DabbyOWL/PDE_Inverse_Problem_Benchmarking

PDEInvBench是一个全面的数据集，用于偏微分方程（PDE）逆问题的神经网络设计与探索。该数据集包含五个PDE系统：2D反应扩散（使用Fitzhugh-Nagumo方程模拟化学模式形成）、2D纳维-斯托克斯（无外力流体流动）、2D湍流（受迫纳维-斯托克斯，模拟完全发展的湍流）、1D Korteweg-De Vries（描述浅水波中的孤子动力学）和2D达西流（模拟多孔介质中的地下水流）。数据集规模超过120万次模拟，提供多分辨率架构（如64×64、128×128、256×256、512×512、2048×2048等分辨率），覆盖抛物型、双曲型和椭圆型PDE分类。参数空间系统探索包括反应扩散的k、Du、Dv参数（范围分别为[0.005,0.1]、[0.01,0.5]、[0.01,0.5]）、纳维-斯托克斯的ν参数（范围[10⁻⁴,10⁻²]）、湍流的ν参数（范围[10⁻⁵,10⁻²]）、KdV的δ参数（范围[0.8,5]）以及达西流的片常数扩散系数。数据以HDF5格式存储，组织为训练、验证、测试和分布外（包括非极端和极端）划分，用于评估模型在参数空间内的泛化能力。数据集还包括物理和数学多样性、参数归一化统计、以及详细的数据加载和预处理指南。PDEInvBench is a comprehensive dataset for neural network design and exploration of partial differential equation (PDE) inverse problems. The dataset includes five PDE systems: 2D Reaction Diffusion (modeling chemical pattern formation using Fitzhugh-Nagumo equations), 2D Navier-Stokes (unforced fluid flow), 2D Turbulent Flow (forced Navier-Stokes, simulating fully developed turbulence), 1D Korteweg-De Vries (describing soliton dynamics in shallow water waves), and 2D Darcy Flow (modeling groundwater flow through porous media). The dataset contains over 1.2 million individual simulations and provides a multi-resolution architecture (e.g., 64×64, 128×128, 256×256, 512×512, 2048×2048 resolutions), covering parabolic, hyperbolic, and elliptic PDE classifications. Systematic parameter space exploration includes k, Du, Dv parameters for Reaction Diffusion (ranges [0.005,0.1], [0.01,0.5], [0.01,0.5] respectively), ν parameter for Navier-Stokes (range [10⁻⁴,10⁻²]), ν parameter for Turbulent Flow (range [10⁻⁵,10⁻²]), δ parameter for KdV (range [0.8,5]), and piecewise constant diffusion coefficients for Darcy Flow. Data is stored in HDF5 format, organized into train, validation, test, and out-of-distribution (including non-extreme and extreme) splits for evaluating model generalization across parameter spaces. The dataset also features physical and mathematical diversity, parameter normalization statistics, and detailed guidelines for data loading and preprocessing.