Jiayu Ma

Wenjie Cheng, Haiyang Fu, Liang Wang et al.

Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning architecture to learn fluid partial differential equations (PDEs) of a plasma system based on the data acquired from a fully kinetic model. The learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effects such as Landau damping. Based on the learned fluid closure, the data-driven, multi-moment fluid modeling can well reproduce all the physical quantities derived from the fully kinetic model. The calculated damping rate of Landau damping is consistent with both the fully kinetic simulation and the linear theory. The data-driven fluid modeling of PDEs for complex physical systems may be applied to improve fluid closure and reduce the computational cost of multi-scale modeling of global systems.

Yilan Qin, Jiayu Ma, Mingle Jiang et al.

Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale or multiscale systems. One of the long-standing problems in plasma physics is the integration of kinetic physics into fluid models, which is often achieved through sophisticated analytical closure terms. In this paper, we successfully construct a multi-moment fluid model with an implicit fluid closure included in the neural network using machine learning. The multi-moment fluid model is trained with a small fraction of sparsely sampled data from kinetic simulations of Landau damping, using the physics-informed neural network (PINN) and the gradient-enhanced physics-informed neural network (gPINN). The multi-moment fluid model constructed using either PINN or gPINN reproduces the time evolution of the electric field energy, including its damping rate, and the plasma dynamics from the kinetic simulations. In addition, we introduce a variant of the gPINN architecture, namely, gPINN$p$ to capture the Landau damping process. Instead of including the gradients of all the equation residuals, gPINN$p$ only adds the gradient of the pressure equation residual as one additional constraint. Among the three approaches, the gPINN$p$-constructed multi-moment fluid model offers the most accurate results. This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.

Huanghai Liu, Quzhe Huang, Qingjing Chen et al. · pku

In recent years, Large Language Models (LLMs) have been widely applied to legal tasks. To enhance their understanding of legal texts and improve reasoning accuracy, a promising approach is to incorporate legal theories. One of the most widely adopted theories is the Four-Element Theory (FET), which defines the crime constitution through four elements: Subject, Object, Subjective Aspect, and Objective Aspect. While recent work has explored prompting LLMs to follow FET, our evaluation demonstrates that LLM-generated four-elements are often incomplete and less representative, limiting their effectiveness in legal reasoning. To address these issues, we present JUREX-4E, an expert-annotated four-element knowledge base covering 155 criminal charges. The annotations follow a progressive hierarchical framework grounded in legal source validity and incorporate diverse interpretive methods to ensure precision and authority. We evaluate JUREX-4E on the Similar Charge Disambiguation task and apply it to Legal Case Retrieval. Experimental results validate the high quality of JUREX-4E and its substantial impact on downstream legal tasks, underscoring its potential for advancing legal AI applications. The dataset and code are available at: https://github.com/THUlawtech/JUREX