Coupling of Lagrangian Mechanics and Physics-Informed Neural Networks for the Identification of Migration Dynamics

Abstract

Highlights: What are the main findings? We have developed a dynamic migration model based on the physical principles of Lagrangian mechanics, which enables us to address the limitations of conventional migration models that rely on macroeconomic indicators. We investigated the external forces through the physics-informed neural networks in the dynamic equation and explained these forces by using socio-economic indicators. What is the implication of the main finding? Our model can be utilized by administrators in smart cities to evaluate the impact of regional development initiatives or government regulations on the migration patterns of citizens. Analyzing the invariant density of transfer operators can assist in determining primary migration directions. An essential aspect of any government in a smart city is to examine the issues of internal and external migration. Migration is a complex phenomenon. In order to effectively manage it, it is not only necessary to be able to accurately predict migration patterns but also to understand which factors influence these patterns. Current approaches to the development of migration models rely on macroeconomic indicators without considering the specificities of intraregional interactions among individuals. In this paper, we propose a method for determining the dynamics of migration balance based on Lagrangian mechanics. We derive and interpret the potential energy of a migration network by introducing specific functions that determine migration patterns. The solution of the migration equations and selection of parameters, as well as external forces, are achieved through the use of physics-informed neural networks. We also use external factors to explain the non-homogeneity in the dynamic equation through the use of a regression model. We analyze settlement priorities using transfer operator theory and invariant density. The findings obtained enable the assessment of migration flows and analysis of external migration factors.