A Continuous-Discrete Switching Dynamical Model for Multi-Agent Interactions

Modeling collective behavior in agent-based systems is a grand scientific challenge, particularly when underlying dynamics must be inferred from noisy, incomplete, and irregularly sampled natural data. To address this, we develop a structured continuous-discrete switching linear dynamical system for multi-agent behavior. Our framework makes three key contributions: it gives the latent state a physical position--velocity interpretation and parameterizes directed cross-agent dynamics through relative motion; it handles partial and complete missingness without pre-imputation; and it defines latent dynamics in continuous time, separating the behavioral process from the observation grid. We evaluate the model in simulation and on longitudinal video and acoustic recordings from a socially interacting family of Mongolian gerbils. In simulation, we recover filtered position--velocity trajectories and model parameters under substantial random missingness. Gerbil-derived missingness patterns reveal a harder regime, where prolonged agent-specific gaps degrade recovery far more than random masking and produce corresponding drift and uncertainty in fitted trajectories. Together, these results establish an interpretable framework for naturalistic multi-agent dynamics and motivate robust modeling of naturalistic data missingness patterns.