In this paper, we propose a data-driven method to discover multiscale chemical reactions governed by the law of mass action. First, we use a single matrix to represent the stoichiometric coefficients for both the reactants and products in a system without catalysis reactions. The negative entries in the matrix denote the stoichiometric coefficients for the reactants and the positive ones for the products. Second, we find that the conventional optimization methods usually get stuck in the local minima and could not find the true solution in learning the multiscale chemical reactions. To overcome this difficulty, we propose a partial-parameters-freezing (PPF) technique to progressively determine the network parameters by using the fact that the stoichiometric coefficients are integers. With such a technique, the dimension of the searching space is gradually reduced in the training process and the global mimina can be eventually obtained. Several numerical experiments including the classical Michaelis-Menten kinetics and the hydrogen oxidation reactions verify the good performance of our algorithm in learning the multiscale chemical reactions. The code is available at \url{https://github.com/JuntaoHuang/multiscale-chemical-reaction}.
翻译:在本文中,我们提出一种数据驱动方法,以发现由大规模行动法规范的多尺度化学反应。首先,我们使用一个单一矩阵,以代表反应器和产品在系统中的静态系数,而没有催化反应。矩阵中的负条目表示反应器的静态系数和产品的积极系数。第二,我们发现常规优化方法通常被困在当地微型中,在学习多尺度化学反应时无法找到真正的解决办法。为了克服这一困难,我们建议采用一个部分参数解冻(PPPFF)技术,以逐步确定网络参数,方法是使用静态系数是整数这一事实。有了这样一种技术,搜索空间的尺寸在培训过程中逐渐缩小,最终可以取得全球米微值。包括古典的Michaelis-Menten动能学和氢氧化反应在内的一些数字实验可以验证我们在学习多尺度化学反应时的算法的良好性表现。代码可以在url{https://githubub.com/JunHOOstary-stalction.