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This paper presents a physics-informed machine learning (ML) framework toconstruct reduced-order models (ROMs) for reactive-transport quantities ofinterest (QoIs) based on high-fidelity numerical simulations. QoIs includespecies decay, product yield, and degree of mixing. The ROMs for QoIs areapplied to quantify and understand how the chemical species evolve over time.First, high-resolution datasets for constructing ROMs are generated by solvinganisotropic reaction-diffusion equations using a non-negative finite elementformulation for different input parameters. Non-negative finite elementformulation ensures that the species concentration is non-negative (which isneeded for computing QoIs) on coarse computational grids even under highanisotropy. The reactive-mixing model input parameters are a time-scaleassociated with flipping of velocity, a spatial-scale controlling small/largevortex structures of velocity, a perturbation parameter of the vortex-basedvelocity, anisotropic dispersion strength/contrast, and molecular diffusion.Second, random forests, F-test, and mutual information criterion are used toevaluate the importance of model inputs/features with respect to QoIs. Third,Support Vector Machines (SVM) and Support Vector Regression (SVR) are used toconstruct ROMs based on the model inputs. Then, SVR-ROMs are used to predictscaling of QoIs. Qualitatively, SVR-ROMs are able to describe the trendsobserved in the scaling law associated with QoIs. Fourth, the scaling law'sexponent dependence on model inputs/features are evaluated using $k$-meansclustering. Finally, in terms of the computational cost, the proposed SVM-ROMsand SVR-ROMs are $\mathcal{O}(10^7)$ times faster than running a high-fidelitynumerical simulation for evaluating QoIs.

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing