# Predicting Effective Diffusivity of Porous Media from Images by Deep Learning

arXiv: https://arxiv.org/abs/1912.05532 · HTML: https://mlsanity.com/paper/1912.05532/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2019.

## Built on by (most cited first, 11 of 11)

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- [Point-Cloud Deep Learning of Porous Media for Permeability Prediction](https://mlsanity.com/paper/2107.14038/) (2021)
- [Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks](https://mlsanity.com/paper/2310.19274/) (2023)
- [Estimating relative diffusion from 3D micro-CT images using CNNs](https://mlsanity.com/paper/2208.03337/) (2022)
- [Deep learning for diffusion in porous media](https://mlsanity.com/paper/2304.02104/) (2023)
- [Vision Mamba for Permeability Prediction of Porous Media](https://mlsanity.com/paper/2510.14516/) (2025)
- [Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations](https://mlsanity.com/paper/2511.21369/) (2025)
- [Deep Convolutional Neural Networks Predict Elasticity Tensors and their Bounds in Homogenization](https://mlsanity.com/paper/2109.03020/) (2021)
- [Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net](https://mlsanity.com/paper/2205.00134/) (2022)
- [Statistical learning of structure-property relationships for transport in porous media, using hybrid AI modeling](https://mlsanity.com/paper/2503.21560/) (2025)
- [Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inference](https://mlsanity.com/paper/2603.14907/) (2026)

## Abstract (arXiv)

We report the application of machine learning methods for predicting the effective diffusivity (De) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28-0.98), and effective diffusivity spanning more than one order of magnitude (), e.g., >95% of predicted De have truncated relative error of <10% when the true De is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with De < 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true De < 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.