论文标题
使用库存和流程图建模的分类框架
A Categorical Framework for Modeling with Stock and Flow Diagrams
论文作者
论文摘要
库存和流程图已经是流行病学的重要工具，但是类别理论使我们可以进一步将这些图作为数学实体本身。在本章中，我们使用使用软件stockflow.jl创建的传染病模型来解释分类方法的好处。我们首先解释了库存流图的类别，并注意这些图的语法及其语义之间的明确分离，展示了软件中已经实现的三个示例：ODES，因果环图图和系统结构图。然后，我们求助于以模块化方式从较小的方法中构建大型库存流图的两种方法：组成和分层。最后，我们介绍了用于基于图的协作建模的开源ModelCollab软件。此基于Web的软件的图形用户界面使建模者可以利用此处讨论的想法，而无需了解其分类基础。
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created with our software, StockFlow.jl, to explain the benefits of the categorical approach. We first explain the category of stock-flow diagrams and note the clear separation between the syntax of these diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then turn to two methods for building large stock-flow diagrams from smaller ones in a modular fashion: composition and stratification. Finally, we introduce the open-source ModelCollab software for diagram-based collaborative modeling. The graphical user interface of this web-based software lets modelers take advantage of the ideas discussed here without any knowledge of their categorical foundations.
