The forward and inverse analysis of tunnel based on weak form physics-informed deep learning

In recent years, the advent of artificial intelligence based on artificial neural network promotes the development of data-driven methods. Nevertheless, data-driven approaches exhibit poor performance when data is limited. Physics-Informed Neural Networks (PINNs) have emerged as a compelling solution to address data scarcity. Although PINNs offer a breakthrough in handling limited data, it is rarely used in geotechnical engineering. To overcome limitations of traditional PINNs in geotechnical engineering, this paper proposes a weak form PINNs based on the principle of minimum potential energy. The proposed method constructs the force balance equation at the sample point through a weak form as the loss function of the neural network. Compared with traditional PINNs, the proposed method shows better training efficiency and robustness in geotechnical engineering. To validate the efficiency of this proposed approach, we take the diversion tunnels in the Jinping II Hydropower Station as a real-world engineering example. The example includes forward and inverse analysis of linear elastic problem and forward analysis of elastoplastic problems, and the results demonstrate that the proposed deep learning method has ability to predict displacement, stress fields around tunnels and the material parameters.