Background/Purpose <p>Although active material-based self-vibration systems have attracted considerable attention, predicting their behavior and addressing control challenges remains difficult.</p> Methods <p>To effectively tackle these issues, this article presents a method based on a backpropagation neural network for predicting the frequency and amplitude of a liquid crystal elastomer self-vibration system, as well as for inverse design. The system consists of a mass block and two liquid crystal elastomer strings. Based on the dynamic liquid crystal elastomer model, the dynamic governing equations of the liquid crystal elastomer self-vibrating system were established. By solving them using the fourth-order Runge–Kutta method, accurate solutions for the self-vibration frequency and amplitude under different parameter conditions were obtained and used to construct the training and testing datasets for the backpropagation neural network.</p> Results <p>The trained backpropagation neural network exhibited strong generalization capability when predicting previously unseen data. The results show that backpropagation neural networks can quickly and effectively predict system behavior. In addition, this study proposes a novel inverse design method that infers the system's parameter combinations from known amplitude and frequency values, significantly improving design efficiency.</p> Conclusion <p>Compared to traditional numerical methods, backpropagation neural networks can significantly reduce computational time. In contrast to other models such as deep convolutional neural networks or recurrent neural networks, backpropagation neural network offers a favorable balance between computational efficiency and predictive accuracy for small- to medium-sized datasets. Overall, this study provides deeper insights into the dynamics of self-vibrating systems and offers new strategies and theoretical foundations for their implementation and construction.</p>