A Kriging-Informed Machine Learning Framework for Spatial Property Estimation

Accurate spatial prediction from sparse measurements is a fundamental challenge in geoscience applications, including reservoir characterization, environmental monitoring, and subsurface modeling. This study introduces a kriging-informed machine learning framework that integrates geostatistical methods with modern neural architectures to enhance prediction accuracy under data-scarce conditions. The approach augments sparse real measurements with a dense ordinary-kriging grid to generate synthetic training samples, constructing a spatial prior k(x,y) evaluated at arbitrary locations via inverse-distance weighting over kriged nodes. Input features combine centered coordinates (Xc,Yc), low-order polynomial terms (Xc2,Yc2,XcYc), and the kriging-based spatial prior k(x,y). Three established methods including Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Multilayer Perceptron (MLP) are benchmarked against the Kolmogorov–Arnold Network (KAN), an advanced model that replaces fixed activations with learnable univariate basis functions. Models are trained on 60% of data using a multi-fidelity strategy (synthetic + real with 10× replication) and evaluated on a held-out 40% test set. KAN achieves superior performance: test R2=0.934 (95% CI: [0.843, 0.967]), RMSE =133.89 (95% CI: [102.27, 163.69]), representing a 31% error reduction versus ordinary kriging alone (R2=0.859). Sensitivity analysis across synthetic-to-real ratios (3:1 to 10:1) confirms robust performance (R2=0.934±0.002), and five-fold cross-validation yields consistent generalization (R2=0.876±0.098). The framework is generalizable to spatial estimation tasks with sparse measurements and demonstrates that hybrid geostatistical-machine learning approaches achieve accurate, stable predictions from limited field data.