Abstract

In this talk, I will present a framework for estimating parameters in PDE models for collective dynamics using data from individual trajectories. The method is developed for a model for crowd dynamics, in particular unidirectional flow in a corridor, where we explore the connection between a density-dependent stochastic differential equation and a nonlinear partial differential equation for the density of pedestrians. In this case, I will explore identifiability  of parameters appearing in the model, introduce optimisation and Bayesian methods to perform the identification, and analyse the performance of this methodology in various realistic situations. I will conclude with ongoing work consisting of identifying parameters in PDE models for cell-cell adhesion.