Coupled Graph ODE for Learning Interacting System Dynamics

Many real-world systems such as social networks and moving planets are dynamic in nature, where a set of coupled objects are connected via the interaction graph and exhibit complex behavior along the time. For example, the COVID-19 pandemic can be considered as a dynamical system, where objects represent geographical locations (e.g., states) whose daily confirmed cases of infection evolve over time. Outbreak at one location may influence another location as people travel between these locations, forming a graph. Thus, how to model and predict the complex dynamics for these systems becomes a critical research problem. Existing work on modeling graph-structured data mostly assumes a static setting. How to handle dynamic graphs remains to be further explored. On one hand, features of objects change over time, influenced by the linked objects in the interaction graph. On the other hand, the graph itself can also evolve, where new interactions (links) may form and existing links may drop, which may in turn be affected by the dynamic features of objects. In this paper, we propose coupled graph ODE: a novel latent ordinary differential equation (ODE) generative model that learns the coupled dynamics of nodes and edges with a graph neural network (GNN) based ODE in a continuous manner. Our model consists of two coupled ODE functions for modeling the dynamics of edges and nodes based on their latent representations respectively. It employs a novel encoder parameterized by a GNN for inferring the initial states from historical data, which serves as the starting point of the predicted latent trajectories. Experiment results on the COVID-19 dataset and the simulated social network dataset demonstrate the effectiveness of our proposed method.