  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.
