Representing and preserving complex (non-Gaussian) spatial patterns in aquifer flow properties during model calibration are challenging. Conventional parameterization methods that rely on linear/Gaussian assumptions are not suitable for representation of property maps with more complex spatial patterns. Deep learning techniques, such as Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN), have recently been proposed to address this difficulty by learning complex spatial patterns from prior training images and synthesizing similar realizations using low-dimensional latent variables with Gaussian distributions. The resulting Gaussian latent variables lend themselves to calibration with the ensemble Kalman filter-based updating schemes that are suitable for parameters with Gaussian distribution. Despite their superior performance in generating complex spatial patterns, these generative models may not provide desirable properties that are needed for parameterization of model calibration problems, including robustness, smoothness in the latent domain, and reconstruction fidelity. This paper introduces the second generation of style-based Generative Adversarial Networks (StyleGAN) for parameterization of complex subsurface flow properties and compares its model calibration properties and performance with those of the convolutional VAE and GAN architectures. Numerical experiments involving model calibration with the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in single-phase and two-phase fluid flow examples are used to assess the capabilities and limitations of these methods. The results show that parameterization with StyleGANs provides superior performance in terms of reconstruction fidelity and flexibility, underscoring its potential for improving the representation and reconstruction of complex spatial patterns in subsurface flow model calibration problems.

中文翻译：

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使用基于样式的生成对抗网络 （StyleGAN） 改进复杂地下水流属性的参数化


在模型校准期间，在含水层流动属性中表示和保留复杂（非高斯）空间模式具有挑战性。依赖于线性/高斯假设的传统参数化方法不适合表示具有更复杂空间模式的属性映射。最近提出了变分自动编码器 （VAE） 和生成对抗网络 （GAN） 等深度学习技术，通过从先前的训练图像中学习复杂的空间模式并使用具有高斯分布的低维潜在变量合成类似的实现来解决这一困难。由此产生的高斯潜在变量适合使用基于集成卡尔曼滤波器的更新方案进行校准，该方案适用于具有高斯分布的参数。尽管这些生成模型在生成复杂的空间模式方面表现出色，但它们可能无法提供模型校准问题参数化所需的理想属性，包括鲁棒性、潜在域中的平滑性和重建保真度。本文介绍了第二代基于风格的生成对抗网络 （StyleGAN），用于复杂地下水流属性的参数化，并将其模型校准属性和性能与卷积 VAE 和 GAN 架构的模型校准属性和性能进行了比较。在单相和两相流体流动示例中，涉及使用具有多重数据同化的 Ensemble Smoother （ES-MDA） 进行模型校准的数值实验用于评估这些方法的功能和局限性。 结果表明，使用 StyleGAN 进行参数化在重建保真度和灵活性方面提供了卓越的性能，强调了它在改善地下水流模型校准问题中复杂空间模式的表示和重建的潜力。