Deep learning-driven performance prediction and design of high-DoF MEMS resonators.

The design of microelectromechanical systems (MEMS) resonators has long been hindered by high computational costs and restricted structural degrees of freedom. This study introduces a structural design framework based on a residual network-enabled solver (ResNES) for rapid physical performance prediction and efficient optimization of MEMS resonators. The resonant frequencies of in-plane vibration modes are employed as the representative physical properties to demonstrate the complete design workflow. A stochastic topology generation strategy is proposed to efficiently create diverse resonator designs by batch-generating elastic beams with high degrees of freedom (DoF) within a defined design space. Systematic evaluations reveal that fully-trained ResNES achieves a computational speed improvement of nearly three orders of magnitude compared to the finite element method (FEM), enabling millisecond-scale physical performance prediction with mean errors below 3%. The discrepancy between ResNES predictions and experimental measurements remains below 5%, validating the framework's capability to bridge analysis and fabrication seamlessly. Furthermore, ResNES is integrated with a self-built particle swarm optimization algorithm to minimize resonant frequencies and maximize frequency spacing. Comparative analyses demonstrate that this collaborative optimization scheme enables multi-objective optimization, identifying optimal designs from tens of millions of potential topologies within minutes. Compared to conventional FEM-based methods, even when accounting for the time costs of data preparation and ResNES training, the collaborative optimization scheme reduces the overall design cycle by at least 70% while further improving physical performance metrics by 25%. This work establishes a scalable paradigm for intelligent MEMS structural design, advancing the development of high-performance MEMS devices.