[2604.02335] Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling

Computer Science > Machine Learning arXiv:2604.02335 (cs) [Submitted on 19 Jan 2026] Title:Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling Authors:Martin Špetlík, Jan Březina View a PDF of the paper titled Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling, by Martin \v{S}petl\'ik and Jan B\v{r}ezina View PDF 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, e...