群体动力学中环境力与相互作用力的同时推断

中文摘要 AI 辅助

群体动力学广泛存在于物理、生物及工程应用领域，例如细胞迁移、群体机器人学、社会动力学和动物行为。这类系统的核心特征是智能体间的局部相互作用涌现出大规模协调行为，因此理解产生观测到的涌现动力学的局部相互作用是一个基础问题。我们关注通用的相互作用学习方法，这类方法可描述由相互作用核定义的广泛群体动力学物理系统，且无需对该核的解析形式做先验假设（即采用非参数形式）。这种基于核的方法的优势在于其纳入了模型的底层物理规律（即群体动力学），而更通用的方程学习方法可能会忽略这一点，从而可能限制其模型精度和预测能力。本研究将现有变分学习方法扩展至同时包含相互作用核与环境力/智能体内力的群体系统，所提出的框架可在非参数推断相互作用核的同时，采用半参数或全非参数表示学习环境力。该方法在多个基准模型上得到验证，这些基准模型涉及同步、对齐、吸引-排斥及外部环境力。我们还基于该非参数学习框架引入了模型选择程序，以识别能最优解释给定轨迹观测集的模型。通过利用学习到的模型的特征识别能力，该程序可区分不同的群体动力学框架，并直接从轨迹数据中恢复机械相互作用机制。

英文摘要

Collective dynamics arise in a wide range of physical, biological, and engineering applications. Examples include cell migration, swarm robotics, social dynamics, and animal behavior. A defining characteristic of these systems is the emergence of large-scale coordination from local interactions among agents; a fundamental question is thus to understand the local interactions that give rise to the observed emergent dynamics. We are interested in methods for learning interactions generally, which can describe a wide class of physical systems exhibiting collective dynamics defined by an interaction kernel, without a priori assumptions on the analytical form of this kernel (i.e. it is nonparametric). The advantage of this kernel-based approach is that it incorporates the underlying physics of the model (i.e. collective dynamics), which more general equation-learning approaches may ignore, potentially limiting their effectiveness for model accuracy and predictions. In this work, we extend existing variational learning approaches to collective systems with both interaction kernels and environmental/intra-agent forces. The proposed framework simultaneously infers the interaction kernel non-parametrically while learning the environmental force using either semi-parametric or fully nonparametric representations. The methodology is validated on several benchmark models exhibiting synchronization, alignment, attraction-repulsion, and external environmental forces. We also introduce a model-selection procedure based on our nonparametric learning framework to identify models that optimally explain a given set of trajectory observations. By exploiting the feature-identification capability of the learned models, the proposed procedure can distinguish among different collective dynamics frameworks and recover mechanistic interaction mechanisms directly from trajectory data.

发表机构

• Clarkson University（克拉克森大学）
• University of Houston（休斯顿大学）

机构由 AI 辅助整理，请以论文原文为准。