Optimal Sensor Placement via a POD-QR Framework for High-Fidelity 3D Temperature Field Reconstruction in Large-Scale Ultra-Low Temperature Chest Freezers

) ULT chest freezers under stable operating conditions. To our knowledge, it is the first realization of high-fidelity cryogenic temperature field reconstruction coupled with sparse sensor layout optimization tailored to large-volume ULT chest freezers. First, high-resolution reference temperature fields were constructed via universal kriging interpolation, validated with leave-one-out cross-validation (LOOCV) to achieve mean absolute error (MAE) ≤0.67 °C and coefficient of determination R2>0.92. Principal component analysis (PCA) was then applied to training data to extract a tailored proper orthogonal decomposition (POD) basis. The first three principal components captured 99.8% of cumulative energy. Optimal sensor locations were determined via QR-column pivoting on the rank-3 POD basis, converging to a minimal configuration of 3 sensors (a 94% reduction from the 48-sensor full-scale setup). This sparse sensor network achieved exceptional reconstruction performance: grid-level MAE ≤0.079 °C and root mean squared error (RMSE) ≤0.093 °C against reference fields (R2≥0.999), while point-level validation against experimental measurements yielded MAE ≤0.502 °C and RMSE ≤0.842 °C (R2≥0.971). The results demonstrate that, for large-scale ULT chest freezers, the proposed data-driven approach is capable of automatically determining an optimal sparse sensor subset and enabling reliable 3D cryogenic temperature field reconstruction for efficient thermal monitoring. By resolving the trade-off between monitoring accuracy, space efficiency, and cost-effectiveness, this framework provides a scientifically rigorous alternative to empirical sensor deployment standards, offering practical scalability for cryogenic biobanking applications.