Distilling human mobility models with symbolic regression

TL;DR

This paper introduces a symbolic regression approach to automatically discover interpretable human mobility models from data, recovering known formulas and uncovering new ones like an exponential-power-law decay.

Contribution

It presents a systematic, data-driven method to derive human mobility models, reducing reliance on intuition and physical analogies, and revealing underlying mathematical structures.

Findings

Recovered classical models such as gravity and radiation models.

Discovered a new exponential-power-law decay model.

Demonstrated progressive incorporation of key mobility variables.

Abstract

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.