arXiv:2604.02335cs.LGcs.NA2026-04被引 2

用3D卷积神经网络快速预测裂隙介质等效水力导率,提速超100倍。

Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling

论文配图:Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling
图 1 · 摘自论文原文
  • 设计3D卷积网络+全连接层的代理模型,从体素化域预测等效导率张量
  • 误差低于0.22,且在多种裂隙参数下保持高精度
  • 适合需要大量重复计算的地下水模拟场景,尤其适合GPU加速

三维裂隙结晶岩介质中的地下水流动建模需考虑由裂隙引起的强空间异质性。精细尺度的离散裂隙-基质(DFM)模拟虽能捕捉复杂结构,但计算成本高昂,尤其在需多次评估时。为此,本文采用多级蒙特卡洛(MLMC)框架,通过数值均质化方法在不同精度层级间上采样子分辨率裂隙效应。为降低传统3D数值均质化的成本,开发了一种代理模型,可从表示基质与裂隙导率张量场的体素化3D域中预测等效水力导率张量Keq。裂隙尺寸、方向和开度基于自然观测分布采样。代理模型结合3D卷积神经网络与前馈层,兼顾局部空间特征与全局交互。在三种不同裂隙-基质导率对比度下训练了三个代理模型,性能在广泛裂隙网络参数和基质场相关长度下评估。训练模型在多数测试案例中达到归一化均方根误差低于0.22的高精度。通过两个宏观尺度问题验证实际应用:计算等效导率张量和预测受限3D域的出流。结果表明,基于代理的上采样在保持精度的同时显著降低计算成本,GPU推理速度提升超过100倍。

原文摘要 · Abstract (English)

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.

裂隙介质代理模型水力建模3D CNN

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