Leveraging Attention Mechanisms in Neural Networks for High-Order Accuracy in Particle-in-Cell Simulations

This paper introduces a novel approach to enhance the accuracy of charge density calculations in particle-in-cell (PIC) simulations by leveraging attention mechanisms in neural networks (NNs). We propose a three-network architecture comprising a 1st-order-pre-trainer, a 2nd-order-improver, and a discriminator network. The 1st-order-pre-trainer is initially trained on a large dataset to predict charge densities from particle positions and charges. Subsequently, it is fine-tuned with the 2nd-order-improver and discriminator network using a smaller dataset to achieve near 2nd-order accuracy. Our approach substitutes the traditional particle interpolation process in JefiPIC with a meticulously trained NN. The results demonstrate that PIC simulations enhanced by NNs can simulate plasmas and electromagnetic (EM) fields with significantly enhanced accuracy, achieving an absolute accuracy improvement exceeding 10% when compared to a 1st-order PIC simulator and a relative accuracy improvement of over 50% in comparison to other direct training techniques. Furthermore, our method has the potential to diminish the reliance on acquiring real labels, which are often difficult to observe. This work highlights the potential of integrating artificial intelligence (AI) techniques to improve the precision and efficiency of PIC simulations, paving the way for future advancements in plasma and nuclear physics research.