This paper deals with the micro–macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in [ N. Bellomo, N. Outada, J. Soler, Y. Tao and M. Winkler, Chemotaxis and cross diffusion models in complex environments: Modeling towards a multiscale vision, Math. Models Methods Appl. Sci. 32 (2022) 713–792]. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. We refer to a selection of case studies, in detail, the transport of virus models, social dynamics, and Keller–Segel in a fluid. The second part shows how a Hilbert-type approach can be developed to derive models at the macroscale from the underlying description provided by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models corresponding to the selected case studies. Finally, a forward look into the future research perspectives is proposed.

本文讨论了根据活性粒子动力学理论方法提供的底层描述来进行模型的微观-宏观推导。我们根据 [N. Bellomo、N. Outada、J. Soler、Y. Tao 和 M. Winkler，复杂环境中的趋化性和交叉扩散模型：面向多尺度视觉的建模》中提出的定义来考虑所谓的奇异模型，数学。模型方法应用。科学。 32（2022）713–792]。演讲的第一部分重点是对文献中已知的一些现象学模型的调查和批判性分析。我们参考了一系列案例研究，详细介绍了病毒模型的传输、社会动力学和流体中的凯勒-西格尔模型。第二部分展示了如何开发希尔伯特型方法，以便根据活性粒子动力学理论提供的底层描述导出宏观尺度的模型。第三部分涉及与所选案例研究相对应的宏观模型的推导。最后对未来的研究前景进行了展望。