The weighted multi-scale connections networks for macrodispersivity estimation

Macrodispersivity is critical for predicting solute behaviors with dispersive transport models. Conventional methods of estimating macrodispersivity usually need to solve flow equations and are time-consuming. Convolutional neural networks (CNN) have recently been proven capable of efficiently mapping the hydraulic conductivity field and macrodispersivity. However, the mapping accuracy still needs further improvement. In this paper, we present a new network shortcut connection style called weighted multi-scale connections (WMC) for convolutional neural networks to improve mapping accuracy. We provide empirical evidence showing that the WMC can improve the performance of CNN in macrodispersivity estimation by implementing the WMC in CNNs (CNN without short-cut connections, ResNet, and DenseNet), and evaluating them on datasets of macrodispersivity estimation. For the CNN without short-cut connections, the WMC can improve the estimating R² by at least 3% on three datasets of conductivity fields. For ResNet18, the WMC improved the estimated R² by an average of 2.5% on all three datasets. For ResNet34, the WMC improved the estimated R² by an average of 5.6%. For ResNet50, the WMC improved the estimated R² by an average of 16%. For ResNet101, the WMC improved the estimating R² by an average of 30%. For DenseNets, the improved estimated R² ranges from 0.5% to 5%. The WMC can strengthen feature propagation of different sizes and alleviate the vanishing-gradient issue. Moreover, it can be implemented to any CNN with down-sampling layers or blocks.