PDE Training Dataset

该数据集是一个综合性的数据集，包含了用于训练 UGrid 模型以解决各种线性偏微分方程的（M, b, f）组合对。该数据集包括16,000对专为Helmholtz和扩散问题设计的组合，其独特的系数场是随机抽取的。训练数据中的几何形状仅限于类似“甜甜圈”的形状，且所有训练数据中的f场均限制为零。此外，该数据集包含了不同规模的数据集；特别地，它在大型数据集上进行了训练。该任务的目的是训练一个用于线性偏微分方程的神经网络求解器。

This is a comprehensive dataset containing (M, b, f) triplets for training the UGrid model to solve various linear partial differential equations (PDEs). It includes 16,000 such triplets specifically designed for Helmholtz and diffusion problems, where the unique coefficient fields are randomly sampled. The geometrical domains in the training data are restricted to "donut"-shaped structures, and the source term fields f across all training samples are constrained to be zero. Additionally, this dataset covers multiple variants with different scales; notably, it is trained on large-scale datasets. The objective of this task is to train a neural network solver for linear partial differential equations.