Collective Motion and Path-Entropy

集体运动是一个迷人的和高度现代化的研究领域，涵盖应用数学，物理学，动物学，机器人和机器学习。只有随着计算能力的进步，对这一主题的研究才成为可能，使科学家能够探索成群的鸟类，鱼群和蜂群所表现出的现象。这些非凡的自然现象的动机和执行尚未得到很好的理解。除了视觉上的吸引力，集体运动还有各种潜在的应用，如CGI图形，机器人和群体智能。自90年代中期以来，人们一直在研究集体运动的“自上而下”模型。这种类型的模型强制执行特定的动态，广泛模仿观察到的行为，如对齐，凝聚力和避免碰撞。虽然这些模型产生了一些理论上的可能性，并与物理学中的自旋模型有密切的相似之处，但它们复制真实世界场景的全部复杂性的能力有限，阻碍了它们的实用性。最近的工作探索了集体运动和群集使用“自下而上”的模型，分别使用“未来状态最大化”和“路径熵最大化”的原则，由因果熵力的动机。在这些模型中，每只鸟都利用投射的视觉状态来制定任何重新定向的决定。这两种模型都可以产生高度有序的凝聚力，表现出边缘不透明的羊群。然而，这两种模型仅在2D中进行了研究。这从根本上限制了它们对涉及全3D运动的系统（鸟、鱼等）的适用性，从而难以与实验进行比较。在这篇博士论文中，我们希望扩展以前的工作，以模拟3D的flockingbirds。以前的3D模型是“自上而下”的，例如由三个简单规则（分离，对齐和内聚）定义的身体模型。我们渴望提供更深入的了解群集行为和有效性的应用程序的“自下而上”模型的三维集体运动。我们的核心研究问题是：我们如何将2D投影方法转化为3D视觉刺激？我们能否创建计算效率更高的视觉投影改进模型，例如使用“光线追踪”技术？鸡群是否显示边缘混浊？该算法是否产生了让人联想到自然界中所见的流形的复杂结构？

Collective Motion is a captivating and highly contemporary area of study that spans applied mathematics, physics, zoology, robotics and machine learning. Research into the subject has only become possible with the advancement of computational capabilities, enabling scientists to explore phenomena exhibited by flocking birds, schooling fish, and swarming bees. The motivation and execution of these remarkable natural occurrences are not yet well understood. Beyond the visual allure, there are various potential applications of Collective Motion, in fields such as CGI graphics, robotics and swarm intelligence. Research has been undertaken on "top-down" models of Collective Motion since the mid-90s. This style of model enforces specific dynamics that broadly mimic observed behaviours, such as alignment, cohesion and collision avoidance. While these models yield some insights into theoretical possibilities, and have close analogies with spin models within physics, their limited ability toreplicate the full complexity of real-world scenarios hampers their practical applicability. More recent work has explored Collective Motion and flocking using "bottom-up" models, using the principals of "Future State Maximization" and "Path-Entropy Maximization" respectfully, motivated by Causal Entropic Forces. In these models, each bird utilizes projected visual states to formulate anydecision to reorientate. Both models can produce highly ordered cohesive flocks that demonstrate marginal opacity. However, both models have only been studied in 2D. This fundamentally limits their applicability to systems involving motion in full 3D (birds, fish etc) and thereby makes comparison with experiment difficult. In this PhD thesis, we are looking to expand previous work to simulate flockingbirds in 3D. Previous 3D models are "top-down", such as the Boids Model which is defined by three simple rules (separation, alignment, and cohesion). We aspire to provide a deeper understanding into flocking behaviour and the validity of the application of "bottom-up" models to 3D Collective Motion. Our core research questions are: How can we translate the 2D projection method to present visualstimulus in 3D? Can we create improved models for visual projection that are computationally efficient, e.g. using "ray tracing" techniques? Do the flocks demonstrate marginal opacity? Does the algorithm produce complex structures reminiscent of the manifolds seen in nature?