Dispersion coefficients and the average solute transport velocity are pivotal for groundwater solute transport modeling. Accurately and efficiently determining these parameters is challenging due to difficulties in directly correlating them with pore-space structure. To address this issue, we introduced the Physics-enhanced Convolutional Neural Network-Transformer (PhysenCT-Net), an innovative model designed to concurrently estimate the longitudinal dispersion coefficient and average solute transport velocity in three-dimensional porous media. PhysenCT-Net exhibited excellent predictive performance on unseen testing datasets and significantly reduced computational demands. Comprehensive evaluations confirmed its robust generalization across various flow conditions and pore structures. Notably, the longitudinal dispersion coefficient predictions closely align with established empirical relationships involving flow velocity, affirming the model’s physical interpretability and potential to aid in simulating transport phenomena in porous media.

Dispersion coefficients and the average solute transport velocity are pivotal for groundwater solute transport modeling. Accurately and efficiently determining these parameters is challenging due to difficulties in directly correlating them with pore-space structure. To address this issue, we introduced the Physics-enhanced Convolutional Neural Network-Transformer (PhysenCT-Net), an innovative model designed to concurrently estimate the longitudinal dispersion coefficient and average solute transport velocity in three-dimensional porous media. PhysenCT-Net exhibited excellent predictive performance on unseen testing datasets and significantly reduced computational demands. Comprehensive evaluations confirmed its robust generalization across various flow conditions and pore structures. Notably, the longitudinal dispersion coefficient predictions closely align with established empirical relationships involving Péclet number, affirming the model’s physical interpretability and potential to aid in simulating transport phenomena in porous media.

The direct acquisition of the permeability of porous media by digital images helps to enhance our understanding of and facilitate research into the problem of subsurface flow. A complex pore space makes the numerical simulation methods used to calculate the permeability quite time-consuming. Deep learning models represented by three-dimensional convolutional neural networks (3D CNNs), as a promising approach to improving efficiency, have made significant advances concerning predicting the permeability of porous media. However, 3D CNNs only have the ability to represent the local information of 3D images, and they cannot consider the spatial correlation between 2D slices, a significant factor in the reconstruction of porous media. This study combines a 2D CNN and a self-attention mechanism to propose a novel CNN-Transformer hybrid neural network that can make full use of the 2D slice sequences of porous media to accurately predict their permeability. In addition, we added physical information to the slice sequences and built a PhyCNN-Transformer model to reflect the impact of physical properties on permeability prediction. In terms of dataset preparation, we used the publicly available DeePore porous media dataset with the labeled permeability calculated by pore network modelling (PNM). We compared the two transformer-based models with a 3D CNN in terms of parameter number, training efficiency, prediction performance, and generalization, and the results showed significant improvement. Combined with the transfer learning method, we demonstrate the superior generalization ability of the transformer-based models to unfamiliar samples with small sample sizes.