## 1 Introduction
We take wave propagation for our case study as it is an essential phenomenon in engineering due to its ability to transfer energy and information through a medium without the bulk motion of the medium itself. Waves are a fundamental concept in many engineering disciplines. In particular, PINNs have been explored and applied to full waveform inversion (FWI) due to their ability to solve inverse problems with noisy inputs [20; 21; 22; 23]. The wave equation provides a mathematical framework for understanding and predicting how waves propagate through various physical systems. While numerous numerical methods have been developed for solving wave equations, the emergence of PINNs has garnered significant interest as a data-driven approach [24; 25; 26; 27]. We believe that transfer learning is a key technique to address the training difficulties for high-frequency and multi-scale problems. Transfer learning focuses on transferring knowledge between domains, aiming to enhance model performance in the target domain by leveraging the knowledge gained from the source [28]. Several research works show that the effectiveness of transfer learning comes not only from learning \"Good\" cross-domain feature representation [29; 30], but also lies in its ability to learn high-level statistics from source domain data [31]. Fine-tuning is perhaps the most widely used transfer learning technique in deep learning. This technique involves initializing the current model with weights learned from pre-training, then training part or all of these weights on the current task's data to save training time and accommodate smaller datasets, for example, applications in medical image analysis [32]. Recent work demonstrates that adversarial training in the source data can improve the ability of models to transfer to new domains [33]. For PINN, transfer learning involves training a network to solve the desired PDEs from an initial model [34]. It enables training PINNs with a reduced amount of data and training costs [35; 36; 37]. Moreover, it addresses the challenge of insufficient high-fidelity data in numerous scientific computing cases [38]. Through transfer learning, PINNs demonstrate their capability to effectively solve intricate PDEs, positioning themselves as a valuable tool in addressing complex engineering challenges, such as fracture mechanics [39] and flows in porous media [40]. In summary, this manuscript addresses these issues faced by PINNs when confronted with high-frequency and multi-scale problems. By investigating transfer learning and scrutinizing the performance of various optimizers, we aim to provide valuable insights into improving the efficacy and versatility of PINNs for challenging physical simulations. The rest of the paper is organized as follows: The second section briefly introduces PINNs, emphasizing the crucial components pertinent to our study. In the third section, we show two studies where transfer learning is employed to train PINNs for solving partial differential equations (PDEs) from low to high frequencies. Additionally, we explore best practices for selecting the base model. The final section summarizes our findings and offers conclusions while suggesting potential future research directions.