# Deep-learning-based upscaling method for geologic models via theory-guided convolutional neural network

arXiv: https://arxiv.org/abs/2201.00698 · HTML: https://mlsanity.com/paper/2201.00698/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modeling](https://mlsanity.com/paper/2011.08618/) (2020)
- [A machine learning approach for efficient uncertainty quantification using multiscale methods](https://mlsanity.com/paper/1711.04315/) (2017)
- [A Bayesian Multiscale Deep Learning Framework for Flows in Random Media](https://mlsanity.com/paper/2103.09056/) (2021)

## Built on by (most cited first, 1 of 1)

- [Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling](https://mlsanity.com/paper/2604.02335/) (2026)

## Abstract (arXiv)

Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic models (e.g., hydraulic conductivity) from fine-scale (high-resolution grids) to coarse-scale systems. Numerical upscaling methods have been proven to be effective and robust for coarsening geologic models, but their efficiency remains to be improved. In this work, a deep-learning-based method is proposed to upscale the fine-scale geologic models, which can assist to improve upscaling efficiency significantly. In the deep learning method, a deep convolutional neural network (CNN) is trained to approximate the relationship between the coarse grid of hydraulic conductivity fields and the hydraulic heads, which can then be utilized to replace the numerical solvers while solving the flow equations for each coarse block. In addition, physical laws (e.g., governing equations and periodic boundary conditions) can also be incorporated into the training process of the deep CNN model, which is termed the theory-guided convolutional neural network (TgCNN). With the physical information considered, dependence on the data volume of training the deep learning models can be reduced greatly. Several subsurface flow cases are introduced to test the performance of the proposed deep-learning-based upscaling method, including 2D and 3D cases, and isotropic and anisotropic cases. The results show that the deep learning method can provide equivalent upscaling accuracy to the numerical method, and efficiency can be improved significantly compared to numerical upscaling.