3D and 4D PDE Systems
收藏arXiv2025-09-30 收录
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https://jwcho5576.github.io/spinn.github.io/
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资源简介：
该数据集包含了多种三维（扩散、亥姆霍兹、克莱因-戈登和纳维-斯托克斯方程）和四维（克莱因-戈登和纳维-斯托克斯方程）偏微分方程系统，用于评估所提出的可分离物理信息神经网络（SPINN）与普通物理信息神经网络（PINN）的性能对比。实验采用了不同的随机种子进行，详细的实验设置已在附录中提供。对于SPINN，其配置点数量可达到256^3。该任务旨在解决多维度偏微分方程问题。
This dataset comprises systems of partial differential equations (PDEs) in three-dimensional (diffusion, Helmholtz, Klein-Gordon, and Navier-Stokes equations) and four-dimensional (Klein-Gordon and Navier-Stokes equations) spaces, designed for performance comparison between the proposed separable physics-informed neural network (SPINN) and the standard physics-informed neural network (PINN). Experiments were conducted with different random seeds, and detailed experimental settings are provided in the appendix. The number of collocation points for SPINN can reach up to 256³. This task aims to solve multi-dimensional partial differential equation problems.
