How Important Are the Critical Points in Selecting the Optimal Samples for Accurate Estimation of Subsurface Soil Moisture?

We propose a novel physics-aware sampling framework to extract the most informative training instances (critical points) from the conventional 70% training data set using six diversified sampling strategies. These critical points are used to train a spectral Fourier Neural Operator (FNO) augmented with a lagged term to predict subsurface soil moisture (20 and 40 cm) from near-surface observations (5 cm). This approach is evaluated at eight stations of the International Soil Moisture Network spanning two climatic regimes (Dwc: monsoon-influenced subarctic; and BWk: arid and cold desert) with hourly soil moisture measurements available at these depths. We demonstrate that judiciously selected training subsets achieve predictive accuracy comparable or even superior to the full-training-data baseline model. Uncertainty-based sampling is optimal for Dwc stations (with 10% training data). Distribution-based selection excels at BWk sites incorporating training proportions between 10% and 62% with minimal nRMSE. Temporal analysis of the selection of critical points reveals significant climatic controls.