Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data

Gomes, Susana N.; Stuart, Andrew M.; Wolfram, Marie-Thérèse

doi:10.1137/18m1215980

Cited by 45 publications

(34 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These methods have been proven to be useful also in the case of nonlinear boundary conditions and were also used by Burger and Pietschmann [7] to show existence of stationary solutions to a nonlinear PDE for unidirectional pedestrian flows with nonlinear inflow and outflow conditions. The respective time dependent result was subsequentially presented in [14].…”

Section: Michael Fischer Gaspard Jankowiak and Marie-therese Wolframmentioning

confidence: 99%

“…Stationary solutions of a similar model were recently investigated by Burger and Pietschmann, see [7]. The existence of the respective transient solutions was then shown in [14]. It is guaranteed under the following assumptions: (A1) Let Ω ⊂ R 2 with boundary ∂Ω in C 2 .…”

mentioning

confidence: 99%

“…where m(ρ) = ρ(1−ρ) is the mobility function and u = δE δρ = (log ρ−log(1−ρ)+2βφ) the so-called entropy variable. Note that the proof is a straightforward adaptation of the one presented in [14], hence we omit its details in the following.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Micro- and macroscopic modeling of crowding and pushing in corridors

Fischer¹,

Jankowiak²,

Wolfram³

2020

Networks &Amp; Heterogeneous Media

Self Cite

View full text Add to dashboard Cite

Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper, we propose and validate different mathematical models at the micro-and macroscopic levels to study the influence of both effects. We calibrate the models with experimental data and compare the results at the micro-as well as macroscopic levels. Our numerical simulations reproduce qualitative experimental features on both levels, and indicate how geometry and motivation level influence the observed pedestrian density. Furthermore, we discuss the dynamics of solutions for different modeling approaches and comment on the analysis of the respective equations.

show abstract

Section: Michael Fischer Gaspard Jankowiak and Marie-therese Wolframmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Micro- and macroscopic modeling of crowding and pushing in corridors

Fischer¹,

Jankowiak²,

Wolfram³

2020

Networks &Amp; Heterogeneous Media

Self Cite

View full text Add to dashboard Cite

show abstract

“…This proof is based one implicit Euler discretization, following e.g. [BP16,GSW18], to which we refer for more details. We start by rewriting (40), using the entropy variable u and exploiting its formal gradient flow structure, as…”

Section: Existence Of the Time Dependent Problemmentioning

confidence: 99%

On Fokker-Planck equations with In- and Outflow of Mass

Burger¹,

Humpert²,

Pietschmann³

2020

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

Motivated by modeling transport processes in the growth of neurons, we present results on (nonlinear) Fokker-Planck equations where the total mass is not conserved. This is either due to in-and outflow boundary conditions or to spatially distributed reaction terms. We are able to prove exponential decay towards equilibrium using entropy methods in several situations. As there is no conservation of mass it is difficult to exploit the gradient flow structure of the differential operator which renders the analysis more challenging. In particular, classical logarithmic Sobolev inequalities are not applicable any more. Our analytic results are illustrated by extensive numerical studies.

show abstract

“…Moreover, comparisons to real data and statistical model fitting, e.g. in evacuation dynamics, helped in the optimization of sites and obstacles [6,7,21,36,38,39,40,49,53]. Especially, in evacuation dynamics it is important to include the structure of the surrounding into the model.…”

mentioning

confidence: 99%

An anisotropic interaction model with collision avoidance

Totzeck¹

2020

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of the force vector resulting from the interaction of two agents. In this way the anisotropy is leading to a smooth evasion behaviour. In fact, the proposed model generalizes the standard models, and compensates their drawback of not being able to avoid collisions. Moreover, the model allows for formal passage to the limit 'number of particles to infinity', leading to a mesoscopic description in the mean-field sense. Possible applications are autonomous traffic, swarming or pedestrian motion. Here, we focus on the latter, as the model is validated numerically using two scenarios in pedestrian dynamics. The first one investigates the pattern formation in a channel, where two groups of pedestrians are walking in opposite directions. The second experiment considers a crossing with one group walking from left to right and the other one from bottom to top. The well-known pattern of lanes in the channel and travelling waves at the crossing can be reproduced with the help of this anisotropic model at both, the microscopic and the mesoscopic level. In addition, the 'right-before-left' and 'left-before-right' rule appear intrinsically for different anisotropy parameters.

show abstract

Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data

Cited by 45 publications

References 40 publications

Micro- and macroscopic modeling of crowding and pushing in corridors

Micro- and macroscopic modeling of crowding and pushing in corridors

On Fokker-Planck equations with In- and Outflow of Mass

An anisotropic interaction model with collision avoidance

Contact Info

Product

Resources

About