  Prediction and control of chemical mixing are vital for many scientific areas
such as subsurface reactive transport, climate modeling, combustion,
epidemiology, and pharmacology. Due to the complex nature of mixing in
heterogeneous and anisotropic media, the mathematical models related to this
phenomenon are not analytically tractable. Numerical simulations often provide
a viable route to predict chemical mixing accurately. However, contemporary
modeling approaches for mixing cannot utilize available spatial-temporal data
to improve the accuracy of the future prediction and can be compute-intensive,
especially when the spatial domain is large and for long-term temporal
predictions. To address this knowledge gap, we will present in this paper a
deep-learning (DL) modeling framework applied to predict the progress of
chemical mixing under fast bimolecular reactions. This framework uses
convolutional neural networks (CNN) for capturing spatial patterns and long
short-term memory (LSTM) networks for forecasting temporal variations in
mixing. By careful design of the framework -- placement of non-negative
constraint on the weights of the CNN and the selection of activation function,
the framework ensures non-negativity of the chemical species at all spatial
points and for all times. Our DL-based framework is fast, accurate, and
requires minimal data for training.
