Ising Model for Interpolation of Spatial Data on Regular Grids.

Area of Science:

• Computational physics
• Data science
• Geostatistics

Background:

• Spatial data interpolation is crucial for various fields, including remote sensing and environmental science.
• Existing methods may struggle with non-Gaussian or complex spatial correlations.
• Accurate and efficient data gap filling remains a significant challenge.

Purpose of the Study:

• To introduce and evaluate the Ising model with nearest-neighbor correlations (INNC) for spatial data interpolation.
• To demonstrate the applicability of INNC for both classification and regression tasks on gridded data.
• To assess the performance of INNC against standard interpolation techniques.

Main Methods:

• Application of the Ising model with nearest-neighbor correlations (INNC) to spatial data.
• Utilizing Monte Carlo simulations conditioned on observed data for predicting values at unmeasured points.
• Approximating continuous variables by discretizing them into a user-defined number of classes for regression.
• Minimizing an energy measure of the data to ensure global consistency.

Main Results:

• INNC effectively interpolates spatially correlated data on regular grids.
• The method demonstrates strong performance in both classification and regression tasks.
• INNC shows competitive accuracy and computational efficiency compared to standard interpolation methods.
• The non-parametric nature of INNC makes it suitable for non-Gaussian datasets.

Conclusions:

• The Ising model with nearest-neighbor correlations (INNC) offers a robust and efficient approach for spatial data interpolation.
• INNC is a versatile tool for filling data gaps in gridded datasets, such as satellite imagery.
• This method provides a valuable alternative for handling complex spatial data where traditional methods may fall short.