Physics-informed neural network modeling of one-dimensional wave propagation under broadband and long-duration incident waves

This paper presents a physics-informed neural network (PINN) to model one-dimensional wave propagation in visco-elastic media for seismic site response analysis. Dimensionless relations are introduced to effectively scale the loss terms associated with the wave equation, as well as initial and boundary conditions, during PINN training. Several problem settings with varying complexities demonstrate the effectiveness of the proposed approach compared to the standard (vanilla) PINN and those enhanced with self-adaptive weighting and Fourier feature strategies for handling broadband frequency wave propagation problems with real-world mechanical properties. The results show the dimensionless PINN has less than 9% normalized error in all cases, while the other variants had at least 40% error. Additionally, we present how sequential transfer learning over short intervals can be used to reduce the number of iterations required for the same problem by half, where new boundary conditions are applied to the system. This approach, combined with spatial domain decomposition, can enhance the prediction accuracy of wave responses in layered media subjected to long-duration incident waves, such as earthquake ground motions.