The mathematical modeling of crowds is complicated by the fact that crowds possess the behavioral ability to develop and adapt moving strategies in response to the context. For example, in emergency situations, people tend to alter their walking strategy in response to fear. To be able to simulate these situations, we consider a kinetic model of crowd dynamics that features the level of stress as a parameter and propose to estimate this key parameter by solving an inverse crowd dynamics problem. This paper states the mathematical problem and presents a method for its numerical solution. We show some preliminary results based on a synthetic data set, i.e., test cases where the exact stress level is known and the crowd density data are generated numerically by solving a forward crowd dynamics problem.

翻译：人群的数学建模因人群具备根据情境发展和适应移动策略的行为能力而变得复杂。例如，在紧急情况下，人们倾向于因恐惧而改变其行走策略。为了能够模拟这些情况，我们考虑一个以压力水平为参数的人群动力学动力学模型，并建议通过求解逆人群动力学问题来估计这一关键参数。本文阐述了该数学问题，并提出了一种数值求解方法。我们展示了一些基于合成数据集的初步结果，即已知精确压力水平、且人群密度数据通过求解正向人群动力学问题数值生成的测试案例。