In this research, we introduce an innovative three-network architecture that
comprises an encoder-decoder framework with an attention mechanism. The
architecture comprises a 1st-order-pre-trainer, a 2nd-order-improver, and a
discriminator network, designed to boost the order accuracy of charge density
in Particle-In-Cell (PIC) simulations. We acquire our training data from our
self-developed 3-D PIC code, JefiPIC. The training procedure starts with the
1st-order-pre-trainer, which is trained on a large dataset to predict charge
densities based on the provided article positions. Subsequently, we fine-tune
the 1st-order-pre-trainer, whose predictions then serve as inputs to the
2nd-order-improver. Meanwhile, we train the 2nd-order-improver and
discriminator network using a smaller volume of 2nd-order data, thereby
achieving to generate charge density with 2nd-order accuracy. In the concluding
phase, we replace JefiPIC's conventional particle interpolation process with
our trained neural network. Our results demonstrate that the neural
network-enhanced PIC simulation can effectively simulate plasmas with 2
nd-order accuracy. This highlights the advantage of our proposed neural
network: it can achieve higher-accuracy data with fewer real labels.Comment: 8 pages, 10 figure