Adaptive Lag Binning and Physics-Weighted Variograms: A LOOCV-Optimised Universal Kriging Framework with Trend Decomposition for High-Fidelity 3D Cryogenic Temperature Field Reconstruction

Biobanks rely on ultra-low-temperature (ULT) storage for irreplaceable specimens, where precise 3D temperature field reconstruction is critical to preserve integrity. This is the first study to apply geostatistical methods to ULT field reconstruction in cryogenic biobanking systems. We address critical gaps in sparse-sensor environments where conventional interpolation fails due to vertical thermal stratification and non-stationary trends. Our physics-informed universal kriging framework introduces (1) the first domain-specific adaptation of universal kriging for 3D cryogenic temperature field reconstruction; (2) eight novel lag-binning methods explicitly designed for sparse, anisotropic sensor networks; and (3) a leave-one-out cross-validation-driven framework that automatically selects the optimal combination of trend model, binning strategy, logistic weighting, and variogram model fitting. Validated on real data collected from a 3000 L operating cryogenic chest freezer, the method achieves sub-degree accuracy by isolating physics-guided vertical trends (quadratic detrending dominant) and stabilising variogram estimation under sparsity. Unlike static approaches, our framework dynamically adapts to thermal regimes without manual tuning, enabling centimetre-scale virtual sensing. This work establishes geostatistics as a foundational tool for cryogenic thermal monitoring, with direct engineering applications in biobank quality control and predictive analytics.