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Human mobility is well described by closed-form gravity-like models learned automatically from data

Author

Listed:
  • Oriol Cabanas-Tirapu

    (Universitat Rovira i Virgili)

  • Lluís Danús

    (Universitat Rovira i Virgili
    University of Pennsylvania)

  • Esteban Moro

    (Massachusetts Institute of Technology
    Northeastern University)

  • Marta Sales-Pardo

    (Universitat Rovira i Virgili)

  • Roger Guimerà

    (Universitat Rovira i Virgili
    ICREA)

Abstract

Modeling human mobility is critical to address questions in urban planning, sustainability, public health, and economic development. However, our understanding and ability to model flows between urban areas are still incomplete. At one end of the modeling spectrum we have gravity models, which are easy to interpret but provide modestly accurate predictions of flows. At the other end, we have machine learning models, with tens of features and thousands of parameters, which predict mobility more accurately than gravity models but do not provide clear insights on human behavior. Here, we show that simple machine-learned, closed-form models of mobility can predict mobility flows as accurately as complex machine learning models, and extrapolate better. Moreover, these models are simple and gravity-like, and can be interpreted similarly to standard gravity models. These models work for different datasets and at different scales, suggesting that they may capture the fundamental universal features of human mobility.

Suggested Citation

  • Oriol Cabanas-Tirapu & Lluís Danús & Esteban Moro & Marta Sales-Pardo & Roger Guimerà, 2025. "Human mobility is well described by closed-form gravity-like models learned automatically from data," Nature Communications, Nature, vol. 16(1), pages 1-13, December.
  • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-56495-5
    DOI: 10.1038/s41467-025-56495-5
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    References listed on IDEAS

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    1. Oscar Fajardo-Fontiveros & Ignasi Reichardt & Harry R. De Los Ríos & Jordi Duch & Marta Sales-Pardo & Roger Guimerà, 2023. "Fundamental limits to learning closed-form mathematical models from data," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    2. Filippo Simini & Gianni Barlacchi & Massimilano Luca & Luca Pappalardo, 2021. "A Deep Gravity model for mobility flows generation," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    3. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    4. Esteban Moro & Dan Calacci & Xiaowen Dong & Alex Pentland, 2021. "Mobility patterns are associated with experienced income segregation in large US cities," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    5. Lenormand, Maxime & Bassolas, Aleix & Ramasco, José J., 2016. "Systematic comparison of trip distribution laws and models," Journal of Transport Geography, Elsevier, vol. 51(C), pages 158-169.
    6. Filippo Simini & Marta C. González & Amos Maritan & Albert-László Barabási, 2012. "A universal model for mobility and migration patterns," Nature, Nature, vol. 484(7392), pages 96-100, April.
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