Field reconstruction improved by combining local and global estimates
Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates
Artificial Intelligence
Summary
Many physical measurements are incomplete or have gaps, making it hard to see the full picture of what is happening. The authors developed a method that first guesses parts of the missing data locally and then improves these guesses by looking at a bigger picture. This approach helps them fill in gaps more accurately, especially in real-world ocean data where incomplete observations are common. Their method outperforms previous techniques by learning how local details fit into a global structure.
What this means in practice
- •For environmental monitoring teams: Generate more accurate maps of ocean conditions by filling in missing sensor data using locally informed global corrections.
- •For remote sensing engineers: Improve reconstruction of spatial fields from incomplete satellite or aerial sensor data by refining local estimates with global models.
Authors
Renhao Zhong, Zihan Zhou, Chiyuan Ma, Tianshu Yu
Abstract
Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented observations.Existing context--query work establishes how held-out observations provide valid training targets, but this does not make the complete-field distribution identifiable when every training field is incomplete.With finite data, weak evidence of sharp transitions and localized variations can further favor averaged predictions that attenuate local detail.A structural prior is therefore needed to favor plausible completions; local spatial relationships offer one grounded in the observations.We propose a locally constructed, globally revisable estimator that explicitly learns local field estimates and subsequently corrects them using full-domain observations.A shared coordinate-conditioned predictor learns from incomplete patches, allowing relatively well-observed neighborhoods to provide direct supervision of local structure.Its overlapping predictions are reconciled into an observation-conditioned consensus field.A full-domain estimator retains the original observations and learns a residual correction around this frozen field estimate, allowing locally constructed structure to be revised by broader evidence.The local estimate serves as both an explicit input, accompanied by its discrepancies with the observations, and a prediction starting point that the global model can revise.On three real-world ocean datasets with authentic observation gaps, our estimator achieves the lowest MSE and highest PSNR on withheld source-supported values, reducing MSE by 28.9\%--34.5\% against the strongest external baseline.