## 1 Introduction
When beam parameters are unknown, a physics- and data-driven PINN can determine the beam response with minimal monitored data. When the training data are incomplete, the performance of PINNs often surpasses that of existing data-driven DL networks [13]. Although PINN has demonstrated significant potential in addressing computational physics problems involving sparse, noisy, unstructured, and multi-fidelity data, they still encounter numerous challenges when it comes to structural vibration problems under moving loads. PINN can only serve as a solver for specific parameter domains. When it comes to predicting dynamic responses over a broad range of parameter domains, the stability of PINN is not satisfactory. Each minor adjustment to the model means that retraining is necessary, a limitation that undoubtedly increases computational costs and makes it inconvenient to apply to practical engineering [20]. Constructing PINN-based surrogate models is seen as a way to enhance prediction generalization across broad parameter spaces [21; 22; 23]. Traditional PINN-based surrogate models can make wide-ranging predictions across parameter spaces by dynamically combining input parameters. However, these models face three key practical limitations: First, they struggle with computational efficiency as more parameters are added. This \"dimensionality problem\" becomes especially serious in complex cases like tuning multiple hyperparameters together, modeling interacting physical systems, or simulating time-dependent processes. The computational load grows much faster than for simpler PINN models. Second, the models need large amounts of training data to work accurately. Their prediction quality depends heavily on having enough data points covering the parameter space. With too little data, errors become much larger at the edges of the parameter range. The problem gets worse for systems with multiple scales or sudden physical changes. Most importantly, to work across all possible parameter values, the models must simplify the underlying physics. They use less complex versions of the governing equations and are less strict about satisfying physical laws exactly. While this helps the models fit data overall, it leads to bigger mistakes when dealing with special cases like sharp boundaries or critical parameter values where the physics changes suddenly. These limitations reduce how much we can trust the models in realistic, complex situations. Based on the above considerations, our study addresses these challenges by developing a novel transfer learning [24; 25]-enhanced PINN framework that strategically combines localized physical modeling with data-driven generalization. This hybrid approach enables accurate prediction of steady-state beam responses under moving loads across broad parameter ranges while significantly reducing the experimental or computational data needed for model training--a crucial advancement for practical engineering applications where comprehensive parameter testing is often infeasible. The proposed methodology begins by establishing local PINN models trained on displacement data obtained at strategically distributed points throughout the parameter space. These sampled points form the source domain, with their immediate adjacent regions designated as target domains. Leveraging transfer learning techniques, the initially trained source domain models undergo systematic refinement to achieve proper adaptation to each corresponding target domain. Ultimately, predictions generated by all localized PINN models across both source and target domains are integrated to construct a comprehensive PINN-based surrogate model capable of representing the system's behavior across the full parameter spectrum. Transfer learning can significantly reduce the required input data volume for target domain tasks [26; 27]. However, the transfer strategies employed in transfer learning can substantially impact the predictive performance of the resulting target domain models [28; 29; 30].