Human mobility is a fundamental aspect of social behavior, with broad applications in transportation, urban planning, and epidemic modeling. Represented by the gravity model and the radiation model, established analytical models for mobility phenomena are often discovered by analogy to physical processes. Such discoveries can be challenging and rely on intuition, while the potential of emerging social observation data in model discovery is largely unexploited. 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.

翻译：人类移动是社会行为的基本方面，在交通规划、城市设计和传染病建模等领域具有广泛应用。以引力模型和辐射模型为代表的现有移动现象分析模型，通常是通过类比物理过程而发现的。这类发现往往具有挑战性且依赖于直觉，而新兴社会观测数据在模型发现中的潜力尚未得到充分开发。本文提出一种系统化方法，利用符号回归从人类移动数据中自动发现可解释模型。我们的方法不仅发现了距离衰减效应和经典引力模型等已知公式，还发现了如指数-幂律衰减等先前未知的模型——该模型可通过最大熵原理解释。通过放宽对模型表达式复杂度的约束，我们进一步展示了人类移动的关键变量如何逐步融入模型，使得该框架成为直接从观测数据揭示复杂社会现象潜在数学结构的强大工具。