社会经济和生命科学中动力学模型的不确定性量化
Uncertainty quantification for kinetic models in socio-economic and life sciences
AI总结：
本文探讨了在社会经济和生命科学中应用动力学模型时，由于缺乏基本原理导致的参数不确定性问题，并介绍了非线性Vlasov和福克-计划克方程的数学描述及不确定性量化方法。
摘要：
动力学方程在建模大量相互作用粒子系统中起着关键作用。最近，经典动力学理论的遗产在社会经济和生命科学中找到了新的应用，其中由大量代理体特征的过程自发地产生社会结构。众所周知的例子包括意见动力学中集群的形成、财富分布中的不平等现象、群体模型中的聚集和 milling 行为、生物系统中的同步现象以及行人交通中的车道形成。然而，构建描述上述过程的动力学模型却面临缺乏基本原理的困难，因为物理力被经验性社会力取代。这些经验性力通常旨在再现观察到的系统行为，如社会结构的出现，并且在最佳情况下仅以建模参数的统计信息形式存在。因此，参数不确定性特征中的随机输入应被视为建模过程中的本质特征。在本文的综述中，我们介绍了几种此类动力学模型的例子，它们数学上由非线性Vlasov和福克-计划克方程描述，并展示了不同的不确定性量化数值方法，这些方法保留了动力学解的主要特征。
英文摘要：
Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
