Deep Learning Surrogate for Predicting Equivalent Hydraulic Conductivity Tensors from Discrete Fracture-Matrix Models

Core Concepts

A deep learning surrogate model can efficiently predict equivalent hydraulic conductivity tensors from discrete fracture-matrix models, enabling accelerated multiscale simulations of groundwater flow in fractured rock.

Abstract

The article presents a deep learning surrogate model for predicting equivalent hydraulic conductivity tensors from discrete fracture-matrix (DFM) models. The key highlights are:

The surrogate combines a convolutional neural network (CNN) for feature extraction and a feed-forward neural network (FNN) for regression. It takes as input the spatial random fields of matrix hydraulic conductivities and the properties of discrete fractures, and predicts the equivalent hydraulic conductivity tensor.

Three independent surrogates are trained, each with a different ratio of fracture to matrix hydraulic conductivity (Kf/Km = 1e3, 1e5, 1e7). As the Kf/Km ratio increases, the distribution of the equivalent hydraulic conductivity becomes more complex, leading to a decline in the surrogate's prediction accuracy.

The prediction accuracy improves as the fracture density decreases, regardless of the Kf/Km ratio. The surrogates also exhibit varying performance for different correlation lengths of the input spatial random fields.

The trained surrogates can provide a 4x to 28x speedup compared to numerical homogenization, depending on the number of homogenization blocks used.

The accuracy of the upscaled hydraulic conductivity field obtained using the surrogates is directly correlated with the precision of the equivalent hydraulic conductivity tensor predictions. However, the impact of the upscaling method on the accuracy of the final macroscale results can be mild.

Stats

The equivalent hydraulic conductivity tensor exhibits a more complex distribution as the ratio of fracture to matrix hydraulic conductivity (Kf/Km) increases.
The prediction accuracy of the surrogates improves as the fracture density decreases, regardless of the Kf/Km ratio.
The speedup gained by using the surrogates varies from 4x to 28x, depending on the number of homogenization blocks.

Quotes

"As the ratio Kf/Km increases, the gap between non-percolated and percolated samples widens."
"Considering kxx and kyy, we observe that for Dataset A, the equivalent tensor is predominantly determined by matrix elements. For Dataset B, we note an increased impact of fractures."
"Although using a larger training dataset generally improves the prediction accuracy of deep neural networks, it may not effectively address the issues associated with underrepresented data if the distribution of the additional training data remains the same."

Key Insights Distilled From

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

by Mart... at arxiv.org 04-24-2024

https://arxiv.org/pdf/2401.04823.pdf

Deeper Inquiries

How can the training dataset be augmented to better capture the tails of the equivalent hydraulic conductivity tensor distribution, especially for high Kf/Km ratios

To better capture the tails of the equivalent hydraulic conductivity tensor distribution, especially for high Kf/Km ratios, the training dataset can be augmented in the following ways:

Data Generation: Generate additional samples with extreme values of the hydraulic conductivity tensor components. This can be achieved by introducing synthetic data points that represent the tails of the distribution.
Data Balancing: Ensure that the training dataset is balanced across the entire range of the equivalent hydraulic conductivity tensor distribution. This can involve oversampling or undersampling techniques to address the imbalance in the dataset.
Outlier Detection: Identify and include outliers in the training dataset that represent the extreme values of the tensor components. These outliers can help the model learn to predict accurately in the tail regions of the distribution.
Data Transformation: Apply data transformation techniques such as feature scaling, normalization, or log transformation to emphasize the differences in the extreme values of the tensor components, making them more prominent during training.

What are the potential limitations of the current surrogate architecture, and how could it be improved to handle more complex fracture-matrix interactions

The current surrogate architecture may have the following limitations and areas for improvement:

Complexity of Interactions: The current architecture may struggle to capture the intricate interactions between fractures and the matrix, especially in cases of high Kf/Km ratios. To address this, the architecture could be enhanced by incorporating attention mechanisms or graph neural networks to better model these complex relationships.
Model Generalization: The surrogate model may face challenges in generalizing to unseen data with different characteristics. To improve generalization, techniques like dropout regularization, data augmentation, and transfer learning can be employed.
Handling Non-linearity: If the interactions between fractures and the matrix exhibit non-linear behavior, the surrogate architecture may need to incorporate non-linear activation functions or more complex neural network structures to capture these nuances effectively.
Feature Engineering: Enhancing the feature representation of the input data, such as including higher-order interactions or domain-specific features, can improve the model's ability to learn the underlying patterns in the data.

Can the proposed surrogate modeling approach be extended to 3D discrete fracture-matrix models, and what additional challenges might arise in that case

Extending the proposed surrogate modeling approach to 3D discrete fracture-matrix models presents several challenges:

Increased Complexity: Moving from 2D to 3D models introduces a higher level of complexity due to the additional dimension. This complexity can impact the training process, model architecture, and computational resources required.
Spatial Considerations: In 3D models, spatial relationships and interactions become more intricate, requiring the surrogate model to capture volumetric features and dependencies accurately.
Computational Resources: Training and inference on 3D models demand more computational resources and memory, which may pose challenges in terms of scalability and efficiency.
Data Representation: Representing 3D data in a format suitable for neural networks, such as volumetric grids or point clouds, requires careful preprocessing and feature extraction techniques to maintain spatial information effectively.