PID-GraphVAE: 2D CFD datasets, trained models, and identification records for 'From compression to discovery'

This dataset contains four ZIP archives supporting the study on flow field representation and equation discovery. flow2d_coordinate.zip provides the mesh coordinates (exported from the first Fluent CSV file) shared across all 2-D flow cases. flow2d_dataset.zip holds the three 2-D transient CFD datasets (backward-facing step, cylinder pair, and pitching NACA0018) in HDF5 format, ready for training and testing. flow2d_model.zip includes model weight files for every test case: both fixed‑topology and data‑driven topology variants under three random initialisation seeds per case. flow2d_sindy_results.zip contains the sparse identification of nonlinear dynamics (SINDy) outputs for both topology approaches, including the discovered governing equations and coefficient tables.