Lei Wang

E. O. Asante-Asamani, Lei Wang, Zeyun Yu

Numerical solutions of partial differential equations (PDEs) on manifolds continues to generate a lot of interest among scientists in the natural and applied sciences. On the other hand, recent developments of 3D scanning and computer vision technologies have produced a large number of 3D surface models represented as point clouds. Herein, we develop a simple and efficient method for solving PDEs on closed surfaces represented as point clouds. By projecting the radial vector of standard radial basis function(RBF) kernels onto the local tangent plane, we are able to produce a representation of functions that permits the replacement of surface differential operators with their Cartesian equivalent. We demonstrate, numerically, the efficiency of the method in discretizing the Laplace Beltrami operator.

Lei Wang, Heyang Gao, Xiaohe Bo et al.

Leveraging large language model (LLM) based agents to simulate human social behaviors has recently gained significant attention. In this paper, we introduce a novel social simulator called YuLan-OneSim. Compared to previous works, YuLan-OneSim distinguishes itself in five key aspects: (1) Code-free scenario construction: Users can simply describe and refine their simulation scenarios through natural language interactions with our simulator. All simulation code is automatically generated, significantly reducing the need for programming expertise. (2) Comprehensive default scenarios: We implement 50 default simulation scenarios spanning 8 domains, including economics, sociology, politics, psychology, organization, demographics, law, and communication, broadening access for a diverse range of social researchers. (3) Evolvable simulation: Our simulator is capable of receiving external feedback and automatically fine-tuning the backbone LLMs, significantly enhancing the simulation quality. (4) Large-scale simulation: By developing a fully responsive agent framework and a distributed simulation architecture, our simulator can handle up to 100,000 agents, ensuring more stable and reliable simulation results. (5) AI social researcher: Leveraging the above features, we develop an AI social researcher. Users only need to propose a research topic, and the AI researcher will automatically analyze the input, construct simulation environments, summarize results, generate technical reports, review and refine the reports--completing the social science research loop. To demonstrate the advantages of YuLan-OneSim, we conduct experiments to evaluate the quality of the automatically generated scenarios, the reliability, efficiency, and scalability of the simulation process, as well as the performance of the AI social researcher.