基于物理信息的机器学习反应混合过程预测模型
Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing
摘要：
本文提出了一个物理信息的机器学习（ML）框架，构建降阶模型（ROM）的反应性传输感兴趣的量（QoI）的高保真数值模拟的基础上。QoI包括物种衰变、产物产率和混合程度。QOI的ROM用于量化和了解化学物质如何随时间演变。首先，高分辨率的数据集，用于构建ROM通过求解各向异性反应扩散方程，使用非负有限元公式为不同的输入参数。非负有限元公式确保了即使在高各向异性下，在粗计算网格上的物质浓度也是非负的（这是计算QoS所需的）。反应混合模型输入参数是与速度翻转相关的时间尺度、控制速度的小/大涡旋结构的空间尺度、基于涡旋的速度的扰动参数、各向异性分散强度/对比度和分子扩散。其次，随机森林，F-检验，和互信息标准被用来评估模型输入/功能的重要性相对于生活质量。第三，支持向量机（SVM）和支持向量回归（SVR）被用来构建ROM的基础上的模型输入。然后，SVR-ROM用于预测QoI的缩放。定性地，SVR-ROM能够描述在与QoI相关的缩放定律中观察到的趋势。第四，使用$k$ -均值聚类评估缩放定律对模型输入/特征的指数依赖性。最后，在计算成本方面，所提出的SVM-ROM和SVR-ROM比运行用于评估QoS的高保真数值模拟快$\mathcal{O}(10^7)$倍。
英文摘要：
This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simulations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction-diffusion equations using a non-negative finite element formulation for different input parameters. Non-negative finite element formulation ensures that the species concentration is non-negative (which is needed for computing QoIs) on coarse computational grids even under high anisotropy. The reactive-mixing model input parameters are a time-scale associated with flipping of velocity, a spatial-scale controlling small/large vortex structures of velocity, a perturbation parameter of the vortex-based velocity, anisotropic dispersion strength/contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. Then, SVR-ROMs are used to predict scaling of QoIs. Qualitatively, SVR-ROMs are able to describe the trends observed in the scaling law associated with QoIs. Fourth, the scaling law's exponent dependence on model inputs/features are evaluated using $k$-means clustering. Finally, in terms of the computational cost, the proposed SVM-ROMs and SVR-ROMs are $\mathcal{O}(10^7)$ times faster than running a high-fidelity numerical simulation for evaluating QoIs.
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