Input-optimized physics-informed neural networks for wave propagation problems in laminated structures

Accurate prediction of wave propagation characteristics in laminated structures is crucial for engineering applications, such as ultrasonic examination and composite material optimization. This study develops a novel framework based on extended physics-informed neural networks (XPINNs) to enable the analysis and prediction of wave propagation in laminated structures. The XPINNs with domain decomposition are extended to model multilayered laminated structures, with each sub-PINN governing an individual component layer. An innovative hybrid-handed coordinate system is proposed to address compatibility conditions among layers and unify all inputs of sub-PINNs, developing an input-optimized framework named unified-input XPINNs (Uni-XPINNs). Three types of errors, including the relative root mean square error, the relative absolute error, and the mean square error, are utilized to assess the performance of the proposed framework against analytical solutions and finite element simulations. Based on the obtained prediction models, the study investigates the impact of body forces on wave propagations in laminated structures. Numerical results demonstrate high accuracy in predicting wave propagation in laminate structures, with a maximum error of 3.063% for all cases discussed. It is observed that body forces significantly affect wave propagation when they exceed a specific threshold. Below this threshold, their impacts are minimal. This research explores the application of machine learning methods to solve wave propagation problems, offering alternatives to traditional theoretical methods and numerical simulations.