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 ...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 andanisotropic 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 andfor long-term temporal predictions. To address this knowledge gap, we will present inthis paper a deep learning (DL) modeling framework applied to predict the progress ofchemical mixing under fast bimolecular reactions. This framework uses convolutionalneural networks (CNN) for capturing spatial patterns and long short-term memory(LSTM) networks for forecasting temporal variations in mixing. By careful design ofthe framework—placement of non-negative constraint on the weights of the CNN andthe 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. The time needed to obtain a forecastusing the model is a fraction (≈ O(10−6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinitynorm) for capturing local-scale mixing features such as interfacial mixing, only 24%to 32% of the sequence data for model training is required. To achieve the same levelof accuracy for capturing global-scale mixing features, the sequence data required formodel training is 64% to 70% of the total spatial-temporal data. Hence, the proposedapproach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modelingreactive-transport in a wide range of applications.展开更多
文摘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 andanisotropic 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 andfor long-term temporal predictions. To address this knowledge gap, we will present inthis paper a deep learning (DL) modeling framework applied to predict the progress ofchemical mixing under fast bimolecular reactions. This framework uses convolutionalneural networks (CNN) for capturing spatial patterns and long short-term memory(LSTM) networks for forecasting temporal variations in mixing. By careful design ofthe framework—placement of non-negative constraint on the weights of the CNN andthe 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. The time needed to obtain a forecastusing the model is a fraction (≈ O(10−6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinitynorm) for capturing local-scale mixing features such as interfacial mixing, only 24%to 32% of the sequence data for model training is required. To achieve the same levelof accuracy for capturing global-scale mixing features, the sequence data required formodel training is 64% to 70% of the total spatial-temporal data. Hence, the proposedapproach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modelingreactive-transport in a wide range of applications.
