Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modeling

TL;DR

This paper introduces a Theory-guided Auto-Encoder framework that integrates governing equations into CNN training for efficient surrogate modeling, uncertainty quantification, and inverse modeling in subsurface flow problems.

Contribution

The novel TgAE framework embeds discretized governing equations into CNN training, enhancing surrogate accuracy and extrapolation ability with limited data.

Findings

TgAE achieves high accuracy in surrogate modeling of subsurface flows.

The framework improves efficiency in uncertainty quantification tasks.

TgAE demonstrates good extrapolation and inverse modeling performance.

Abstract

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.