标题： 目标驱动的动态随机场框架 显示英文标题

标题： A Framework for Objective-Driven Dynamical Stochastic Fields

摘要： 场提供了一种描述由相互作用和动态组件组成的复杂系统的通用方法。 特别是，这些动力学和随机系统中的某些系统可能会表现出旨在实现特定目标的目标导向行为，我们将其称为$\textit{intelligent fields}$。 然而，由于其固有的复杂性，开发此类系统的正式理论描述并有效将其描述转化为实际应用仍然具有挑战性。 本文提出了三个基本原理——完整配置、局部性和目的性——以建立理解智能场的理论框架。 此外，我们从人工智能应用的角度探讨了设计此类场的方法。 这项初步研究旨在为未来在理解和利用此类目标驱动的动力随机场的潜力方面的理论发展和实际进步奠定基础。 显示英文摘要

摘要： Fields offer a versatile approach for describing complex systems composed of interacting and dynamic components. In particular, some of these dynamical and stochastic systems may exhibit goal-directed behaviors aimed at achieving specific objectives, which we refer to as $\textit{intelligent fields}$. However, due to their inherent complexity, it remains challenging to develop a formal theoretical description of such systems and to effectively translate these descriptions into practical applications. In this paper, we propose three fundamental principles -- complete configuration, locality, and purposefulness -- to establish a theoretical framework for understanding intelligent fields. Moreover, we explore methodologies for designing such fields from the perspective of artificial intelligence applications. This initial investigation aims to lay the groundwork for future theoretical developments and practical advances in understanding and harnessing the potential of such objective-driven dynamical stochastic fields.