Evolved Differential Model for Sporadic Graph Time-Series Prediction

Sensing signals of many real-world network systems, such as traffic network or microgrid, could be sparse and irregular in both spatial and temporal domains due to reasons such as cost reduction, noise corruption, or device malfunction. It is a fundamental but challenging problem to model the continuous dynamics of a system from the sporadic observations on the network of nodes, which is generally represented as a graph. In this paper, we propose a deep learning model called Evolved Differential Model (EDM) to model the continuous-time stochastic process from partial observations on graph. Our model incorporates diffusion convolutional network to parameterize continuous-time system dynamics by graph Ordinary Differential Equation (ODE) and graph Stochastic Differential Equation (SDE). The graph ODE is applied to accurately capture the spatial-temporal relation and extract hidden features from the data. The graph SDE can efficiently capture the underlying uncertainty of the network systems. With the recurrent ODE-SDE scheme, EDM can serve as an accurate online predictive model that is effective for either monitoring or analyzing the real-world networked objects. Through extensive experiments on several datasets, we demonstrate that EDM outperforms existing methods in online prediction tasks.