# CNN-powered micro- to macro-scale flow modeling in deformable porous media

arXiv: https://arxiv.org/abs/2501.06466 · HTML: https://mlsanity.com/paper/2501.06466/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 69 references that are in the map.
- First posted on arXiv 11 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph](https://mlsanity.com/paper/2104.05608/) (2021)

## Abstract (arXiv)

This work introduces a novel application for predicting the macroscopic intrinsic permeability tensor in deformable porous media, using a limited set of micro-CT images of real microgeometries. The primary goal is to develop an efficient, machine-learning (ML)-based method that overcomes the limitations of traditional permeability estimation techniques, which often rely on time-consuming experiments or computationally expensive fluid dynamics simulations. The novelty of this work lies in leveraging Convolutional Neural Networks (CNN) to predict pore-fluid flow behavior under deformation and anisotropic flow conditions. Particularly, the described approach employs binarized CT images of porous micro-structure as inputs to predict the symmetric second-order permeability tensor, a critical parameter in continuum porous media flow modeling. The methodology comprises four key steps: (1) constructing a dataset of CT images from Bentheim sandstone at different volumetric strain levels; (2) performing pore-scale simulations of single-phase flow using the lattice Boltzmann method (LBM) to generate permeability data; (3) training the CNN model with the processed CT images as inputs and permeability tensors as outputs; and (4) exploring techniques to improve model generalization, including data augmentation and alternative CNN architectures. Examples are provided to demonstrate the CNN's capability to accurately predict the permeability tensor, a crucial parameter in various disciplines such as geotechnical engineering, hydrology, and material science. An exemplary source code is made available for interested readers.