开放动力系统作为多项式函子的共代数,在预测处理中的应用

T. S. C. Smithe
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引用次数: 4

摘要

我们提出了具有一般时间演化的开放动力系统的类别作为由多项式接口索引的共代数的类别,并展示了如何扩展共代数框架以捕获常见的科学应用,如常微分方程,开放马尔可夫过程和随机动力系统。然后,我们将Spivak的operad Org扩展到这个设置,并构造了相关的一元范畴,其模态表示分层开放系统;当它们的接口很简单时,这些类别提供典型的共子体结构。我们使用“拉普拉斯学说”举例说明这些结构,它为主动推理提供了动态语义,并指出了与贝叶斯反演和共代数逻辑的一些联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Open dynamical systems as coalgebras for polynomial functors, with application to predictive processing
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.
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