# A deep learning modeling framework to capture mixing patterns in reactive-transport systems

arXiv: https://arxiv.org/abs/2101.04227 · HTML: https://mlsanity.com/paper/2101.04227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 68 references that are in the map.
- First posted on arXiv 11 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Horovod: fast and easy distributed deep learning in TensorFlow](https://mlsanity.com/paper/1802.05799/) (2018)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Unsupervised Machine Learning Based on Non-Negative Tensor Factorization for Analyzing Reactive-Mixing](https://mlsanity.com/paper/1805.06454/) (2018)
- [Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing](https://mlsanity.com/paper/1908.10929/) (2019)
- [A Comparative Study of Machine Learning Models for Predicting the State of Reactive Mixing](https://mlsanity.com/paper/2002.11511/) (2020)
- [Large-scale Optimization-based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies](https://mlsanity.com/paper/1506.08435/) (2015)

## Built on by (most cited first, 3 of 3)

- [CoolPINNs: A Physics-informed Neural Network Modeling of Active Cooling in Vascular Systems](https://mlsanity.com/paper/2303.05300/) (2023)
- [SWAT Watershed Model Calibration using Deep Learning](https://mlsanity.com/paper/2110.03097/) (2021)
- [Deep Learning to Estimate Permeability using Geophysical Data](https://mlsanity.com/paper/2110.10077/) (2021)

## Abstract (arXiv)

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.