Information bottleneck-based correlation analysis with graph neural ODEs for network reconstruction

Dynamical interacting systems are ubiquitous in nature and society, yet forecasting latent interacting systems presents significant challenges due to their unobservable network structures and dynamic rules—particularly for continuous dynamical systems. Drawing inspiration from graph neural ordinary differential equations (Graph-NODE) and information bottleneck theory, this study proposes an information bottleneck-based correlation analysis model with graph neural ODEs (IBCA-GNODE). Our framework introduces a Message-Passing NODE block (MP-NODE) that predicts node states by sampling from a parameterized adjacency matrix. By applying information bottleneck theory, the IBCA-GNODE model extracts correlation features from MP-NODE outputs to infer node correlations, thereby guiding updates to the parameterized matrix and enabling more accurate network reconstruction. Experimental results demonstrate that IBCA-GNODE successfully reconstructs diverse network structures across multiple dynamical systems while consistently outperforming baseline models.