In machine learning, the most commonly used and effective algorithm is the artificial neural network (ANN) algorithm, which has the advantages of fast computing speed, strong self-learning ability, good robustness etc.. Among the ANNs, back-propagating neural network (BPNN) is one of the most commonly used neural network, which is composed of multi-layer neurons connected to each other to form a network structure. However, due to the lack of theoretical support for the selection of initial parameters and activation function, it often leads to slow convergence and local optimization, and drags the convergence and generalization ability. At the same time, in the mechanical problems, it is difficult to solve some complex problems with complicated models. With the help of artificial neural network algorithms, the numerical computation efficiency can be effectively improved and a new solution can be provided for some complex mechanical problems. On the one hand, based on the loss function analysis of mechanics and the basic theory of fracture mechanics, this work proposes two different improvement schemes of BP algorithm. The selection of weights and thresholds and activation function are optimized respectively. Numerical analysis shows that the improved algorithm can improve the accuracy, convergence and efficiency of numerical results. On the other hand, a deep extended causal convolution network is constructed based on the WaveNet model to repair the missing experimental data of shale fracturing.

The proposed new algorithms have higher accuracy, efficiency and convergence for solving the three-dimensional surface reconstruction problem and crack propagation problem. Moreover, the missing shale fracturing experimental data can also be repaired on the selected deep learning algorithms.