# Modeling cities

## TL;DR

This paper reviews how physics-based models and concepts are used to understand complex urban systems, focusing on city growth, spatial organization, and activity distribution, and discusses future open problems in the science of cities.

## Contribution

It provides a comprehensive overview of physics-inspired modeling approaches for cities and highlights open challenges for developing a scientific framework of urban systems.

## Key findings

- Physics tools bridge theory and empirical data in urban modeling
- State-of-the-art models address city growth and spatial patterns
- Open problems remain in fully understanding urban complexity

## Abstract

Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines such as quantitative geography, spatial economics, geomatics and urbanism, and more recently physics. (Statistical) Physics plays a major role by bringing tools and concepts able to bridge theory and empirical results, and we will illustrate this on some fundamental aspects of cities: the growth of their surface area and their population, their spatial organization, and the spatial distribution of activities. We will present state-of-the-art results and models but also open problems for which we still have a partial understanding and where physics approaches could be particularly helpful. We will end this short review with a discussion about the possibility of constructing a science of cities.