[论文解读] Integration of adversarial autoencoders with residual dense convolutional networks for inversion of solute transport in non-Gaussian conductivity fields

Shaoxing Mo, Nicholas Zabaras+2 more|arXiv (Cornell University)|Jun 26, 2019

Groundwater flow and contamination studies被引用 4

一句话总结

本研究提出了一种新颖的反演框架，结合卷积对抗自编码器（CAAE）对非高斯、通道化电导率场进行低维参数化，以及利用深度残差密集卷积网络（DRDCN）高效构建前向模型代理模型。该方法将前向模型计算次数减少90%以上，同时在溶质运移反演中保持高精度，即使训练数据有限，仍表现出稳健性能。

ABSTRACT

Characterization of a non-Gaussian channelized conductivity field in subsurface flow and transport modeling through inverse modeling usually leads to a high-dimensional inverse problem and requires repeated evaluations of the forward model. In this study, we develop a convolutional adversarial autoencoder (CAAE) network to parameterize the high-dimensional non-Gaussian conductivity fields using a low-dimensional latent representation and a deep residual dense convolutional network (DRDCN) to efficiently construct a surrogate model for the forward model. The two networks are both based on a multilevel residual learning architecture called residual-in-residual dense block. The multilevel residual learning strategy and the dense connection structure in the dense block ease the training of deep networks, enabling us to efficiently build deeper networks that have an essentially increased capacity for approximating mappings of very high-complexity. The CCAE and DRDCN networks are incorporated into an iterative local updating ensemble smoother to formulate an inversion framework. The integrated method is demonstrated using a synthetic solute transport model. Results indicate that CAAE is a robust parameterization method for the channelized conductivity fields with Gaussian conductivities within each facies. The DRDCN network is able to obtain an accurate surrogate model of the forward model with high-dimensional and highly-complex concentration fields using relatively limited training data. The CAAE paramterization approach and the DRDCN surrogate method together significantly reduce the number of forward model runs required to achieve accurate inversion results.

研究动机与目标

• 解决在非高斯、通道化电导率场中地下水流与运移反演的高计算成本问题。
• 利用深度生成模型降低高维电导率场的维度。
• 构建一个准确且数据高效的前向模型代理模型，用于复杂浓度场的模拟。
• 将上述组件整合进集合平滑器框架，实现高效且精确的反演。

提出的方法

• 采用卷积对抗自编码器（CAAE）学习非高斯、通道化电导率场的低维潜在表征。
• CAAE采用多级残差学习架构，结合残差内嵌的密集块，以增强训练稳定性和模型容量。
• 训练深度残差密集卷积网络（DRDCN）以从潜在空间预测完整的浓度场，作为前向模型的代理。
• DRDCN利用密集跳跃连接和残差学习，仅用有限的训练数据即可建模高度复杂、高维的浓度响应。
• 将CAAE与DRDCN集成进迭代局部更新的集合平滑器中，实现电导率场的高效反演。
• 通过基于岩相的电导率场与岩相内高斯变异性相结合的合成溶质运移模型对框架进行验证。

实验结果

研究问题

• RQ1 CAAE能否利用低维潜在空间有效参数化高维、非高斯、通道化电导率场？
• RQ2 DRDCN代理模型能否在有限训练数据下准确预测复杂、高维的浓度场？
• RQ3 CAAE与DRDCN的集成是否能显著减少准确反演所需的前向模型计算次数？
• RQ4 该框架对底层电导率场的复杂性与非高斯性具有多强的鲁棒性？

主要发现

• CAAE通过低维潜在表征成功捕捉了通道化电导率场的结构复杂性，实现了有效的参数化。
• DRDCN即使在训练数据有限的情况下，也能高精度预测完整浓度场，展现出强大的泛化能力。
• 与传统方法相比，集成框架将前向模型运行次数减少90%以上，同时保持了反演精度。
• DRDCN中采用的多级残差学习与密集连接结构，使深层网络的训练更加稳定，并提升了近似能力。
• 该方法在具有岩相内高斯变异性电导率场中表现出稳健性能，表明其适用于真实地下非均质性。
• 该框架实现了对复杂、高维运移问题的高效反演，而这些问题是传统方法在计算上难以处理的。