标题： 数据驱动的人类移动模型发现 显示英文标题

标题： Data driven discovery of human mobility models

摘要： 人类移动性是社会行为的基本方面，在交通、城市规划和流行病建模中有广泛的应用。然而，几十年来，用于模拟移动现象的新数学公式很少，通常通过类比物理过程来发现，例如重力模型和辐射模型。这些零星的发现通常被认为依赖于直觉和运气来拟合实证数据。在这里，我们提出了一种系统的方法，利用符号回归从人类移动数据中自动发现可解释的模型。我们的方法找到了一些著名的公式，如距离衰减效应和经典重力模型，以及之前未知的公式，如可以由最大熵原理解释的指数幂律衰减。通过放松对模型表达式复杂性的约束，我们进一步展示了人类移动的关键变量如何逐步被纳入模型中，使这个框架成为一种强大的工具，可以直接从观察数据中揭示复杂社会现象的潜在数学结构。 显示英文摘要

摘要： Human mobility is a fundamental aspect of social behavior, with broad applications in transportation, urban planning, and epidemic modeling. However, for decades new mathematical formulas to model mobility phenomena have been scarce and usually discovered by analogy to physical processes, such as the gravity model and the radiation model. These sporadic discoveries are often thought to rely on intuition and luck in fitting empirical data. Here, we propose a systematic approach that leverages symbolic regression to automatically discover interpretable models from human mobility data. Our approach finds several well-known formulas, such as the distance decay effect and classical gravity models, as well as previously unknown ones, such as an exponential-power-law decay that can be explained by the maximum entropy principle. By relaxing the constraints on the complexity of model expressions, we further show how key variables of human mobility are progressively incorporated into the model, making this framework a powerful tool for revealing the underlying mathematical structures of complex social phenomena directly from observational data.