论文标题
开放动态系统作为多项式函子的凝结膜，并应用于预测处理
Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing
论文作者
论文摘要
我们介绍了具有一般时间演化的开放动力系统类别，即由多项式接口的核心类别，并显示这如何扩展煤层框架以捕获常见的科学应用，例如普通的微分方程，开放马尔可夫过程和随机动态系统。然后，我们将Spivak的Operad Org扩展到此设置，并构建相关的单体类别，其形态代表层次结构开放系统；当它们的界面很简单时，这些类别提供了典型的共同体结构。我们使用“拉普拉斯学说”来体现这些结构，该构造提供了用于主动推断的动力学语义，并指示与贝叶斯反转和煤层逻辑的某些连接。
We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such as ordinary differential equations, open Markov processes, and random dynamical systems. We then extend Spivak's operad Org to this setting, and construct associated monoidal categories whose morphisms represent hierarchical open systems; when their interfaces are simple, these categories supply canonical comonoid structures. We exemplify these constructions using the 'Laplace doctrine', which provides dynamical semantics for active inference, and indicate some connections to Bayesian inversion and coalgebraic logic.
