  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.
