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

Amplifying Sine Unit: An Oscillatory Activation Function for Deep Neural Networks to Recover Nonlinear Oscillations Efficiently