Theory-guided Auto-Encoder for surrogate construction and inverse modeling

A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate\nconstruction and is further used for uncertainty quantification and inverse\nmodeling tasks. The framework is built based on the Auto-Encoder (or\nEncoder-Decoder) architecture of convolutional neural network (CNN) via a\ntheory-guided training process. In order to achieve the theory-guided training,\nthe governing equations of the studied problems can be discretized and the\nfinite difference scheme of the equations can be embedded into the training of\nCNN. The residual of the discretized governing equations as well as the data\nmismatch constitute the loss function of the TgAE. The trained TgAE can be used\nto construct a surrogate that approximates the relationship between the model\nparameters and responses with limited labeled data. In order to test the\nperformance of the TgAE, several subsurface flow cases are introduced. The\nresults show the satisfactory accuracy of the TgAE surrogate and efficiency of\nuncertainty quantification tasks can be improved with the TgAE surrogate. The\nTgAE also shows good extrapolation ability for cases with different correlation\nlengths and variances. Furthermore, the parameter inversion task has been\nimplemented with the TgAE surrogate and satisfactory results can be obtained.\n