Physics-Informed Sinusoidal Networks for Ultrasonic Lamb Wave Reconstruction from Sparse Data

Abstract

Ultrasonic guided wave (UGW) inspection has established itself as an effective non-destructive testing (NDT) method. Although the use of machine learning has recently improved damage detection capabilities, purely data-driven models are limited by their dependence on extensive labeled datasets and their lack of physical interpretability. Additionally, standard multi-layer perceptrons (MLPs) suffer from spectral bias (F-Principle), prioritizing low-frequency patterns while failing to capture high-frequency components essential for UGW reconstruction. By embedding the underlying partial differential equations into the training process, Physics-Informed Neural Networks (PINNs) \cite{Raissi} offer a robust solution for data-scarce environments. Additionally, Sinusoidal Representation Networks (SIRENs) \cite{Sitzmann} leverage periodic activation functions to effectively resolve high-frequency oscillatory phenomena. This study proposes a Physics-Informed Sinusoidal Representation Network (PI-SIREN) which embeds the elastodynamic wave equation into the learning process, effectively mitigating spectral bias to enable ultrasonic wavefield reconstruction in data-scarce environments. Specifically, the governing equations for both Kirchhoff-Love and Mindlin-Reissner plate theories are adapted and systematically compared. Numerical results demonstrate that the proposed PI-SIREN model significantly outperforms purely data-driven baselines, achieving substantially lower absolute and relative errors when trained on identical sparse datasets. Specifically, the Mindlin-Reissner implementation yield the most accurate wavefield reconstruction. All simulations were executed using double precision arithmetic combined with a hybrid optimization strategy with transition from first-order Adam to semi-second-order limited-memory BFGS optimizer. In contrast, conventional PINN configurations utilizing standard MLPs with hyperbolic tangent activation functions failed to converge, as they were unable to resolve the high-frequency dynamics inherent to ultrasonic wave propagation.