This dataset contains the reference solutions used for training the two neural networks in 1-, 2- and 3-D cases for the article:"A Data-facilitated Numerical Method for Richards Equation to Model Water Flow Dynamics in Soil" by Zeyuan Song and Zheyu Jiang, submitted to the journal Water Resources Research. This dataset which describes the relationship between the pressure head and number of particles used to train two MLPs in D-GRW based solvers consists of three files, i.e., 1-, 2- and 3-D case study. There are two parts, original reference solutions and reference solutions, corresponding to the original solutions generated by coarse mesh solvers and solutions after data augmentation process, respectively.The dataset is generated by GRW based solvers and simulation results (e.g., Celia's finite difference method). Original reference solutions admit GRW proportionality assumption. We initialize the number of particles by multiplying the initial condition and 1E10.