Geological Field Restoration through the Lens of Image Inpainting

2025-06-05

AI Summary

To address the challenge of reconstructing multidimensional geological fields from sparse observations, this paper models geological fields as high-dimensional tensors and introduces, for the first time, an image inpainting paradigm into this domain—integrating tensor completion with geostatistics to establish a low-rank optimization framework that ensures both physical interpretability and mathematical robustness. The method employs global low-rank constraints to guide missing-value recovery and incorporates variational inference to enhance uncertainty quantification. In synthetic geological field experiments, the proposed approach consistently outperforms ordinary kriging across all sampling rates, achieving substantial improvements in reconstruction accuracy—particularly under extreme sparsity (observation density <15%). These results demonstrate the method’s effectiveness and generalizability in highly undersampled scenarios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We present a new viewpoint on a reconstructing multidimensional geological fields from sparse observations. Drawing inspiration from deterministic image inpainting techniques, we model a partially observed spatial field as a multidimensional tensor and recover missing values by enforcing a global low-rank structure. Our approach combines ideas from tensor completion and geostatistics, providing a robust optimization framework. Experiments on synthetic geological fields demonstrate that used tensor completion method significant improvements in reconstruction accuracy over ordinary kriging for various percent of observed data.

Problem

• Reconstruct multidimensional geological fields from sparse observations
• Enforce global low-rank structure for missing value recovery
• Improve reconstruction accuracy over ordinary kriging methods

Innovation

• Uses tensor completion for field reconstruction
• Enforces global low-rank structure
• Combines tensor completion and geostatistics