  Many industrial and real life problems exhibit highly nonlinear periodic
behaviors and the conventional methods may fall short of finding their
analytical or closed form solutions. Such problems demand some cutting edge
computational tools with increased functionality and reduced cost. Recently,
deep neural networks have gained massive research interest due to their ability
to handle large data and universality to learn complex functions. In this work,
we put forward a methodology based on deep neural networks with responsive
layers structure to deal nonlinear oscillations in microelectromechanical
systems. We incorporated some oscillatory and non oscillatory activation
functions such as growing cosine unit known as GCU, Sine, Mish and Tanh in our
designed network to have a comprehensive analysis on their performance for
highly nonlinear and vibrational problems. Integrating oscillatory activation
functions with deep neural networks definitely outperform in predicting the
periodic patterns of underlying systems. To support oscillatory actuation for
nonlinear systems, we have proposed a novel oscillatory activation function
called Amplifying Sine Unit denoted as ASU which is more efficient than GCU for
complex vibratory systems such as microelectromechanical systems. Experimental
results show that the designed network with our proposed activation function
ASU is more reliable and robust to handle the challenges posed by nonlinearity
and oscillations. To validate the proposed methodology, outputs of our networks
are being compared with the results from Livermore solver for ordinary
differential equation called LSODA. Further, graphical illustrations of
incurred errors are also being presented in the work.
