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

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

doi:10.1137/19m1248479

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…The main idea of the method is to efficiently compute the regression of linear/nonlinear terms to a least-square linear dynamics approximation from experimental or numerical observable data. Despite its first appearance in the fluid dynamics context [ 55 , 56 ], DMD has been used in many other applications such as epidemiology [ 51 ], biomechanics [ 16 ], urban mobility [ 3 ], climate [ 44 ] and aeroelasticity [ 28 ], especially in structure extraction from data and control-oriented methods.…”

Section: Numerical Methods and Dynamic Mode Decompositionmentioning

confidence: 99%

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Barros

Grave

Viguerie

et al. 2021

Engineering with Computers

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Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion–reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD’s ability to extrapolate in time (short-time future estimates).

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Section: Numerical Methods and Dynamic Mode Decompositionmentioning

confidence: 99%

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Barros

Grave

Viguerie

et al. 2021

Engineering with Computers

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“…Mobility data is collected by Google to reflect the reduction of the population mobility during lockdown for each country, by following the movements of Android phones; anonymised data is publicly available [ 21 ]. Similar datasets can be retrieved directly from other sources, such as mobile phone companies [ 22 ]. This dataset captures mobility towards the following locations: “residential”, “workplaces”, “parks”, “retail and recreations”, “transit stations” and “grocery and pharmacy”, which we denote respectively as m residential , m work , m parks , m retail , m transit , m grocery ; the changes in mobility are reported with respect to the baseline values prior to introduction of lockdown measures.…”

Section: Epidemiological Model Using Google Mobilitymentioning

confidence: 99%

Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

et al. 2021

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A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

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“…The method is completely equation-free and data-driven, meaning that little to no assumptions on data must be considered for its applications. DMD was first applied in fluid dynamics applications [47,49], being expanded to many other applications such as epidemiology [44,4], urban mobility [2], biomechanics [15], climate [37] and aeroelasticity [20], especially in structure extraction from data and control-oriented methods. The method consists of creating a linear map of the dynamics of a given spatio-temporal dataset, even if the dynamics is nonlinear, by projecting the finite-dimensional nonlinear data using an infinite dimension operator able to linearly represent the flow map present on (6) for all time steps.…”

Section: Partial Differential Equations and Dynamic Mode Decompositionmentioning

confidence: 99%

Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

Viguerie,

Barros,

Grave

et al. 2021

Preprint

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Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in data, and effectiveness in providing reasonably accurate predictions for certain problems, particularly over short-to-medium time frames. Despite these successes, the application of DMD to certain problems featuring highly nonlinear transient dynamics remains challenging. In such cases, DMD may not only fail to provide acceptable predictions but may indeed fail to recreate the data in which it was trained, restricting its application to diagnostic purposes (i.e., feature identification and extraction). For many such problems in the biological and physical sciences, the structure of the system obeys a compartmental framework, in which the transfer of mass within the system moves within states. In these cases, the behavior of the system may not be accurately recreated by applying DMD to a single quantity within the system, as proper knowledge of the system dynamics, even for a single compartment, requires that the behavior of other compartments is taken into account in the DMD process. In the present work, we demonstrate, theoretically and numerically, that, when performing DMD on a fully coupled PDE system with compartmental structure, one may recover useful predictive behavior, even when DMD performs poorly when acting compartment-wise. We also establish that important physical quantities, such as mass conservation, are maintained in the coupled-DMD extrapolation. The mathematical and numerical analysis suggests that DMD, properly applied, may be a powerful tool when applied to this common class of problems. In particular, we show interesting numerical applications to a continuous delayed-SIRD model for Covid-19, and to a problem from additive manufacturing considering a

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

Cited by 8 publications

References 16 publications

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

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