Novel design of recurrent neural network for the dynamical of nonlinear piezoelectric cantilever mass–beam model

Piezoelectricity spans a wide range of fields, showcasing its practical significance. In the realm of consumer electronics, piezoelectric materials are utilized in buzzers, sensors, and actuators. These components find applications in everyday devices such as mobile phones, wearable gadgets, and home appliances. The aim of study is to present a novel design of layered recurrent neural network (LRNNs) for solving nonlinear piezoelectric cantilever mass–beam (PE-CMB) model representing the excitation frequency dynamics. The proposed PE-CMB model is mathematically represented with highly nonlinear second-order differential system. The synthetic dataset is created using Adams numerical scheme for piezoelectric cantilever beam system, and the data are randomly segmented for training samples to formulate the network and testing samples to record performance on unbiased data and validation samples for controllability of adaptive procedure of training the weights to approximate the solutions of PE-CMB with LRNNs. The efficiency and consistent performance of the LRNNs design are validated through an evaluation process encompassing measures such as achieved accuracy using mean squared error-derived cost functions, plots illustrating learning curves, adaptively controlled parameters, solution dynamics along with associated error analysis, and a statistical analysis involving distribution of error for each instances via histograms and regression metric.