Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations (ODEs). Even though it is often crucial for a fluid model under study to satisfy some given properties, a formal verification is usually challenging. This is because parameters are often not known precisely due to finite-precision measurements and stochastic noise. In this paper, we present a novel technique that allows one to efficiently compute formal bounds on the reachable set of time-varying nonlinear ODE systems that are subject to uncertainty. To this end, we, first, relate the reachable set of a nonlinear fluid model to a family of inhomogeneous continuous time Markov decision processes and, second, provide optimal and suboptimal solutions for the family by relying on optimal control theory. The proposed technique is efficient and can be expected to provide tight bounds. We demonstrate its potential by comparing it with a state-of-the-art over-approximation approach.

中文翻译：

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流体模型的过度近似


流体模型是生化系统定量建模和分析性能模型中流行的形式。主要思想是通过一组紧凑的常微分方程 (ODE) 来近似大规模马尔可夫链。尽管对于所研究的流体模型来说满足某些给定属性通常至关重要，但形式验证通常具有挑战性。这是因为由于有限精度的测量和随机噪声，参数通常无法准确得知。在本文中，我们提出了一种新技术，它允许人们有效地计算受不确定性影响的时变非线性 ODE 系统的可达集的形式边界。为此，我们首先将非线性流体模型的可达集与一系列非齐次连续时间马尔可夫决策过程联系起来，其次，依靠最优控制理论为该系列提供最优和次优解。所提出的技术是有效的并且有望提供严格的界限。我们通过将其与最先进的过度近似方法进行比较来展示其潜力。