Second-Order Graph ODEs for Multi-Agent Trajectory Forecasting

Trajectory forecasting of multiple agents is a fundamental task that has applications in various fields, such as autonomous driving, physical system modeling and smart cities. It is challenging because agent interactions and underlying continuous dynamics jointly affect its behavior. Existing approaches often rely on Graph Neural Networks (GNNs) or Transformers to extract agent interaction features. However, they tend to neglect how the distance and velocity information between agents impact their interactions dynamically. Moreover, previous methods use RNNs or first-order Ordinary Differential Equations (ODEs) to model temporal dynamics, which may lack interpretability with respect to how each agent is driven by interactions. To address these challenges, this paper proposes the Agent Graph ODE, a novel approach that models agent interactions and continuous second-order dynamics explicitly. Our method utilizes a variational autoencoder architecture, incorporating spatial-temporal Transformers with distance information and dynamic interaction graph construction in the encoder module. In the decoder module, we employ GNNs with distance information to model agent interactions, and use coupled second-order ODEs to capture the underlying continuous dynamics by modeling the relationship between acceleration and agent interactions. Experimental results show that our proposed Agent Graph ODE outperforms state-of-the-art methods in prediction accuracy. Moreover, our method performs well in sudden situations not seen in the training dataset.