当化学反应满足机器学习时的超快速反应传输模拟：化学平衡
Ultra-Fast Reactive Transport Simulations When Chemical Reactions Meet Machine Learning: Chemical Equilibrium
摘要：
在反应输运建模过程中，与化学反应计算相关的计算成本通常比输运计算高10-100倍。这些成本中的大部分来自化学平衡计算，该计算在模拟的每个网格单元和每个时间步骤中至少执行一次。计算化学平衡是一个迭代过程，其中每次迭代通常在计算上是如此昂贵，以至于即使每次计算都收敛在单个迭代中，所产生的加速也不会显着。因此，而不是提出一个快速收敛的数值方法来解决化学平衡方程，我们提出了一种机器学习方法，使新的平衡态，以快速和准确地估计，每当以前的平衡计算具有类似的输入条件已经执行。我们展示了这种智能化学平衡方法在反应性输运建模示例中的使用，并表明即使在早期模拟时间，所有平衡计算的大部分都可以快速预测，并且经过一些时间步骤，机器学习加速的化学求解器已经完全训练，可以快速执行所有后续平衡计算，从而加速近两个数量级。我们注意到，我们的新的按需机器学习方法可以应用于任何情况下，其中大量的顺序/并行评估的计算昂贵的功能$f$需要完成，$y=f(x)$。我们注意到，与传统的机器学习算法相比，我们的按需训练方法在实际模拟开始之前不需要基于学习的训练阶段。然而，所引入的按需训练方案需要一阶导数$\partial f/\partial x$用于稍后的智能预测。
英文摘要：
During reactive transport modeling, the computational cost associated with chemical reaction calculations is often 10-100 times higher than that of transport calculations. Most of these costs results from chemical equilibrium calculations that are performed at least once in every mesh cell and at every time step of the simulation. Calculating chemical equilibrium is an iterative process, where each iteration is in general so computationally expensive that even if every calculation converged in a single iteration, the resulting speedup would not be significant. Thus, rather than proposing a fast-converging numerical method for solving chemical equilibrium equations, we present a machine learning method that enables new equilibrium states to be quickly and accurately estimated, whenever a previous equilibrium calculation with similar input conditions has been performed. We demonstrate the use of this smart chemical equilibrium method in a reactive transport modeling example and show that, even at early simulation times, the majority of all equilibrium calculations are quickly predicted and, after some time steps, the machine-learning-accelerated chemical solver has been fully trained to rapidly perform all subsequent equilibrium calculations, resulting in speedups of almost two orders of magnitude. We remark that our new on-demand machine learning method can be applied to any case in which a massive number of sequential/parallel evaluations of a computationally expensive function $f$ needs to be done, $y=f(x)$. We remark, that, in contrast to traditional machine learning algorithms, our on-demand training approach does not require a statistics-based training phase before the actual simulation of interest commences. The introduced on-demand training scheme requires, however, the first-order derivatives $\partial f/\partial x$ for later smart predictions.
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