论文标题
理论指导的自动编码器替代建筑和反向建模
Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modeling
论文作者
论文摘要
提出了一个理论指导的自动编码器（TGAE）框架用于替代结构，并进一步用于不确定性定量和反向建模任务。该框架是基于卷积神经网络（CNN）的自动编码器（或编码器）架构建立的，该体系结构通过理论引导的培训过程。为了实现理论引导的培训，可以将研究问题的管理方程式离散化，并且方程的有限差异方案可以嵌入到CNN的训练中。离散的管理方程式以及数据不匹配的残差构成了TGAE的损失函数。训练有素的TGAE可用于构建替代物，该替代物近似模型参数与响应有限的响应之间的关系有限。为了测试TGAE的性能，引入了几个地下流动案例。结果表明，通过TGAE替代物可以提高TGAE替代物的令人满意的精度和不确定性定量任务的效率。对于具有不同相关长度和方差的病例，TGAE还显示出良好的外推能力。此外，参数反演任务已通过TGAE替代物实现，并且可以获得令人满意的结果。
A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate construction and is further used for uncertainty quantification and inverse modeling tasks. The framework is built based on the Auto-Encoder (or Encoder-Decoder) architecture of convolutional neural network (CNN) via a theory-guided training process. In order to achieve the theory-guided training, the governing equations of the studied problems can be discretized and the finite difference scheme of the equations can be embedded into the training of CNN. The residual of the discretized governing equations as well as the data mismatch constitute the loss function of the TgAE. The trained TgAE can be used to construct a surrogate that approximates the relationship between the model parameters and responses with limited labeled data. In order to test the performance of the TgAE, several subsurface flow cases are introduced. The results show the satisfactory accuracy of the TgAE surrogate and efficiency of uncertainty quantification tasks can be improved with the TgAE surrogate. The TgAE also shows good extrapolation ability for cases with different correlation lengths and variances. Furthermore, the parameter inversion task has been implemented with the TgAE surrogate and satisfactory results can be obtained.
