The incorporation of hard data in geostatistical modeling is crucial for enhancing the accuracy of interpolating or stochastically estimating subsurface spatial features. The hard data at specified points in the model domain serve as a guide in optimizing the unknown parameters to follow the patterns of the hard data. Recently, a novel approach to solving hydrogeologic/reservoir modeling problems has emerged by using deep generative models, specifically generative adversarial networks (GANs), to generate realistic and diverse images of channelized aquifers. This subsequently can be coupled with inverse models to solve parameter estimation problems. This study focused on using an improved GAN, called a progressive growing generative adversarial network (PGGAN), conditioned with hard data to perform parameter estimation of complex facies models by coupling an ensemble smoother with multiple data assimilation (ES-MDA). First, the PGGAN was trained to an image with 128 × 128 resolution. The trained PGGAN was used to generate hydraulic conductivity fields when fed an ensemble of latent variables and hard data. The ES-MDA then was used to update the latent variable with the help of hydraulic head data obtained from the groundwater model. The approach was tested on synthetic hydraulic conductivity data. Results show that this approach was able to perform efficient estimation of an unknown facies model domain. Additionally, the proposed method was applied to a different test case of a facies model exhibiting different statistical characteristics. The results were satisfactory, demonstrating that the method is not constrained to the particular hydraulic conductivity fields introduced in the generator’s training.

中文翻译：

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利用深度学习与渐进式增长的 GAN 和集成平滑器以及多重数据同化进行逆向建模

将硬数据纳入地质统计建模对于提高插值或随机估计地下空间特征的准确性至关重要。模型域中指定点的硬数据可作为优化未知参数以遵循硬数据模式的指南。最近，出现了一种解决水文地质/水库建模问题的新方法，即使用深层生成模型，特别是生成对抗网络（GAN）来生成渠道化含水层的真实且多样化的图像。随后可以与逆模型相结合来解决参数估计问题。这项研究的重点是使用改进的 GAN，称为渐进式生长生成对抗网络 (PGGAN)，以硬数据为条件，通过将集合平滑器与多重数据同化 (ES-MDA) 相结合来执行复杂相模型的参数估计。首先，PGGAN 被训练为分辨率为 128 × 128 的图像。当输入一组潜在变量和硬数据时，经过训练的 PGGAN 用于生成水力传导率场。然后，ES-MDA 借助从地下水模型获得的水头数据来更新潜在变量。该方法在合成水力传导率数据上进行了测试。结果表明，该方法能够对未知相模型域进行有效估计。此外，所提出的方法还应用于显示不同统计特征的相模型的不同测试案例。结果令人满意，表明该方法不受发电机训练中引入的特定水力传导率场的限制。