Study of wave field simulations for non-destructive evaluation using physics informed neural networks

Ultrasonic wave propagation in metals has been widely used method for non destructive material characterization and flaw detection in engineering structures. The recent advances in encoding physics laws in loss function of neural network training has opened new avenues for learning the underlying system parameters from raw ultrasonic signal data. However, the solution of forward and inverse problems of ultrasonic elastic waves within this framework, in complex medium, is still an active area of research. In the present study, a fully connected neural network (FCN) with loss function consisting of elastic wave equation and boundary condition residuals, is trained using ADAM optimizer. We solve two forward problems, in one-dimensional homogeneous and heterogeneous media, the displacement fields inferred from the network output are compared with finite element solutions for validation. The inverse identification of wave speeds from wave field data is also demonstrated. Furthermore, convergence issue related to boundary loss and PDE loss terms in simulation of high frequency waves is examined. In particular, the training dynamics of neural network with these loss functions is analyzed using neural tangent kernel (NTK) theory, providing insights into the spectral bias of FCNs in learning wavefield functions and some alternative strategies for improving network training are recommended.