Physics-informed Diffusion Generation for Geomagnetic Map Interpolation

2026-01-31

AI Summary

Existing geomagnetic scattered-point interpolation methods often lack explicit modeling of underlying physical laws and are highly susceptible to noise, which limits their accuracy. To address this, this work proposes a Physics-guided Diffusion Generation (PDG) framework that innovatively integrates physical priors into the diffusion process. Specifically, PDG constructs a physics-informed mask via local receptive fields and enforces spatial covariance constraints derived from kriging theory, thereby simultaneously achieving denoising and physical consistency. Extensive experiments on four real-world geomagnetic datasets demonstrate that PDG significantly outperforms current state-of-the-art methods, yielding substantial improvements in both interpolation accuracy and physical plausibility.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Geomagnetic map interpolation aims to infer unobserved geomagnetic data at spatial points, yielding critical applications in navigation and resource exploration. However, existing methods for scattered data interpolation are not specifically designed for geomagnetic maps, which inevitably leads to suboptimal performance due to detection noise and the laws of physics. Therefore, we propose a Physics-informed Diffusion Generation framework~(PDG) to interpolate incomplete geomagnetic maps. First, we design a physics-informed mask strategy to guide the diffusion generation process based on a local receptive field, effectively eliminating noise interference. Second, we impose a physics-informed constraint on the diffusion generation results following the kriging principle of geomagnetic maps, ensuring strict adherence to the laws of physics. Extensive experiments and in-depth analyses on four real-world datasets demonstrate the superiority and effectiveness of each component of PDG.

Problem

• geomagnetic map interpolation
• physics-informed
• scattered data interpolation
• detection noise
• laws of physics

Innovation

• Physics-informed
• Diffusion Generation
• Geomagnetic Map Interpolation
• Kriging Constraint
• Noise-robust Interpolation