Optimal transport by a Lagrangian dynamics of population distribution

TL;DR

This paper introduces a Lagrangian dynamical model for human mobility that captures movement patterns using population data, with an efficient algorithm to estimate model parameters, revealing the importance of inertia and dissipation.

Contribution

It develops a novel Lagrangian-based framework and gradient descent method for modeling and understanding human movement dynamics from empirical data.

Findings

Quadratic Lagrangian effectively models movement data.

Inertia and dissipation are equally important in movement dynamics.

Interactions and randomness significantly alter model parameters.

Abstract

Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and (self-)organization in such systems are expected to result in dynamical behaviors that are represented by stationary trajectories of an appropriate effective action. In this study we develop a Lagrangian dynamical model for movement processes, using local population functions as the coordinate variables. An efficient gradient descent algorithm is introduced to estimate the optimal Lagrangian parameters minimizing a local error function of the dynamical process. We show that even a quadratic Lagrangian, incorporating dissipation, effectively captures the dynamics of synthetic and empirical movement data. The inferred models reveal that inertia and dissipation are of comparable importance, while interactions and randomness in the movements induce significant qualitative changes in model parameters. Our results provide an interpretable and generative model for human mobility, with potential applications in movement prediction.