Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modeling
This work provides an incremental improvement in surrogate modeling for subsurface flow problems, potentially benefiting engineers and researchers in this domain by offering a more efficient approach to uncertainty quantification and inverse modeling.
This paper proposes a Theory-guided Auto-Encoder (TgAE) framework that integrates discretized governing equations into the training of a Convolutional Neural Network (CNN) for surrogate construction. It demonstrates satisfactory accuracy in approximating the relationship between model parameters and responses for subsurface flow cases, improving the efficiency of uncertainty quantification and achieving satisfactory results in parameter inversion.
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.