Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance

2026-03-06

AI Summary

This study addresses the non-uniqueness inherent in three-dimensional joint gravity-magnetic inversion, a challenge inadequately tackled by conventional methods and most machine learning models that yield only single-point solutions without characterizing the full solution space. To overcome this limitation, the work proposes a physics-informed probabilistic inversion framework that, for the first time, integrates rectified flow with Ginzburg–Landau (GL) theory. Leveraging the Noddyverse dataset, the approach incorporates a GL-based regularization term and a plug-and-play physics-guided module, combined with a variational autoencoder (VAE) to enable probabilistic reconstruction of subsurface density fields. The method effectively mitigates solution non-uniqueness, introduces a general-purpose physics-guided architecture, and releases the first open-source VAE model tailored for 3D density field inversion, thereby establishing a new paradigm and providing practical tools for geophysical inverse problems.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

Subsurface ore detection is of paramount importance given the gradual depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. One such promising new method is joint magnetic and gravitational inversion. Given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them remains an ill-posed inverse problem. Although joint inversion of multiple properties mitigates the non-uniqueness problem in magnetic and gravitational data, deterministic algorithms converge to a single regularized solution and thus do not capture the distribution of possible solutions. Similarly, most machine learning based techniques predict a single solution without modelling the entire distribution. In this paper, we introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.

Problem

• joint inversion
• gravity and magnetic data
• ill-posed inverse problem
• subsurface ore detection
• 3D density reconstruction

Innovation

• rectified flow
• Ginzburg-Landau regularizer
• joint inversion
• physics-informed generative modeling
• 3D density VAE