The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement. To this aim, we put in place an algorithm based on the combination of two methods: first, we use the dynamic mode decomposition to create a mathematical model describing the mass transfer; second, we use the notion of Wasserstein distance (also known as earth mover's distance) to reconstruct the underlying velocity field that is responsible for the displacement. Finally, we consider a real-life application: the algorithm is employed to study the travel flows of people in large populated areas using, as input data, density profiles (i.e., the spatial distribution) of people in given areas at different time instants. These kinds of data are provided by the Italian telecommunication company TIM and are derived by mobile phone usage.

Understanding Mass Transfer Directions via Data-Driven Models with Application to Mobile Phone Data / Alla, Alessandro; Balzotti, Caterina; Briani, Maya; Cristiani, Emiliano. - In: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. - ISSN 1536-0040. - 19:2(2020), pp. 1372-1391. [10.1137/19M1248479]

Understanding Mass Transfer Directions via Data-Driven Models with Application to Mobile Phone Data

Alla, Alessandro;Balzotti, Caterina
;
Briani, Maya;Cristiani, Emiliano
2020

Abstract

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement. To this aim, we put in place an algorithm based on the combination of two methods: first, we use the dynamic mode decomposition to create a mathematical model describing the mass transfer; second, we use the notion of Wasserstein distance (also known as earth mover's distance) to reconstruct the underlying velocity field that is responsible for the displacement. Finally, we consider a real-life application: the algorithm is employed to study the travel flows of people in large populated areas using, as input data, density profiles (i.e., the spatial distribution) of people in given areas at different time instants. These kinds of data are provided by the Italian telecommunication company TIM and are derived by mobile phone usage.
Data-driven methods, dynamic mode decomposition, Wasserstein distance, earth mover's distance, cellular data, presence data
01 Pubblicazione su rivista::01a Articolo in rivista
Understanding Mass Transfer Directions via Data-Driven Models with Application to Mobile Phone Data / Alla, Alessandro; Balzotti, Caterina; Briani, Maya; Cristiani, Emiliano. - In: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. - ISSN 1536-0040. - 19:2(2020), pp. 1372-1391. [10.1137/19M1248479]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1408570
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