The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters of the fracture networks and quantifying their uncertainties based on observing data is a nontrivial task because inverse modeling of fractured model is strongly nonlinear and non-Gaussian distributed. To address this issue, a novel inverse modeling framework is proposed for the estimation of the fracture networks. The hierarchical parameterization method is adopted in this work. For a small number of large fractures, each fracture is characterized by fracture length, azimuth and coordination of the fracture center. For dense small fractures, fracture density and fractal dimension are utilized to characterize the fracture networks. Moreover, we adopt variational auto-encoder and generative adversarial network (VAE-GAN) and fuse the GAN objective with prior constraint information to capture the distribution of the parameters of complex fracture networks and to satisfy the prior knowledge of fracture fields, thereby mapping the high-dimensional complex parameter distribution into low-dimensional continuous parameter field. Afterwards, relying on the Bayesian framework, ensemble smoother is adopted based on the collected data from hydraulic tomography to reduce the uncertainty of the fracture distribution. Two numerical cases with different complexity are used to test the performance of the proposed framework. The results show that the proposed algorithm can estimate effectively the distribution of the fracture fields after providing sufficient prior constraint information and hydraulic head measurements.
Hydrogeophysical characterization of transport processes in fractured rock by combining push-pull tracer tests and single-hole ground penetrating radar
A convolutional neural network for prestack fracture detection
China University of Petroleum - Beijing（中国石油大学（北京））；PST Service Corporation（PST服务公司）；Beijing Concord O&M Wind Power Technology Co., Ltd.（北京康科德运维风电技术有限公司）
Evolution of the Stress and Strain field in the Tyra field during the Post-Chalk Deposition and Seismic Inversion of fault zone using Informed-Proposal Monte Carlo
Rapid seismic domain transfer: Seismic velocity inversion and modeling using deep generative neural networks
Imperial College London（帝国理工学院）；Open Energi Ltd.（Open Energi有限公司）；Technical University of Denmark（丹麦技术大学）；Euclidity SL（Euclidity SL公司）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Expero Inc.（Expero公司）
Feature-based Inversion of 2.5D Controlled Source Electromagnetic Data using Generative Priors
Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University（电子工程系，北京信息科学与技术国家研究中心（BNRist），清华大学）；Faculty of Math and Computer Science, Weizmann Institute of Science（数学与计算机科学学院，魏兹曼科学研究所）
Training-image based geostatistical inversion using a spatial generative adversarial neural network
Belgian Nuclear Research Centre（比利时核研究中心）；Normandie Univ（诺曼底大学）；UNIROUEN（鲁昂大学）；UNIHAVRE（勒阿弗尔大学）；INSA Rouen（鲁昂国立应用科学学院）；LITIS（鲁昂信息科学与技术实验室）；University of Lausanne（洛桑大学）
Integrating Deep Neural Networks with Full-waveform Inversion: Reparametrization, Regularization, and Uncertainty Quantification
全波形反演（FWI）是一种精确的成像方法，通过最小化记录和预测地震波形之间的失配来模拟速度结构。然而，FWI的强非线性拟合振荡波形导致可以陷入局部极小值的优化。我们提出了一种基于神经网络的全波形反演方法（NNFWI），通过用生成神经网络表示速度模型，将深度神经网络与FWI集成在一起。神经网络可以自然地将空间相关性作为正则化引入到生成的速度模型中，这抑制了梯度中的噪声并减轻了局部最小值。神经网络产生的速度模型输入到传统FWI中使用的相同偏微分方程（PDE）求解器。使用自动微分计算神经网络和PDE的梯度，自动微分通过声学PDE和神经网络层反向传播梯度以更新生成神经网络的权重。一维速度模型，Marmousi模型，和2004年BP模型的实验表明，NNFWI可以减轻局部极小值，特别是成像高对比度的功能，如盐体，并显着提高了反演存在噪声。在神经网络模型中添加dropout层还允许通过Monte Carlo dropout分析反演结果的不确定性。NNFWI开辟了一条将深度学习和FWI结合起来的新途径，以利用深度神经网络的特性和PDE求解器的高精度。由于NNFWI不需要额外的训练数据和优化循环，它提供了一个有吸引力的和直接的替代传统的FWI。
Data-driven Full-waveform Inversion Surrogate using Conditional Generative Adversarial Networks
Universidade Federal do Espírito Santo（巴西联邦圣埃斯皮里图大学）；Instituto Federal do Espírito Santo（圣埃斯皮里图联邦理工学院）；Exploração e Produção Petróleo Brasileiro S.A.（巴西国家石油公司勘探与生产部门）
SURGIN: SURrogate-guided Generative INversion for subsurface multiphase flow with quantified uncertainty
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University（同济大学土木工程学院地质工程系）；Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University（教育部同济大学地质与地下工程重点实验室）；Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST)（卡布斯科学与技术大学（KAUST）物理科学与工程系）；State Key Laboratory of Marine Geology, Tongji University（同济大学海洋地质国家重点实验室）；Tencent SSV（腾讯SSV）；Tencent SD（腾讯SD）
