PDEBench Datasets

This dataset contains benchmark data, generated with numerical simulation based on different PDEs, namely 1D advection, 1D Burgers', 1D and 2D diffusion-reaction, 1D diffusion-sorption, 1D, 2D, and 3D compressible Navier-Stokes, 2D Darcy flow, and 2D shallow water equation. This dataset is intended to progress the scientific ML research area. In general, the data are stored in HDF5 format, with the array dimensions packed according to the convention [b,t,x1,...,xd,v], where b is the batch size (i.e. number of samples), t is the time dimension, x1,...,xd are the spatial dimensions, and v is the number of channels (i.e. number of variables of interest). More detailed information are also provided in our Github repository (https://github.com/pdebench/PDEBench) and our submitting paper to NeurIPS 2022 Benchmark track.本数据集包含基于各类偏微分方程（Partial Differential Equations，PDEs）通过数值模拟生成的基准数据，具体涵盖一维平流方程、一维伯格斯方程、一维与二维扩散反应方程、一维扩散吸附方程、一维、二维及三维可压缩纳维-斯托克斯方程、二维达西流方程以及二维浅水波方程。本数据集旨在推动科学机器学习领域的研究进展。总体而言，数据以HDF5格式存储，数组维度遵循[b, t, x₁, …, x_d, v]的约定，其中b为批量大小（即样本总数），t为时间维度，x₁至x_d为空间维度，v为通道数（即目标变量的数量）。更多详细信息可参阅我们的GitHub仓库（https://github.com/pdebench/PDEBench）以及提交至NeurIPS 2022基准赛道的论文。