A Comparative Study of Physics-Informed and Finite Element-Informed Neural Networks for Non-Uniform Material Identification in Beams with Limited Measurements
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Identification of spatially varying material properties in beam structures is a challenging inverse problem, particularly when only sparse measurement data are available. This study presents a comparative investigation of Physics-Informed Neural Networks (PINNs) and Finite Element–Informed Neural Networks (FEINNs) for identifying non-uniform Young’s modulus (E) distributions in beam structures using sparse displacement measurements. A clamped–clamped straight beam with a spatially varying E with spatially varying material properties along the axial direction are considered. In the PINN framework, neural networks approximate both the displacement field and material distribution by enforcing governing equations, boundary conditions, and measurement data within a unified loss function. In contrast, FEINN embeds the governing physics through finite element discretization, while a neural network is used to infer unknown material parameters by minimizing the residual of the weak form of the governing equations, with measurements and boundary conditions imposed as constraints. The methods are evaluated in terms of accuracy, robustness to sparse measurements, convergence, and computational efficiency. The results show that PINNs offer mesh-free modeling, while FEINNs exhibit greater robustness, consistent prediction and faster convergence under limited data. These results provide practical guidance for selecting physics-guided neural network frameworks for inverse material identification.
