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Parameter estimation for macroscopic pedestrian dynamics models from microscopic data

Gomes, Susana N. and Stuart, Andrew M. and Wolfram, Marie-Therese (2019) Parameter estimation for macroscopic pedestrian dynamics models from microscopic data. SIAM Journal on Applied Mathematics, 79 (4). pp. 1475-1500. ISSN 0036-1399. https://resolver.caltech.edu/CaltechAUTHORS:20190719-112058516

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Abstract

In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories---microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories, and for differing channel geometries.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/18M1215980DOIArticle
https://arxiv.org/abs/1809.08046arXivDiscussion Paper
Additional Information:© 2019 Society for Industrial and Applied Mathematics. Received by the editors September 21, 2018; accepted for publication (in revised form) May 23, 2019; published electronically August 6, 2019. The work of the first and second authors was supported by the EPSRC Programme grant EQUIP. The work of the first author was also supported by the Leverhulme Trust via the Early Career Fellowship ECF-2018-056. The work of the second and third authors was supported by a Royal Society international collaboration grant. The work of the third author was partially supported by the Austrian Academy of Sciences via the New Frontier's grant NST-001. SG thanks Imperial College London for the use of computer facilities. The authors are grateful to Grigorios Pavliotis for helpful discussions.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Leverhulme TrustECF-2018-056
Royal SocietyUNSPECIFIED
Österreichische Akademie der WissenschaftenNST-001
Subject Keywords:macroscopic pedestrian models, generalized McKean-Vlasov equations, parameter estimation, optimization-based and Bayesian inversion
Issue or Number:4
Classification Code:AMS subject classifications: 35K20, 35R30, 62F15
Record Number:CaltechAUTHORS:20190719-112058516
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190719-112058516
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97297
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Jul 2019 20:04
Last Modified:03 Oct 2019 21:30

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