PID-GraphVAE: Physics-informed disentangled graph VAE for cascade-aware equation discovery

Official implementation of "From compression to discovery: representations whose structure reveals the governing equations".   PID-GraphVAE (physics-informed disentangled graph variational autoencoder) is a co-design of representation learning and sparse equation discovery: a graph VAE partitions its latent space into physics-anchored subspaces along a candidate energy-cascade hierarchy, a cascaded mutual-information objective preserves the cross-scale couplings, the inter-subspace topology is discovered from the latent dynamics, and a cascade-aware sparse identification distills closed-form reduced-order models.   This archive is the frozen snapshot accompanying the submission (release v1.0-submission). Active development continues at the GitHub repository linked below. The CFD datasets, trained model weights, latent trajectories, and identification records are deposited separately.