Inverse design of MEMS micro-beam resonators using physics-guided machine learning framework

Abstract This paper presents a physics-guided machine learning (PGML) framework for the inverse design of Microelectromechanical systems (MEMS) micro-beam resonators. By embedding physical domain knowledge directly into a deep neural network architecture, the proposed method allows for accurate and efficient prediction of key physics parameters of the resonator—including length, width, thickness, gap, excitation voltage and detection voltage—based solely on specified target resonance frequencies. To ensure the physical reliability and consistency of the training data, a high-fidelity dataset was generated through COMSOL-MATLAB co-simulation, capturing the complex electromechanical behavior of the micro-beams under various geometric configurations. The neural network model is trained using the mean squared error loss function, enabling it to learn precise mappings from frequency inputs to geometric outputs. Extensive testing demonstrates that the model achieves high prediction accuracy across a broad frequency range from 0.1 MHz to 0.6 MHz, with less than 10% error over the entire range. Furthermore, the paper demonstrates a complete end-to-end workflow, beginning with the inverse design step where target resonance frequencies are input to predict the corresponding micro-beam dimensions. These predicted geometric parameters are then used to fabricate MEMS resonator devices, which undergo experimental testing to validate the model’s predictions. The experimental results closely match the predicted values, confirming both the accuracy and practical applicability of the PGML framework for MEMS resonator design.