On Training Physics-Informed Neural Networks for Oscillating Problems

Physics-Informed Neural Networks (PINNs) offer an efficient approach to solving
partial differential equations (PDEs). In theory, they can provide the solution to
a PDE at an arbitrary point for the computational cost of a single forward pass
of a neural network. However, PINNs often pose challenges during training, ne-
cessitating complex hyperparameter tuning, particularly for PDEs with oscillating
solutions. In this paper, we propose a PINN training scheme for PDEs with oscil-
lating solutions. We analyze the impact of sinusoidal activation functions as model
prior and incorporate self-adaptive weights into the training process. Our experi-
ments utilize the double mass-spring-damper system to examine shortcomings in
training PINNs. Our results show that strong model priors, such as sinusoidal
activation functions, are immensely beneficial and, combined with self-adaptive
training, significantly improve performance and convergence of PINNs.