HOPE: High-order Graph ODE For Modeling Interacting Dynamics

Leading graph ordinary differential equation (ODE) models have offered generalized strategies to model interacting multi-agent dynamical systems in a data-driven approach. They typically consist of a temporal graph encoder to get the initial states and a neural ODE-based generative model to model the evolution of dynamical systems. However, existing methods have severe deficiencies in capacity and efficiency due to the failure to model high-order correlations in long-term temporal trends. To tackle this, in this paper, we propose a novel model named High-order graph ODE (HOPE) for learning from dynamic interaction data, which can be naturally represented as a graph. It first adopts a twin graph encoder to initialize the latent state representations of nodes and edges, which consists of two branches to capture spatio-temporal correlations in complementary manners. More importantly, our HOPE utilizes a second-order graph ODE function which models the dynamics for both nodes and edges in the latent space respectively, which enables efficient learning of long-term dependencies from complex dynamical systems. Experiment results on a variety of datasets demonstrate both the effectiveness and efficiency of our proposed method.

Authors

• Xiao Luo 0001
• Jingyang Yuan
• Zijie Huang 0002
• Huiyu Jiang
• Yifang Qin
• Wei Ju 0001
• Ming Zhang 0004
• Yizhou Sun

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