论文标题
基于梯度的参数校准，用于行人动力学的各向异性相互作用模型
Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics
论文作者
论文摘要
我们提出了各向异性相互作用模型的扩展，该模型可以通过包括特工的身体大小来通过力\ cite {arxiv：1912.04234}进行成对相互作用的碰撞。研究了身体大小对渠道和跨越场景中代理自组织的影响以及基本图。由于该模型被称为普通微分方程的耦合系统，因此我们能够进行严格的适应性分析。然后，我们陈述一个参数校准问题，涉及来自实际实验的数据。我们证明了最小化器的存在并得出相应的一阶最佳条件。在这些条件的帮助下，我们根据数据集的小批量提出了梯度下降算法。我们采用提出的算法来符合避免碰撞的参数和相互作用力的强度参数，从而从实验中给出了实际数据。结果是该方法的可行性。
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.
