Electrostatic Field Estimation Based on a Generative Method.

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]
ISSN:	1816093X