Efficient Inversion of Multiple Magnetic Dipole Models Based on Deep Learning Prior Analysis and Penalty Function Optimization

The inversion of multiple magnetic dipoles plays a critical role in applications such as geological exploration and spacecraft magnetic modeling. The primary challenges include an unknown number of magnetic sources, high sensitivity to noise, and low inversion accuracy. In this article, we propose a novel 3-D inversion method for multiple magnetic dipole models that integrates deep-learning-based prior analysis with a penalty function optimization strategy. A lightweight convolutional attention network, termed magnetic-gradient-tensor-invariant net (MGTI-Net), is developed to extract prior information from the invariants of the magnetic gradient tensor, thereby enabling accurate identification of the dipole count and providing preliminary estimates of their positions. By incorporating a penalty function into an improved least squares estimation framework, the proposed method robustly inverts the spatial positions and magnetic moments of the dipoles. Simulation results demonstrate that MGTI-Net can reliably determine the number of dipoles in a 3-D space and maintain a classification accuracy above 75% even under 50% relative random noise interference. Moreover, the improved least squares estimation can constrain the position and magnetic moment errors within 0.01 m and 0.1 A ⋅ m2, respectively, under 15% relative noise, reducing the error by more than one order of magnitude compared with conventional least squares methods. Experimental findings corroborate the simulation analysis, confirming that the new approach can accurately recover magnetic source parameters.