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.

翻译：许多工业和现实问题表现出高度非线性的周期行为，传统方法可能难以找到其解析解或封闭形式解。这类问题需要具有更强功能且成本更低的前沿计算工具。近年来，深度神经网络因其处理大规模数据的能力和学习复杂函数的普适性而获得广泛研究关注。本文提出一种基于具有响应层结构的深度神经网络的方法，用于处理微机电系统中的非线性振荡问题。我们在设计的网络中集成了多种振荡和非振荡激活函数，如Growing Cosine Unit（GCU，增长余弦单元）、Sine（正弦）、Mish和Tanh，以全面分析它们在高非线性和振动问题中的性能。将振荡激活函数与深度神经网络相结合，在预测底层系统的周期模式方面表现更优。为支持非线性系统的振荡激励，我们提出一种新型振荡激活函数——放大正弦单元（ASU），其在处理微机电系统等复杂振动系统时比GCU更高效。实验结果表明，采用所提ASU激活函数的网络在应对非线性和振荡挑战时更可靠、更鲁棒。为验证所提方法，我们将网络输出与常微分方程求解器Livermore Solver for Ordinary Differential Equations（LSODA）的结果进行了对比，并在工作中提供了误差的图形化展示。