Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass growth. To investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results $\approx {10}^5$ times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

混合现象是控制流体和多孔介质中的流量，物质传输和反应过程的重要机制。反应混合的准确预测对于许多地球和环境科学问题至关重要，例如污染物的归宿和修复，大型藻类的生长以及浮游生物的生长。为了研究在不同情况下（例如各向异性，速度场波动）下混合动力学的演变，建立了基于有限元的数值模型来求解快速，不可逆的双分子反应扩散方程，以模拟一系列反应混合情况。使用不同的模型输入参数集（包括速度场中涡旋结构的各种空间尺度，与速度振荡相关的时间尺度，基于涡旋的速度，各向异性弥散对比度（即纵向弥散与横向弥散之比）和分子扩散的摄动参数。输出包括反应物和产物的浓度曲线。这些模拟的输入和输出分别连接到特征矩阵和标签矩阵，以训练20种旨在模拟系统行为的不同机器学习（ML）模型。基于线性方法，贝叶斯方法，集成学习方法和多层感知器（MLP），对这20种ML仿真器进行了训练，以对混合状态进行分类，并预测表征物种产生，衰变（即平均值）的三个感兴趣量（QoI）。浓度，平均浓度的平方）和混合程度（即物种浓度的方差）。毫不奇怪，线性分类器和回归器无法重现QoI；但是，集成方法（分类器和回归器）和MLP模型可以对反应混合状态和QoI进行准确分类。在集成方法中，随机森林和基于决策树的AdaBoost可以忠实地预测QoI。在运行时，训练有素的ML仿真器产生了结果$\approx {10}^5$比有限元仿真快两倍。由于集成和MLP模型的计算成本低，准确性高，因此它们是用于这些数值模拟的出色仿真器，并且在不确定性量化练习中具有很大的实用性，可能需要进行数千次正向模型运行。