Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning
This addresses a robustness problem for researchers and practitioners using PINNs for complex differential equations, though it is incremental as it builds on existing PINN methods.
The paper tackles the training failure issue of Physics-Informed Neural Networks (PINNs) in high-frequency and multi-scale problems by using transfer learning, resulting in effective training without increasing network parameters, requiring fewer data points and less training time.
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.