Data driven discovery of human mobility models (2501.05684v1)

Abstract: 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.

• The paper introduces a novel data-driven approach using symbolic regression to automatically discover interpretable mathematical models for human mobility.
• Applying symbolic regression to data from multiple countries successfully recovered established models like the gravity model and identified new formulations like an exponential-power-law distance decay, linking findings to the maximum entropy principle.
• The symbolic approach offers advantages over neural networks in discovering simpler, generalizable models with practical implications for urban planning, epidemic modeling, and advancing theoretical understanding of spatial interactions.

Data Driven Discovery of Human Mobility Models

The paper titled "Data driven discovery of human mobility models" introduces a novel approach to understanding human mobility patterns through a machine learning-based symbolic regression framework. The authors challenge decades of intuition-based mobility modeling, dominated by analogies to physical processes such as gravity and radiation, by leveraging a data-driven methodology that uncovers interpretable models directly from human mobility data.

Summary of Methods and Findings

The paper utilizes symbolic regression, a technique capable of deducing function structures and parameters from data without assuming predefined forms, to distill mathematical models describing human mobility. By applying this approach to data from China, the UK, and the US, the authors successfully recovered well-established models, including the exponential decay gravity model, while also identifying new formulations, such as an exponential-power-law distance decay. These findings are linked to the maximum entropy principle, which affords a theoretical foundation to the models discovered.

Symbolic regression not only rediscovered these traditional models but also revealed nuances in geographic distributions of human mobility that are often overlooked, such as heterogeneity between intra- and inter-region flows. The framework systematically integrated key variables like destination attractiveness and distance decay into progressively complex models, demonstrating its utility in capturing the intricate dynamics of human mobility across different scales.

The paper also evaluates the robustness of symbolic regression against traditional neural network-based methods, finding that symbolic models often lead to simpler, more generalizable representations. This highlights the efficiency of symbolic regression in model discovery and its preference for parsimonious solutions—a notable advantage for theoretical interpretation and application in diverse contexts such as urban planning and epidemic modeling.

Implications and Future Directions

The symbolic approach presented in the paper holds significant implications for the field of computational social science. By automating the discovery of mathematically succinct models, this methodology mitigates some of the principal challenges posed by the complexity and high dimensionality of human mobility data.

Practically, this can enhance the accuracy of predictions in urban transport planning and epidemiological modeling, where mobility patterns are critical inputs. Theoretically, it provides a framework for reconciling empirical observations with fundamental principles, advancing the scientific understanding of spatial interaction models.

Moving forward, the integration of symbolic regression with neural network architectures could represent a promising avenue for further refinement. This hybrid approach would potentially extend the scope of symbolic model discovery to incorporate additional complex social phenomena. Researchers could also explore the application of this framework to other domains with intricate data structures, such as environmental system modeling or economic dynamics, to validate its versatility and efficacy.

In conclusion, "Data driven discovery of human mobility models" illustrates the potential of symbolic regression in the automatic formulation of human mobility models, offering both practical tools and theoretical insights. This paper substantially contributes to data-driven science, promising a new paradigm for systematically unearthing laws in social behavior through observational datasets.