Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling

TL;DR

This paper introduces a 3D convolutional neural network surrogate model to efficiently predict hydraulic conductivity tensors in fractured media, significantly reducing computational costs in groundwater flow simulations.

Contribution

A novel deep learning surrogate architecture for 3D tensor upscaling in fractured media, integrated with multilevel Monte Carlo for efficient groundwater modeling.

Findings

Surrogate models achieve normalized RMSE below 0.22 in most cases.

Surrogate-based upscaling maintains accuracy in macro-scale flow problems.

Inference speedup exceeds 100x on GPU compared to traditional methods.

Abstract

Modeling groundwater flow in three-dimensional fractured crystalline media requires accounting for strong spatial heterogeneity induced by fractures. Fine-scale discrete fracture-matrix (DFM) simulations can capture this complexity but are computationally expensive, especially when repeated evaluations are needed. To address this, we aim to employ a multilevel Monte Carlo (MLMC) framework in which numerical homogenization is used to upscale sub-resolution fracture effects when transitioning between accuracy levels. To reduce the cost of conventional 3D numerical homogenization, we develop a surrogate model that predicts the equivalent hydraulic conductivity tensor Keq from a voxelized 3D domain representing tensor-valued random fields of matrix and fracture conductivities. Fracture size, orientation, and aperture are sampled from distributions informed by natural observations. The surrogate architecture combines a 3D convolutional neural network with feed-forward layers, enabling it to capture both local spatial features and global interactions. Three surrogates are trained on data generated by DFM simulations, each corresponding to a different fracture-to-matrix conductivity contrast. Performance is evaluated across a wide range of fracture network parameters and matrix-field correlation lengths. The trained models achieve high accuracy, with normalized root-mean-square errors below 0.22 across most test cases. Practical applicability is demonstrated by comparing numerically homogenized conductivities with surrogate predictions in two macro-scale problems: computing equivalent conductivity tensors and predicting outflow from a constrained 3D domain. In both cases, surrogate-based upscaling preserves accuracy while substantially reducing computational cost, achieving speedups exceeding 100x when inference is performed on a GPU.