Uncertainty Quantification of GAN-Based Image Inpainting of Material’s Stress Fields using Monte Carlo Dropout

Abstract

This research focuses on uncertainty quantification in reconstructing incomplete mechanical stress field maps by utilizing Generative Adversarial Networks (GANs) integrated with dropout mechanisms to introduce noise and variability. Specifically, the study investigates the effects of selectively applying dropout as a source of controlled noise to a GAN-based model known as DeepFill. Two distinct configurations were examined in terms of dropout application: one where dropout was confined exclusively to the first hidden layer and another where it was uniformly distributed across all hidden layers. The dropout rates were varied at 0.2, 0.4, and 0.6 to assess their impact on model performance and reliability. Results demonstrate that applying dropout exclusively to the first hidden layer yields lower uncertainties, even for higher dropout rates. By restricting the introduction of noise to the initial hidden layer, the network benefits from regularization without significantly impacting the stability of deeper layers. This selective application ensures that noise is managed in a controlled manner, allowing the model to generalize better while maintaining consistent predictions. In contrast, applying dropout across all hidden layers amplifies noise throughout the network, leading to larger uncertainties. Moreover, it is observed that the uncertainty increases linearly with the increase in dropout rates. These findings are particularly significant for applications in stress field reconstructions, such as fracture mechanics and non-destructive testing (NDT).