A Comparative Study of Physics-Informed and Finite Element-Informed Neural Networks for Non-Uniform Material Property Identification in Beams with Limited Measurements
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This study compares physics-informed neural network (PINN) and finite element-informed neural network (FEINN) for identifying spatially varying Young’s modulus in Euler–Bernoulli beams from limited measurements. PINN approximates displacement and material fields using separate networks and enforces governing equations through soft constraints. FEINN combines a material network with finite element equilibrium residuals and equality constraints on boundary conditions and measurements. A synthetic benchmark evaluates identification accuracy, computational cost, and sensitivity to initialization, network architecture, and measurement availability. Increasing network capacity improves PINN accuracy, whereas FEINN exhibits lower sensitivity to architecture and initialization and benefits from mesh refinement. FEINN also requires less computational time and provides more consistent results. For the present benchmark, these results demonstrate that FEINN provides a more efficient and stable framework for inverse material identification under limited-measurement conditions.
