Simulating Vibrations of 1D-Continua with Oscillatory Physics-Informed Neural Networks (oPINN)

Abstract The oscillatory Physics-Informed Neural Network (oPINN) Machine Learning architecture is suggested and analyzed for simulating the oscillatory behavior of continua and to estimate eigenfrequencies and eigenmodes. The analysis suggests that oPINN gives stable and accurate results for both free and excited oscillations, also for cases in which the initial condition is non-harmonic and introduces discontinuous first derivatives. Compared to conventional PINN, oPINN leads to significant reduction in computational effort and great increase in both accuracy and stability. Moreover, the oPINN based solution better fulfills the energy conservation requirement compared to conventional predictor-corrector time integration schemes. This advantage is achieved by the application of second-order central differences both in the spatial and temporal domain.