Analyzing the geometric dependence of thermoelastic Q-factor in micro hemispherical resonators via a data-augmented CNN-transformer model

The Q-factor dominated by thermoelasticity ( $${Q}_{{TED}}$$ ) is a non-negligible component of the total quality factor in high-performance design of Micro Hemispherical Resonators (MHRs). However, finite-element analysis (FEA) of $${Q}_{{TED}}$$ is prohibitively time-consuming. This paper presents a rapid and accurate prediction framework based on a hybrid CNN-Transformer model, enhanced by data augmentation via polynomial fitting of FEA simulation results. Ablation studies confirm the optimal architecture, where replacing the feed-forward network with a secondary multi-head self-attention mechanism yields the highest performance. Comparative experiments demonstrate that the proposed model surpasses mainstream prediction methods in both accuracy and robustness, with Monte Carlo Dropout verifying well-calibrated uncertainty. We systematically analyze the influence of geometric parameters (thickness T, height H, and anchor radius r) on $${Q}_{{TED}}$$ through the digital model and physical mechanisms. Results show that an optimal design for maximizing $${Q}_{{TED}}$$ is characterized by low $$H$$ , low $$r$$ , and high $$T$$ . Practical trade-offs and manufacturability considerations are discussed, recommending a low $$r$$ to reduce sensitivity to fabrication variations in $$T$$ and $$H$$ . The framework quickly improves computational efficiency compared to FEA, providing an efficient and reliable tool for the optimization and robust design of MHRs.