🤖 AI Summary
Traditional statistical physics models struggle to capture agents with forward-looking behavior—such as pedestrians—because they rely solely on current or past states. This work proposes a novel statistical physics framework that models agent decisions as responses to anticipated future states. By introducing an observation-based cost function, the approach maps d-dimensional forward-looking agents onto (d+1)-dimensional non-anticipatory chains, enabling analysis through polymer physics methods. The study is the first to systematically incorporate foresight into statistical physics, introducing the concept of an “anticipation horizon” that naturally unifies operational and tactical modeling layers. Remarkably, even with the simplest cost function, the model successfully reproduces complex scenarios such as navigating crowded spaces and alighting from trains, outperforming existing state-of-the-art approaches.
📝 Abstract
Statistical Physics has traditionally dealt with entities that interact merely based on the present, and possibly past, configurations. This reactive framework is inefficient in many situations involving living beings, such as predators chasing a prey, pedestrians, or even robots. This paper introduces a statistical physical framework for the dynamics of anticipatory agents, whose present-time dynamics depend on the prospective system state that they anticipate. We clarify how these dynamics can be expressed in terms of a cost function constructed based on observations and we show that the dynamics of an anticipatory agent in d dimensions can be mapped onto the dynamics of a (non-anticipatory) chain in d + 1 dimensions, with fluctuations acting transversely on the chain to account for the uncertainty about the future state. Insights from polymer Physics help us characterize the dynamics of these chains and delineate an anticipation horizon beyond which the blurry future can be handled in a mean-field way. The foregoing framework is successfully applied to pedestrian dynamics, leading to a seamless integration of operational and tactical levels in an agent-based model. Even with a minimal expression of the cost, the model succeeds in reproducing various experimental scenarios which are challenging for state-of-the-art models, such as crossing cluttered environments or alighting from a crowded train. The transparent and flexible basis of the model allows the straightforward incorporation of additional mechanisms.