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We study a new variant of mathematical prediction-correction model for crowdmotion. The prediction phase is handled by a transport equation where thevector field is computed via an eikonal equation $\Vert \nabla\varphi\Vert=f$,with a positive continuous function $f$ connected to the speed of thespontaneous travel. The correction phase is handled by a new version of theminimum flow problem. This model is flexible and can take into accountdifferent types of interactions between the agents, from gradient flow inWassersetin space to granular type dynamics like in sandpile. Furthermore,different boundary conditions can be used, such as non-homogeneous Dirichlet(e.g., outings with different exit-cost penalty) and Neumann boundaryconditions (e.g., entrances with different rates). Combining finite volumemethod for the transport equation and Chambolle-Pock's primal dual algorithmfor the eikonal equation and minimum flow problem, we present numericalsimulations to demonstrate the behavior in different scenarios.

Prediction-Correction Pedestrian Flow by Means of Minimum Flow Problem