Physics-informed Diffusion Generation for Geomagnetic Map Interpolation

TL;DR

Geomagnetic map interpolation from scattered observations is challenged by measurement noise and the need to respect physical spatial smoothness. The authors propose PDG, a physics-informed diffusion generation framework that uses a physics-informed mask to guide diffusion and a kriging-inspired constraint to enforce spatial physics. On four real-world geomagnetic datasets, PDG achieves substantial accuracy gains, with interpolation error reduced by up to 80% compared with strong baselines, and ablation studies confirming the importance of each component. This work demonstrates a practical approach to integrate physical priors into diffusion models for geophysical data, with potential benefits for navigation, exploration, and precision positioning.

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.

Figures (2)

• Figure 1: The overall framework of PDG.
• Figure 2: High-precision geomagnetic map of dataset A-OutZ. The x-axis denotes longitude, and the y-axis denotes latitude.