Learning Interacting Dynamic Systems with Neural Ordinary Differential Equations

Interacting Dynamic Systems refer to a group of agents which interact with others in a complex and dynamic way. Modeling Interacting Dynamic Systems is a crucial topic with numerous applications, such as in time series forecasting and physical simulations. To accurately model these systems, it is necessary to learn the temporal and relational dimensions jointly. However, previous methods have struggled to learn the temporal dimension explicitly because they often overlook the physical properties of the system. Furthermore, they often ignore the distance information in the relational dimensions. To address these limitations, we propose a Dynamic Data Driven Application Systems (DDDAS) approach called Interacting System Ordinary Differential Equations (ISODE). Our approach leverages the latent space of Neural ODEs to model the temporal dimensions explicitly and incorporates the distance information in the relational dimensions. Moreover, we demonstrate how our approach can dynamically update an agent’s trajectory when obstacles are introduced, without requiring retraining. Our experimental studies reveal that our ISODE DDDAS approach outperforms existing methods in prediction accuracy. We also illustrate that our approach can dynamically adapt to changes in the environment by showing our agent can dynamically avoid obstacles. Overall, our approach provides a promising solution to modeling Interacting Dynamic Systems that can capture the temporal and relational dimensions accurately.