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Asymptotic-Preserving Neural Networks for Multiscale Vlasov–Poisson–Fokker–Planck System in the High-Field Regime

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Abstract

The Vlasov–Poisson–Fokker–Planck (VPFP) system is a fundamental model in plasma physics that describes the Brownian motion of a large ensemble of particles within a surrounding bath. Under the high-field scaling, both collision and field are dominant. This paper introduces two Asymptotic-Preserving Neural Network (APNN) methods within a physics-informed neural network (PINN) framework for solving the VPFP system in the high-field regime. These methods aim to overcome the computational challenges posed by high dimensionality and multiple scales of the system. The first APNN method leverages the micro–macro decomposition model of the original VPFP system, while the second is based on the mass conservation law. Both methods ensure that the loss function of the neural networks transitions naturally from the kinetic model to the high-field limit model, thereby preserving the correct asymptotic behavior. Through extensive numerical experiments, these APNN methods demonstrate their effectiveness in solving multiscale and high dimensional uncertain problems, as well as their broader applicability for problems with long time duration and non-equilibrium initial data.

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Acknowledgements

Shi Jin is partially supported by the Strategic Priority Research Program of Chinese Academy of Sciences XDA25010401, the NSFC Grant No. 12031013, the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities. Zheng Ma is supported by NSFC Grant Nos. 12031013, 92270120 and Foundation of LCP.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shi Jin, Zheng Ma & Tian-ai Zhang

  2. Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shi Jin, Zheng Ma & Tian-ai Zhang

  3. Shanghai Artificial Intelligence Laboratory, Shanghai, China

    Shi Jin

  4. Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zheng Ma

  5. CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China

    Zheng Ma

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Jin, S., Ma, Z. & Zhang, Ta. Asymptotic-Preserving Neural Networks for Multiscale Vlasov–Poisson–Fokker–Planck System in the High-Field Regime. J Sci Comput 99, 61 (2024). https://doi.org/10.1007/s10915-024-02527-z

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  • DOI: https://doi.org/10.1007/s10915-024-02527-z

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