During reactive transport modeling, the computing cost associated with chemical equilibrium calculations can be 10 to 10,000 times higher than that of fluid flow, heat transfer, and species transport computations. These calculations are performed at least once per mesh cell and once per time step, amounting to billions of them throughout the simulation employing high-resolution meshes. To radically reduce the computing cost of chemical equilibrium calculations (each requiring an iterative solution of a system of nonlinear equations), we consider an on-demand machine learning algorithm that enables quick and accurate prediction of new chemical equilibrium states using the results of previously solved chemical equilibrium problems within the same reactive transport simulation. The training operations occur on-demand, rather than before the start of the simulation when it is not clear how many training points are needed to accurately and reliably predict all possible chemical conditions that may occur during the simulation. Each on-demand training operation consists of fully solving the equilibrium problem and storing some key information about the just computed chemical equilibrium state (which is used subsequently to rapidly predict similar states whenever possible). We study the performance of the on-demand learning algorithm, which is mass conservative by construction, by applying it to a reactive transport modeling example and achieve a speed-up of one or two orders of magnitude (depending on the activity model used). The implementation and numerical tests are carried out in Reaktoro (reaktoro.org), a unified open-source framework for modeling chemically reactive systems.

中文翻译：

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加速反应输运建模：用于化学平衡计算的按需机器学习算法

在反应输运建模期间，与化学平衡计算相关的计算成本可能比流体流动、传热和物种输运计算的计算成本高 10 到 10,000 倍。这些计算在每个网格单元和每个时间步至少执行一次，在使用高分辨率网格的整个模拟过程中总计达数十亿次。为了从根本上降低化学平衡计算的计算成本（每个计算都需要非线性方程组的迭代求解），我们考虑了一种按需机器学习算法，该算法能够使用先前求解的结果快速准确地预测新的化学平衡状态同一反应输运模拟中的化学平衡问题。培训操作按需进行，而不是在模拟开始之前，当不清楚需要多少训练点来准确可靠地预测模拟过程中可能发生的所有可能的化学条件时。每个按需训练操作都包括完全解决平衡问题并存储有关刚刚计算的化学平衡状态的一些关键信息（随后在可能的情况下用于快速预测类似状态）。我们研究了按需学习算法的性能，该算法在构造上是大量保守的，通过将其应用于反应式运输建模示例并实现一到两个数量级的加速（取决于所使用的活动模型）。实施和数值测试在 Reaktoro (reaktoro.org) 中进行，