Performance analysis of physics-informed neural networks for a damped forced oscillator system

Abstract

Physics-informed neural networks (PINNs) are a recently developed class of neural networks (NNs) that integrate previous or expected knowledge of a model to the traditional NN architecture, allowing greater predictive power. In this study, we developed PINNs for a two-degree-of-freedom system of damped forced oscillations of two masses, designed to solve for the three damping coefficients of the system using time-series data of the positions and the forces on each mass. We evaluated the performance of the PINNs for different choices of initial guesses for the damping coefficients, sparsity of training data, and levels of random noise added to the training data. Observed values of the root-mean-squared error of the predicted displacements showed the expected increasing trend with the deviation of initial guesses. Interestingly, we found that the predictions are more accurate when random noise is added to the training data and when the data is sparse, in contrast with naive expectations. These findings suggest that applying less tight constraints on the PINN allows it to explore the parameter space more fully and find a more optimal solution, rather than being strong anchored by the initial parameter guesses. We recommend further investigation on this behavior to gain insights that could be generally applicable for optimizing PINN architectures for time-series predictions.