Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology, CRN parameters such as the kinetic reaction rates can be used as control inputs to steer the system toward a given target. Unfortunately, the resulting optimal control problem is nonlinear, therefore, computationally very challenging. We address this issue by introducing an optimality-preserving reduction algorithm for CRNs. The algorithm partitions the original state variables into a reduced set of macro-variables for which one can define a reduced optimal control problem from which one can exactly recover the solution of the original control problem. Notably, the reduction algorithm runs with polynomial time complexity in the size of the CRN. We use this result to reduce reachability and control problems of large-scale protein-interaction networks and vaccination models with hundreds of thousands of state variables.

中文翻译：

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化学反应网络的保优约简

在许多学科中，化学反应网络 (CRN) 是一个已建立的总体模型，定义为耦合非线性常微分方程组。在许多应用中，例如，在系统生物学和流行病学中，CRN 参数（例如动力学反应速率）可用作控制输入，以引导系统朝着给定目标前进。不幸的是，由此产生的最优控制问题是非线性的，因此在计算上非常具有挑战性。我们通过为 CRN 引入一种保持最优性的缩减算法来解决这个问题。该算法将原始状态变量划分为一组简化的宏变量，可以为这些宏变量定义一个简化的最优控制问题，从中可以准确地恢复原始控制问题的解。尤其，缩减算法在 CRN 的大小上以多项式时间复杂度运行。我们使用此结果来减少具有数十万个状态变量的大规模蛋白质相互作用网络和疫苗接种模型的可达性和控制问题。