Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

中文翻译：

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从随机模拟中学习异质反应速率

反应速率方程是常用于描述宏观尺度确定性化学动力学的常微分方程。在微观尺度上，化学动力学是随机的，并且可以通过复制分子的空间运动及其碰撞的复杂动力学系统来捕获。这样的分子动力学系统可以隐式捕获影响反应速率但在宏观模型中未解释的复杂现象。在这项工作中，我们提出了一种数据同化程序，用于从具有多个同时发生反应的物种的分子模拟中学习非均质动力学参数。然后可以将学习到的参数插入确定性反应速率方程中，以预测宏观系统的长时间演化。这样，我们的程序发现了一个有效的反应动力学微分方程。为了演示该程序，我们扩大了形成复杂的共价键网络的分子系统的动力学，该网络严重干扰了反应速率。顺便说一句，我们报告该系统的动力学参数具有特殊的时间和温度依赖性，而网络链闭合循环的概率遵循普遍分布。