Physics of anticipatory active matter, with application to crowd dynamics

Existing AI systems for modeling human behavior operate at the level of individuals or detect events after they occur. As a result, they systematically fail to capture the collective dynamics that determine whether a group remains stable or transitions into escalation or breakdown. We propose a different foundation: a group of interacting humans constitutes a complex dynamical system in the precise mathematical sense, exhibiting emergence, nonlinearity, feedback loops, sensitivity near critical points, and phase transitions between qualitatively distinct regimes. The state of such a system is not located within any single participant; it is distributed across mutual influence loops and observable through the micro-dynamics of the body. We introduce BEHAVE (Behavioral Engine for Human Activity Vector Estimation), a formal framework that models collective dynamics as continuous behavioral fields defined over an interaction space derived from observable physical signals. Kinematic micro-signals (position, velocity, body orientation, gestural activity) are structured into a directed interaction graph and aggregated into a basis of behavioral fields capturing distinct, non-redundant axes of collective state. The framework rests on one theorem and two structural propositions characterizing the tension field, the field basis, and the criticality index. Perception and forecasting layers are implemented using neural models, enabling data-driven learning and approximation of system dynamics. BEHAVE is formulated as a computational system for learning, representing, and forecasting collective dynamics from data. A working pipeline is demonstrated on a 7-agent negotiation snapshot. The same fields, recalibrated, apply to crowd safety, crisis-team dynamics, education, and clinical contexts.

Local pedestrian-vehicle forecasting spans heterogeneous physical scales: pedestrians combine root locomotion with articulated motion, whereas vehicles are rigid bodies described by kinematic state and oriented extent. Existing road-agent forecasters typically omit pedestrian articulation, while pose forecasters leave vehicle futures outside the learned rollout. We introduce PV-WM, a history-only world model over structured post-perception tracks. It recurrently advances pedestrian root motion, 15-joint articulation, and learned vehicle states within a synchronized heterogeneous state. The generated pedestrian and vehicle chunks supply the next recurrent boundary; vehicle boxes are reconstructed from predicted center and heading with observed extent, and P-V geometry is recomputed after every transition. Relative to a matched one-shot complete-state predictor, recurrent execution reduces Root ADE by 12.7% and MPJPE by 14.8%. Feedback interventions show that later predictions depend on the content, temporal order, and pedestrian identity of generated articulation. Across 824 aligned Waymo contexts, with 797 providing valid future vehicle support, PV-WM reduces Root ADE by 5.2%, MPJPE by 7.6%, P-V distance error by 11.9%, and oriented-box closest-approach error by 5.8% relative to a validation-selected Modular Specialist. The single-network model uses 57.1% fewer parameters, 96.5% lower average FLOPs per local scene, and 25.5% lower measured p95 latency. PV-WM unifies this heterogeneous future state while preserving type-specific pedestrian and vehicle dynamics.

Long-term human path forecasting in crowds is critical for autonomous moving platforms (like autonomous driving cars and social robots) to avoid collision and make high-quality planning. Although the current research take into account social interactions for prediction, they don't reveal the exact kinds of social interactions happened among people and how the social interactions affect the decision-making process of pedestrians, which further limits its robustness. Social interactions in pedestrian walking are intuitively massive and hard to label and quantify. In this paper, we explore creatively to quantify and interpret how pedestrians interact with others by proposing Learn to Cluster. Our clustering social interactions is probabilistic latent variable generative, learning directly from sequential trajectory observations, scalable to arbitrary number of pedestrians. Learn to cluster is label-free and can be naturally integrated into the training process of the prediction model. The latent variables will then serve as 'labels' to categorize social interactions. Extensive experiments over several trajectory prediction benchmarks demonstrate that our method is able to learn the patterns of social interactions and effectively integrate the patterns to pedestrian trajectory prediction.