nick-leland/heat1d-pde-dataset

该数据集包含一维热方程与冷却项的数值解，专为科学计算和物理信息神经网络中的机器学习应用设计。数据集由一维热方程的时空解组成，包括边界条件和冷却项。每个样本包括初始状态、最终状态（带噪声和不带噪声）、模拟参数和经过时间。数据集的结构包括初始温度分布、最终温度分布、无噪声的初始状态和最终状态、参数（热扩散率、冷却系数、环境温度）以及状态之间的时间差。

This dataset contains numerical solutions of the 1D heat equation with cooling terms, designed for machine learning applications in scientific computing and physics-informed neural networks. The dataset consists of spatiotemporal solutions to the 1D heat equation with boundary conditions and a cooling term. Each sample includes initial states, final states (with and without noise), simulation parameters, and elapsed times. The dataset structure includes initial temperature distribution, final temperature distribution, noise-free initial and final states, parameters (thermal diffusivity, cooling coefficient, environmental temperature), and the time difference between states.