CARE: Modeling Interacting Dynamics Under Temporal Environmental Variation

Abstract

Modeling interacting dynamical systems, such as fluid dynamics and intermolecular interactions, is a fundamental research problem for understanding and simulating complex real-world systems. Many of these systems can be naturally represented by dynamic graphs, and graph neural network-based approaches have been proposed and shown promising performance. However, most of these approaches assume the underlying dynamics does not change over time, which is unfortunately untrue. For example, a molecular dynamics can be affected by the environment temperature over the time. In this paper, we take an attempt to provide a probabilistic view for time-varying dynamics and propose a model Context-attended Graph ODE (CARE) for modeling time-varying interacting dynamical systems. In our CARE, we explicitly use a context variable to model time-varying environment and construct an encoder to initialize the context variable from historical trajectories. Furthermore, we employ a neural ODE model to depict the dynamic evolution of the context variable inferred from system states. This context variable is incorporated into a coupled ODE to simultaneously drive the evolution of systems. Comprehensive experiments on four datasets demonstrate the effectiveness of our proposed CARE compared with several state-of-the-art approaches.