标题： 通过机器学习的下一代无方程多尺度人群动力学建模 显示英文标题

标题： Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning

摘要： 在人群动力学中弥合微观和宏观建模尺度构成了系统数值分析、优化和控制的重要且开放的挑战。我们提出了一种结合流形和机器学习的方法，从高保真基于代理的模拟中学习隐空间中出现的人群动力学的离散演化算子。该框架建立在我们之前关于下一代无方程算法的研究基础上，用于学习高维和多尺度系统的替代模型。我们的方法是一个四阶段的方法，在高维空间中显式地保持重构动力学的质量。在第一步中，我们使用核密度估计（KDE）从离散微观数据（行人位置）推导出连续宏观场（密度）。在第二步中，基于流形学习，我们构建了一个从宏观环境空间到由对应密度分布的POD参数化的潜在空间的映射。第三步涉及在潜在空间中使用机器学习技术（特别是LSTMs网络和MVARs）学习降阶替代模型（ROMs）。最后，我们根据宏观密度轮廓在高维空间中重构人群动力学。我们证明了通过SVD进行的密度分布的POD重构保持了质量。通过这种“嵌入->在潜在空间中学习->重新提升到环境空间”的流程，我们创建了一个不可用宏观PDE的密度演化的有效解算子。在我们的示例中，我们使用社会力模型在带有障碍物的走廊中生成数据，并施加周期性边界条件。数值结果表明了高精度、鲁棒性和泛化能力，从而允许从基于代理的模拟中快速准确地对人群动力学进行建模/仿真。 显示英文摘要

摘要： Bridging the microscopic and the macroscopic modelling scales in crowd dynamics constitutes an important, open challenge for systematic numerical analysis, optimization, and control. We propose a combined manifold and machine learning approach to learn the discrete evolution operator for the emergent crowd dynamics in latent spaces from high-fidelity agent-based simulations. The proposed framework builds upon our previous works on next-generation Equation-free algorithms on learning surrogate models for high-dimensional and multiscale systems. Our approach is a four-stage one, explicitly conserving the mass of the reconstructed dynamics in the high-dimensional space. In the first step, we derive continuous macroscopic fields (densities) from discrete microscopic data (pedestrians' positions) using KDE. In the second step, based on manifold learning, we construct a map from the macroscopic ambient space into the latent space parametrized by a few coordinates based on POD of the corresponding density distribution. The third step involves learning reduced-order surrogate ROMs in the latent space using machine learning techniques, particularly LSTMs networks and MVARs. Finally, we reconstruct the crowd dynamics in the high-dimensional space in terms of macroscopic density profiles. We demonstrate that the POD reconstruction of the density distribution via SVD conserves the mass. With this "embed->learn in latent space->lift back to the ambient space" pipeline, we create an effective solution operator of the unavailable macroscopic PDE for the density evolution. For our illustrations, we use the Social Force Model to generate data in a corridor with an obstacle, imposing periodic boundary conditions. The numerical results demonstrate high accuracy, robustness, and generalizability, thus allowing for fast and accurate modelling/simulation of crowd dynamics from agent-based simulations.