ON NEURAL NETWORK APPLICATION IN SOLID MECHANICS

A review of the machine learning methods employing the neural network algorithm is presented. Most commonly used neural networks, such as the feedforward neural network including deep learning, the convolutional neural network, the recurrent neural network and the physics-informed neural network, are discussed. A special emphasis is placed on their applications in engineering fields, particularly in solid mechanics. Network architectures comprising layers and neurons as well as different learning processes are highlighted. The feedforward neural network and the recurrent neural network are described in more details. To reduce the undesired vanishing gradient effect within the recurrent neural network architecture, the long short-term memory network is presented. Numerical efficiency and accuracy of both the feedforward and the long short-term memory recurrent network are demonstrated by numerical examples, where the neural network solutions are compared to the results obtained using the standard finite element approaches.