Traditional numer-ical algorithms suffer from severe computational efficiency bottlenecks, while existing deep learning methods are prone to numerical instability and gradient explosion, especially when handling geometric singularities such as sharp corners and non-smooth boundaries. To address these challenges, we propose an electrostatic field estimation framework based on the prediction of electric potential gradient direction. Specifically, by setting the prediction target as the direction of the electric potential gradient, this method inherently avoids the severe gradient oscil-lations caused by geometric singularities, ensuring stable model convergence and high-precision electrostatic field reconstruc-tion. For input data, the framework employs an efficient image based encoding scheme that directly maps complex conductor distributions and boundary conditions into dual-channel im-ages, significantly simplifying data preparation. Subsequently, a deep neural network predicts the electric potential gradient direction field, which is then used to generate equipotential lines. By accurately estimating the electric potential values associated with these lines, the electric field distribution within the entire physical domain is obtained. Notably, compared with mainstream methods such as physics-informed neural networks. (PINNs), the proposed method enables direct inference on unseen samples after training without requiring retraining for new cases. Experimental results on a dataset comprising 60,000 training samples and 5,000 test samples validate the robustness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 2982
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      – SubjectFull: Electrostatic fields
        Type: general
      – SubjectFull: Electric fields
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Electromagnetic compatibility
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Deep learning
        Type: general
      – SubjectFull: Image representation
        Type: general
    Titles:
      – TitleFull: Electrostatic Field Estimation Based on a Generative Method.
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          Name:
            NameFull: Zhou, Pan
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            NameFull: Tu, Liangping
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            NameFull: Wang, Xu
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            NameFull: Mao, Liang
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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