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In this research, we introduce an innovative three-network architecture thatcomprises an encoder-decoder framework with an attention mechanism. Thearchitecture comprises a 1st-order-pre-trainer, a 2nd-order-improver, and adiscriminator network, designed to boost the order accuracy of charge densityin Particle-In-Cell (PIC) simulations. We acquire our training data from ourself-developed 3-D PIC code, JefiPIC. The training procedure starts with the1st-order-pre-trainer, which is trained on a large dataset to predict chargedensities based on the provided article positions. Subsequently, we fine-tunethe 1st-order-pre-trainer, whose predictions then serve as inputs to the2nd-order-improver. Meanwhile, we train the 2nd-order-improver anddiscriminator network using a smaller volume of 2nd-order data, therebyachieving to generate charge density with 2nd-order accuracy. In the concludingphase, we replace JefiPIC's conventional particle interpolation process withour trained neural network. Our results demonstrate that the neuralnetwork-enhanced PIC simulation can effectively simulate plasmas with 2nd-order accuracy. This highlights the advantage of our proposed neuralnetwork: it can achieve higher-accuracy data with fewer real labels.

Leveraging Neural Networks with Attention Mechanism for High-Order Accuracy in Charge Density in Particle-in-Cell Simulation