We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not to be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when disproving equivalences between Markov chains.
翻译:我们引入多式组合,将概率组合法普遍化,以发展一种计算等同关系的算法,可以解释为解除多式差异方程式的概率平衡,这是科学和工程间动态系统无处不在的模型。该算法具有多式时间复杂性,并补充了古典分区-精炼方法,因为:(a)它在当地对系统进行了探索,可能产生等值,但不一定涉及对整个差别方程系统的检查;(b)它可以通过技术得到增强;(c)它允许对配对进行规格,而不应将其包括在产出中。使用原型,这些优势体现在从生物学系统到应用模型减少和比较的案例研究中。值得注意的是,当Markov链之间脱钩时,我们报告了比分区-精炼法小四等量的运行时间。