Liu Na

Hang Hu, Sidi Wu, Guoxiong Cai et al.

Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and oscillations, trained solutions usually suffer low accuracy. In addition, most current works only offer the trained solution for predetermined input parameters. If any change occurs in input parameters, transfer learning or retraining is required, and traditional numerical techniques also need an independent simulation. In this work, a physics-driven GraphSAGE approach (PD-GraphSAGE) based on the Galerkin method and piecewise polynomial nodal basis functions is presented to solve computational problems governed by irregular PDEs and to develop parametric PDE surrogate models. This approach employs graph representations of physical domains, thereby reducing the demands for evaluated points due to local refinement. A distance-related edge feature and a feature mapping strategy are devised to help training and convergence for singularity and oscillation situations, respectively. The merits of the proposed method are demonstrated through a couple of cases. Moreover, the robust PDE surrogate model for heat conduction problems parameterized by the Gaussian random field source is successfully established, which not only provides the solution accurately but is several times faster than the finite element method in our experiments.

Jianwei Sun, Chaoyang Mei, Linlin Wei et al.

The efficacy of large language models (LLMs) is heavily dependent on the quality of the underlying data, particularly within specialized domains. A common challenge when fine-tuning LLMs for domain-specific applications is the potential degradation of the model's generalization capabilities. To address these issues, we propose a two-stage approach for the construction of production prompts designed to yield high-quality data. This method involves the generation of a diverse array of prompts that encompass a broad spectrum of tasks and exhibit a rich variety of expressions. Furthermore, we introduce a cost-effective, multi-dimensional quality assessment framework to ensure the integrity of the generated labeling data. Utilizing a dataset comprised of service provider and customer interactions from the real estate sector, we demonstrate a positive correlation between data quality and model performance. Notably, our findings indicate that the domain-specific proficiency of general LLMs can be enhanced through fine-tuning with data produced via our proposed method, without compromising their overall generalization abilities, even when exclusively domain-specific data is employed for fine-tuning.