We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

翻译：我们研究化学反应网络（CRNs）的动力学，旨在推导其反应速率的上界。由于CRNs固有的非线性和离散结构特性，这一任务充满挑战。为解决此问题，我们采用信息几何方法，利用自然梯度开发出一个非线性系统，该系系统可为CRN动力学提供上界。通过数值模拟验证了该方法，证明其在特定类别的CRNs中能实现更快的收敛速度。该类别的特征由化学物种数、化学反应计量系数的最大值以及反应数量共同决定。我们还将我们的方法与常规方法进行对比，表明后者无法为CRNs的反应速率提供上界。尽管本研究聚焦于CRNs，但从自然科学到工程领域中超图的广泛存在表明，我们的方法可能在包括信息科学在内的更广阔领域得到应用。