Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling

• URL: http://arxiv.org/abs/2604.02335v1
• Date: Mon, 19 Jan 2026 23:53:58 GMT
• Title: Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling
• Abstract summary: We develop a surrogate model that predicts the equivalent hydraulic conductivity tensor Keq from a voxelized 3D domain.<n>Three surrogates are trained on data generated by DFM simulations, each corresponding to a different fracture-to-matrix conductivity contrast.<n>The trained models achieve high accuracy, with normalized root-mean-square errors below 0.22 across most test cases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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