# Constrained Transformer-Based Porous Media Generation to Spatial Distribution of Rock Properties

arXiv: https://arxiv.org/abs/2410.21462 · HTML: https://mlsanity.com/paper/2410.21462/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [AttnGAN: Fine-Grained Text to Image Generation with Attentional Generative Adversarial Networks](https://mlsanity.com/paper/1711.10485/) (2017)
- [Video Probabilistic Diffusion Models in Projected Latent Space](https://mlsanity.com/paper/2302.07685/) (2023)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Generating 3D structures from a 2D slice with GAN-based dimensionality expansion](https://mlsanity.com/paper/2102.07708/) (2021)
- [Stochastic reconstruction of an oolitic limestone by generative adversarial networks](https://mlsanity.com/paper/1712.02854/) (2017)
- [Parametrization of stochastic inputs using generative adversarial networks with application in geology](https://mlsanity.com/paper/1904.03677/) (2019)
- [Using Physics Informed Generative Adversarial Networks to Model 3D porous media](https://mlsanity.com/paper/2409.11541/) (2024)
- [Fast and Scalable Earth Texture Synthesis using Spatially Assembled Generative Adversarial Neural Networks](https://mlsanity.com/paper/2011.06776/) (2020)

## Abstract (arXiv)

Pore-scale modeling of rock images based on information in 3D micro-computed tomography data is crucial for studying complex subsurface processes such as CO2 and brine multiphase flow during Geologic Carbon Storage (GCS). While deep learning models can generate 3D rock microstructures that match static rock properties, they have two key limitations: they don't account for the spatial distribution of rock properties that can have an important influence on the flow and transport characteristics (such as permeability and relative permeability) of the rock and they generate structures below the representative elementary volume (REV) scale for those transport properties. Addressing these issues is crucial for building a consistent workflow between pore-scale analysis and field-scale modeling. To address these challenges, we propose a two-stage modeling framework that combines a Vector Quantized Variational Autoencoder (VQVAE) and a transformer model for spatial upscaling and arbitrary-size 3D porous media reconstruction in an autoregressive manner. The VQVAE first compresses and quantizes sub-volume training images into low-dimensional tokens, while we train a transformer to spatially assemble these tokens into larger images following specific spatial order. By employing a multi-token generation strategy, our approach preserves both sub-volume integrity and spatial relationships among these sub-image patches. We demonstrate the effectiveness of our multi-token transformer generation approach and validate it using real data from a test well, showcasing its potential to generate models for the porous media at the well scale using only a spatial porosity model. The interpolated representative porous media that reflect field-scale geological properties accurately model transport properties, including permeability and multiphase flow relative permeability of CO2 and brine.