Estimating elastic parameters from digital rock images based on multi-task learning with multi-gate mixture-of-experts

Digital rock physics analysis has become an effective approach complementary to traditional experimental physics in estimating elastic parameters from digital rock images to study the relationship between the grain structure and rock mechanical properties. However, conventional numerical simulation requires lots of computational time and GB voxels memory. Recently, the convolutional neural network (CNN) has proven to be a successful method for estimating physical parameters from digital rock images, and multi-parameter simultaneous prediction using multi-task learning has been the focus of attention. But these methods don't achieve satisfactory results due to tasks' mutual interferences that affect network performances such as accuracy, robustness, and efficiency. To address these issues, a multi-task learning network with multi-gate mixture-of-experts was proposed to estimate elastic parameters from two-dimension digital rock images (MMOEROCK) in this paper. Parallel operational expert networks were used to replace traditional serial operational networks in order to reduce the mutual interferences of tasks. Gate networks were used to control the output weights of different expert networks in order to allow selective sharing among independent expert networks. The homoscedastic uncertainty loss function was used to automatically adjust the weight of each task loss function to improve network performance in searching for the optimal solution. The experimental results showed that the R2-scores of the bulk modulus, shear modulus, P wave velocity, and S wave velocity could reach 0.89, 0.92, 0.92, and 0.91 on the validation set and 0.97, 0.96, 0.96, and 0.94 on the test set, respectively, and MMOEROCK after fully training achieved an 800 speedup factor compared with the finite element method.