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Enriched physics-informed neural networks for dynamic Poisson-Nernst-Planck systems

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  • Huang, Xujia
  • Wang, Fajie
  • Zhang, Benrong
  • Liu, Hanqing

Abstract

This paper proposes a meshless deep learning algorithm, called enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations characterized by strong coupling and nonlinear behaviors. EPINNs build upon traditional physics-informed neural networks (PINNs) by incorporating an adaptive loss weight mechanism, which automatically adjusts the weights of the loss functions during training, based on maximum likelihood estimation, to achieve balanced optimization. Additionally, a resampling strategy is introduced to accelerate the convergence of the loss function. Four numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. The results show that EPINNs have better applicability than traditional numerical methods in solving such coupled nonlinear systems. Furthermore, EPINNs outperform traditional PINNs in terms of accuracy, stability, and speed. This work provides a robust and efficient numerical tool for solving PNP equations with arbitrary boundary shapes and conditions.

Suggested Citation

  • Huang, Xujia & Wang, Fajie & Zhang, Benrong & Liu, Hanqing, 2025. "Enriched physics-informed neural networks for dynamic Poisson-Nernst-Planck systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 237(C), pages 231-246.
    • Handle: RePEc:eee:matcom:v:237:y:2025:i:c:p:231-246
    DOI: 10.1016/j.matcom.2025.04.037
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    1. Bhaumik, Bivas & De, Soumen & Changdar, Satyasaran, 2024. "Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 21-36.
    2. Guozheng Wu & Fajie Wang & Lin Qiu, 2023. "Physics-Informed Neural Network For Solving Hausdorff Derivative Poisson Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(06), pages 1-15.
    3. S M, Sivalingam & Kumar, Pushpendra & Govindaraj, Venkatesan, 2023. "A neural networks-based numerical method for the generalized Caputo-type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 302-323.
    4. Wu, Gang-Zhou & Fang, Yin & Wang, Yue-Yue & Wu, Guo-Cheng & Dai, Chao-Qing, 2021. "Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Anwar, Nabeela & Ahmad, Iftikhar & Kiani, Adiqa Kausar & Shoaib, Muhammad & Raja, Muhammad Asif Zahoor, 2024. "Novel intelligent predictive networks for analysis of chaos in stochastic differential SIS epidemic model with vaccination impact," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 251-283.
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