# Point-Cloud Deep Learning of Porous Media for Permeability Prediction

arXiv: https://arxiv.org/abs/2107.14038 · HTML: https://mlsanity.com/paper/2107.14038/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 65 references that are in the map.
- First posted on arXiv 18 Jul 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [Frustum PointNets for 3D Object Detection from RGB-D Data](https://mlsanity.com/paper/1711.08488/) (2017)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [Understanding Convolution for Semantic Segmentation](https://mlsanity.com/paper/1702.08502/) (2017)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Revisiting Small Batch Training for Deep Neural Networks](https://mlsanity.com/paper/1804.07612/) (2018)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Turbulence Enrichment using Physics-informed Generative Adversarial Networks](https://mlsanity.com/paper/2003.01907/) (2020)
- [Fast and Accurate Image Super Resolution by Deep CNN with Skip Connection and Network in Network](https://mlsanity.com/paper/1707.05425/) (2017)
- [Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/2007.02820/) (2020)
- [Predicting Effective Diffusivity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/1912.05532/) (2019)
- [DeePore: a deep learning workflow for rapid and comprehensive characterization of porous materials](https://mlsanity.com/paper/2005.03759/) (2020)
- [ML-LBM: Machine Learning Aided Flow Simulation in Porous Media](https://mlsanity.com/paper/2004.11675/) (2020)

## Built on by (most cited first, 10 of 10)

- [ChatGPT for Programming Numerical Methods](https://mlsanity.com/paper/2303.12093/) (2023)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [A robust single-pixel particle image velocimetry based on fully convolutional networks with cross-correlation embedded](https://mlsanity.com/paper/2111.00395/) (2021)
- [Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks](https://mlsanity.com/paper/2310.19274/) (2023)
- [Machine Learning Visualization Tool for Exploring Parameterized Hydrodynamics](https://mlsanity.com/paper/2406.15509/) (2024)
- [Vision Mamba for Permeability Prediction of Porous Media](https://mlsanity.com/paper/2510.14516/) (2025)
- [A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media](https://mlsanity.com/paper/2402.11568/) (2024)
- [An End-to-End Differentiable, Graph Neural Network-Embedded Pore Network Model for Permeability Prediction](https://mlsanity.com/paper/2509.13841/) (2025)
- [Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains](https://mlsanity.com/paper/2609.00297/) (2026)

## Abstract (arXiv)

We propose a novel deep learning framework for predicting permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the boundary between solid matrix and pore spaces as point clouds and feed them as inputs to a neural network based on the PointNet architecture. This approach overcomes the challenge of memory restriction of graphics processing units and its consequences on the choice of batch size, and convergence. Compared to convolutional neural networks, the proposed deep learning methodology provides freedom to select larger batch sizes, due to reducing significantly the size of network inputs. Specifically, we use the classification branch of PointNet and adjust it for a regression task. As a test case, two and three dimensional synthetic digital rock images are considered. We investigate the effect of different components of our neural network on its performance. We compare our deep learning strategy with a convolutional neural network from various perspectives, specifically for maximum possible batch size. We inspect the generalizability of our network by predicting the permeability of real-world rock samples as well as synthetic digital rocks that are statistically different from the samples used during training. The network predicts the permeability of digital rocks a few thousand times faster than a Lattice Boltzmann solver with a high level of prediction accuracy.