Probabilistic transformation of fracture representations for surrogate modeling of subsurface flow
摘要
This study introduces a probabilistic transformation of fracture representations to improve the accuracy and transferability of deep-learning surrogates for predicting steady-state pressure fields in fractured porous media. Discrete Fracture Network simulations generated 20,000 paired fracture–pressure samples, comprising 10,000 single-fracture and 10,000 two-fracture cases; a balanced mixed dataset was constructed from both categories. Three representations were evaluated: (1) parametric descriptors mapped through a CNN decoder, (2) binary masks, and (3) continuous super-Gaussian probability density functions (PDFs) implemented within a U-Net framework. The probabilistic transformation converts discrete fracture traces into smooth, fixed-dimensional fields suitable for convolutional learning. The wider PDF representation (σ = 0.02) consistently achieved the lowest errors, with test MSEs of 0.301 × 10⁻3 and 0.545 × 10⁻3 for the dedicated single- and two-fracture models, respectively. The mixed-trained model achieved MSEs of 0.425 × 10⁻3 and 0.538 × 10⁻3 on the corresponding single- and two-fracture test subsets. These results represent 20.0 − 49.3% lower errors than the applicable parametric and binary baselines. Single-fracture-trained models degraded by up to 489% on two-fracture cases, whereas two-fracture-trained models transferred to single-fracture cases with only − 17.2% to + 7.6%. Mixed training provided the most balanced performance across the two fracture-count categories included in training. The transverse spread was treated as a representation hyperparameter rather than as a direct physical aperture; the wider spread produced smoother spatial variation and more spatially coherent reconstructions than the narrow PDF (σ = 0.005) or binary masks. Overall, the probabilistic representation improves prediction accuracy, learning stability, and cross-scenario transferability, while providing a flexible basis for future variable-property, three-dimensional, and inverse-modeling applications.