East Asian J. Appl. Math., 14 (2024), pp. 636-656.
Published online: 2024-06
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We consider the global discharge model in plasma simulations using physics-informed neural networks (PINNs). Our method, named Plasma-Simulation PINNs (PS-PINNs), effectively addresses the inherent stiffness and multiphysics aspects of the global model. Logarithmically equidistant points are employed to capture the steep behaviour in state variables during early stages. This distribution, while typical for handling stiffness in standard numerical methods, can hinder neural network (NN) training. To overcome this, we introduce a pre-processing layer featuring logarithmic transformation and standardization, significantly improving neural network training efficiency. In addition, our model addresses the complex interactions between multiple species common in the plasma problem, resulting in numerous physics loss terms. It is important to balance among various loss terms during training. To this end, we employ a self-adaptive loss balanced method to adaptively choose the weights, enhancing training robustness and effectiveness. The effectiveness of the proposed framework is demonstrated through several examples, including the forward and inverse problems in the chlorine global discharge model, and parameter dependency analysis.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-313.170324}, url = {http://global-sci.org/intro/article_detail/eajam/23164.html} }We consider the global discharge model in plasma simulations using physics-informed neural networks (PINNs). Our method, named Plasma-Simulation PINNs (PS-PINNs), effectively addresses the inherent stiffness and multiphysics aspects of the global model. Logarithmically equidistant points are employed to capture the steep behaviour in state variables during early stages. This distribution, while typical for handling stiffness in standard numerical methods, can hinder neural network (NN) training. To overcome this, we introduce a pre-processing layer featuring logarithmic transformation and standardization, significantly improving neural network training efficiency. In addition, our model addresses the complex interactions between multiple species common in the plasma problem, resulting in numerous physics loss terms. It is important to balance among various loss terms during training. To this end, we employ a self-adaptive loss balanced method to adaptively choose the weights, enhancing training robustness and effectiveness. The effectiveness of the proposed framework is demonstrated through several examples, including the forward and inverse problems in the chlorine global discharge model, and parameter dependency analysis.