A Novel Comprehensive Parametric Macromodeling Method for MEMS Sensors Based on the Reduced-Order State-Space Models and Machine Learning Approaches

Transient characteristics are critical for the collaborative design of MEMS devices and interface circuits. However, traditional behavioral models often oversimplify transient dynamics, while interpolation-based parametric model order reduction (PMOR) suffers from the curse of dimensionality and grid constraints. Therefore, a novel comprehensive parametric macromodeling method based on an amalgamation of the reduced-order state-space models (SSMs) and machine learning (ML) for MEMS devices is proposed to parameterize the transient characteristics of the macromodel, referred to as the multi-channel matrix parameterization method (MMPM). This method can map structural parameters directly to system matrices, ensuring both high accuracy and seamless circuit simulator compatibility. Unlike black box ML models, MMPM preserves the physical state-space structure, enabling stable and efficient co-simulation. In MMPM, a multi-channel feed-forward neural network (FNN) is trained on a dataset of physically consistent reduced-order matrices to predict system dynamics under varying geometries. Taking a thermal flow sensor as an example, the method effectively parameterizes critical structural variables to capture full dynamic behaviors, including transient heating/response times and steady-state temperature differences. While the one-time offline construction of the parametric macromodel takes approximately 634.9 s, the subsequent online co-simulation is instantaneous (< 1.0 s), offering a speedup of orders of magnitude compared to finite element analysis (FEA). Validation results demonstrate an average relative error of less than 8.6%, proving that MMPM is a robust, scalable, and efficient approach for comprehensive MEMS macromodeling. [2025-0223]