A data-efficient machine-learning-based structure-process co-optimization framework for Pirani vacuum sensors with diverse applications

Structure-process co-optimization is essential for sensor design, enabling simultaneous satisfaction of performance specifications and fabrication constraints while reducing development time and experimental cost. However, strong coupling and nonlinear interactions among design parameters make multi-objective optimization highly challenging. This work proposes a data-efficient machine-learning-based structure-process co-optimization framework for the automated synthesis of manufacturable Pirani vacuum sensors. Gaussian process regression serves as a surrogate model to predict key performance metrics, while particle swarm optimization explores the high-dimensional design space. Critical process limitations, including the deep reactive ion etching aspect ratio and buried-oxide-to-heater thickness ratio, are explicitly incorporated to ensure manufacturability. By flexibly configuring optimization objectives, the framework supports scenario-oriented designs, including high-vacuum detection, wide-range pressure sensing, and compact low-power operation. With limited technology computer-aided design simulations, the method rapidly converges to optimized structures that simultaneously satisfy performance targets and fabrication limits, providing a data-efficient and manufacturable solution for application-specific Pirani vacuum sensor design.