Physics Informed Neural Network for Solution of Duffing Oscillators

Physics Informed Neural Networks (PINNs) have shown promising results for solving forward and inverse problems of dynamical systems represented as partial differential equations. Their elegant formulation enables excellent solution approximation for forward dynamics along with simultaneous system parameter identification for inverse dynamic problems. The present paper discusses the performance of PINNs to find the approximate solution of systems governed by non-linear duffing oscillators under different forcing conditions. The use of periodic and non-periodic activation functions for the neural network has been studied and compared, and it was seen that periodic activation functions had good convergence and accuracy. The PINN approach was seen to have a very good performance in approximating the solution of non linear duffing oscillators, but are limited by the spectral bias a common problem encountered by neural networks, where the high frequency components are learned much slowly than the low frequency components.