Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates

Abstract:Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented this http URL 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 this http URL 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 this http URL 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 this http URL 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 this http URL 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 this http URL 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.

Artificial Intelligence (cs.AI)

arXiv:2610.05375 [cs.AI]

(or arXiv:2610.05375v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.05375 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.