Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems. Through two case studies, we discovered that transfer learning can effectively train PINN to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We elaborately described our training strategy, including optimizer selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.

翻译：物理信息神经网络（PINN）是一种数据驱动的偏微分方程与常微分方程求解器，为正向与反问题求解提供了统一框架。然而，目标函数的复杂性常导致训练失败，这一问题在高频与多尺度问题中尤为突出。我们提出采用迁移学习来增强PINN训练的鲁棒性与收敛性：从低频问题开始训练，逐步过渡到高频问题。通过两个案例研究，我们发现迁移学习能够在不增加网络参数的前提下，有效训练PINN实现从低频到高频问题的近似求解，并且所需数据点与训练时间更少。我们详细描述了包含优化器选择的训练策略，并提出了利用迁移学习训练神经网络以求解更复杂问题的指导原则。