How many people will travel, during a given week, between two cities such as Dallas and Austin, in Texas? Answering this question is important for many socially relevant contexts. For example, being able to predict how many people travel from one city to another is necessary to design efficient public transportation infrastructures. Or think about the COVID-19 pandemic, and how understanding mobility patterns was key to forecast the spread and progression of the disease. Altering such patterns was one of the tools that policymakers had in their hands to try to contain the pandemic, and deviations from expected mobility informed about how the population was responding to the epidemic scenario and to policies being implemented.

The importance of this problem has been long recognized and, therefore, models for human mobility have existed for decades. In particular, since the mid-20th century, so-called “gravity models” have been used to understand and predict human mobility. Gravity models draw inspiration from Newton's law of gravitation, conceptualizing movement between locations as a function of their population sizes and the distance between them. These models assume that larger populations attract more movement, while greater distances act as a deterrent. Widely used in transportation planning, analysis of trade flows, migration studies, and epidemiology, gravity models provide a simplified framework for understanding and predicting spatial interactions and flow patterns. However, due to their simplicity, they can only predict mobility flows approximately.

With the advent of artificial intelligence in recent years, researchers have started to develop much more accurate machine learning models of mobility. Unlike the original gravity models, which predicted flows based on population and distance alone, new “deep gravity” models use all sorts of information about origin and destination, such as the density of restaurants or schools or road connectivity, besides population and distance. These models are very accurate at predicting human mobility but, unlike the original gravity models, are difficult to interpret and do not  provide real insight into the mechanisms responsible for people’s mobility choices.

So, can we have the cake and eat it too? Can we use machine learning to come up with models that are as predictive as the most sophisticated artificial intelligence models, but interpretable and as simple as the original gravity models? To answer this question, we used a so-called “Bayesian machine scientist,” a computational framework designed to automatically discover mathematical models from data. The Bayesian machine scientist works by exploring the vast space of possible equations, guided by probabilistic inference, to identify the most plausible models that explain the observed data (in our case, mobility flows). The method combines techniques from machine learning, statistical physics, and Bayesian statistics to efficiently balance model complexity and accuracy, making it a powerful tool for scientific discovery and data-driven modeling.

The Bayesian machine scientist identified relatively simple human mobility models that are at least as accurate as deep gravity models and that, in fact, extrapolate even better when interrogated about new geographical regions. Perhaps even more surprisingly, these highly predictive models are very similar to the original gravity models—as it turns out, gravity models, with population and distance alone, needed only a few tweaks to capture very accurately the reality of human mobility between cities.

There is still a long road ahead to fully understand how and why humans move as part of their daily lives. For example, the machine scientist identified other models, not quite as simple as gravity models (but still gravity-like) and using features other than population and distance, such as road connectivity, that predict mobility even better. With the new results, however, we hope that new steps will be made on solid grounds.