Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

TL;DR

This paper extends an anisotropic pedestrian interaction model to include collision avoidance via force rotation and body size, providing a rigorous calibration method using gradient descent with real experimental data.

Contribution

It introduces a novel extension of the interaction model with collision avoidance, and develops a gradient-based calibration method with proven existence of solutions.

Findings

Model successfully incorporates collision avoidance and body size effects.

Calibration algorithm effectively fits parameters to real experimental data.

Rigorous analysis ensures well-posedness and optimality conditions are satisfied.

Abstract

We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces \cite{arXiv:1912.04234} by including the agents' body size. The influence of the body size on the self-organization of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimizer and derive the corresponding first-order optimality conditions. With the help of these conditions we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.