CSG-ODE: ControlSynth Graph ODE For Modeling Complex Evolution of Dynamic Graphs

Graph Neural Ordinary Differential Equations (GODE) integrate the Variational Autoencoder (VAE) framework with differential equations, effectively modeling latent space uncertainty and continuous dynamics, excelling in graph data evolution and incompleteness. However, existing GODE face challenges in capturing time-varying relationships and nonlinear node state evolution, which limits their ability to model complex dynamic graphs. To address these issues, we propose the ControlSynth Graph ODE (CSG-ODE). In the VAE encoding phase, CSG-ODE introduces an information transmission-based inter-node importance weighting mechanism, integrating it with latent correlations to guide adaptive graph convolutional recurrent networks for temporal node embedding. During decoding, CSG-ODE employs ODE to model node dynamics, capturing nonlinear evolution through sub-networks with nonlinear activations. For scenarios or prediction tasks that require stability, we extend CSG-ODE to stable CSG-ODE (SCSG-ODE) by constraining weight matrices to learnable anti-symmetric forms, theoretically ensuring enhanced stability. Experiments on traffic, motion capture, and simulated physical systems datasets demonstrate that CSG-ODE outperforms state-of-the-art GODE, while SCSG-ODE achieves both superior performance and optimal stability.

Graph Neural ODE (GODE) integrate the Variational Autoencoder (VAE) framework with differential equations to model uncertainty and continuous dynamics in evolving graphs. However, they struggle with capturing time-varying relationships and nonlinear node state evolution. To overcome these limitations, we propose ControlSynth Graph ODE (CSG-ODE). In the VAE encoding phase, CSG-ODE introduces an information transmission-based inter-node importance weighting mechanism, guiding adaptive graph convolutional recurrent networks for temporal node embeddings. During decoding, it models nonlinear node dynamics using ODE with sub-networks and nonlinear activations. For scenarios or tasks that require stability, we extend CSG-ODE to SCSG-ODE by using learnable anti-symmetric weight matrices, theoretically ensuring enhanced stability. Experiments show that CSG-ODE outperforms existing methods, and SCSG-ODE offers both accuracy and optimal stability.