Physics-Informed Neural Networks-Based Wide-Range Parameter Displacement Inference for Euler–Bernoulli Beams on Foundations Under a Moving Load Using Sparse Local Measurements

This study develops a novel physics-informed neural network (PINN) framework for predicting steady-state dynamic responses of infinite Euler–Bernoulli (E–B) beams on foundations under moving loads. By combining localized PINN modeling with transfer learning techniques, our approach achieves high-fidelity predictions across broad parameter ranges while significantly reducing data requirements. Numerical results show that the method maintains accuracy with less than half the training data of conventional PINN models (15 target domains) and remains effective with just four domains for approximate solutions. Key findings demonstrate that optimal spatial distribution—rather than quantity—of target domains ensures robustness against noise and parameter variations. The framework advances data-efficient surrogate modeling, enabling reliable predictions in data-scarce scenarios with applications to complex engineering systems where experimental data are limited.