Physics-informed Neural Networks for Structural Dynamics and Vibration Analysis: A Comprehensive Review

Abstract

Physics-informed neural networks (PINNs) have undergone a rapid and transformative evolution between 2021 and 2025, emerging as powerful mesh-free alternatives to traditional numerical solvers for structural dynamics. Conventional approaches—finite element, finite difference, and boundary element methods—struggle with high-order PDEs, extreme stiffness, geometric and material nonlinearities, long-duration transient analyses, and ill-posed inverse problems arising from sparse or noisy measurements. This review consolidates more than 50 recent contributions demonstrating how modern PINN architectures directly address these limitations through auxiliary-variable formulations, separable space-time decompositions, causal and structure-preserving training, hierarchical/adaptive weighting, Runge-Kutta-based temporal embeddings, and hybrid physics-data-driven frameworks. Across benchmark beam, plate, cable, truss, instability, SHM, and multiphysics problems, advanced PINNs consistently achieve displacement and stress errors below 10⁻³–10⁻⁴ for linear systems and 0.5–2% for nonlinear or post-buckling regimes, while delivering computational speedups of 10²–10⁶ over conventional time-marching schemes. Emerging PINN variants further enable robust identification of distributed stiffness, damping, ductility, nonlinear boundary behavior, and unknown excitation using minimal instrumentation—paving the way for real-time digital twins and structural health monitoring. The review highlights how operator-learning extensions (e.g., Fourier Neural Operators, Kolmogorov-Arnold Networks) and hybrid PINN-FEM strategies are overcoming remaining challenges in long-time stability and 3D scalability. Overall, the period 2021–2025 marks a decisive transition wherein PINNs have matured into high-performance, physics-consistent computational engines capable of solving forward, inverse, and multiphysics structural dynamics problems with remarkable accuracy, efficiency, and interpretability.