Integration of deep learning with the discrete element method for porosity prediction in gravel-bed rivers

Porosity is a key parameter governing the hydraulic, geomorphic, and ecological functions of gravel-bed rivers. Although the discrete element method (DEM) can reproduce particle-scale packing structures with high accuracy, its computational cost limits its application for rapid porosity assessment. To address this limitation, this study proposes an integrated framework that combines DEM simulations with deep learning (DL) models, including a two-dimensional convolutional neural network (2D-CNN) and a long short-term memory (LSTM) network. DEM-generated grayscale images and grain-size distributions (GSDs) were used to train the 2D-CNN and LSTM models, respectively, under clogging and penetration scenarios. The results show that the 2D-CNN achieved the highest predictive accuracy, with R values of 0.9712 and 0.9509 for the penetration and clogging cases, respectively, outperforming both the LSTM model and the empirical Yu model. Although the LSTM model also provided satisfactory predictions, its accuracy was generally lower than that of the 2D-CNN. These findings demonstrate that integrating DEM-generated datasets with DL provides an efficient surrogate framework for rapid porosity prediction over the range of GSDs considered in this study, thereby reducing the need for computationally intensive DEM simulations.