Untrained physically informed neural network for image reconstruction of magnetic field sources

TL;DR

This paper introduces a physically informed neural network approach for efficiently reconstructing magnetic source configurations from stray field measurements, improving accuracy and robustness over traditional methods.

Contribution

The paper presents a novel neural network method with physics-based loss functions for inverse magnetic field reconstruction, reducing numerical artefacts and enhancing robustness.

Findings

Significant improvement over traditional reconstruction methods

Robust to different magnetisation directions and measurement orientations

Applicable to various measurement techniques beyond the demonstrated case

Abstract

Predicting measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying source-configuration based on measurement data. A key difficulty arises from the fact that such reconstructions often involve ill-posed transformations and that they are prone to numerical artefacts. Here, we develop a numerically efficient method to tackle this inverse problem for the reconstruction of magnetisation maps from measured magnetic stray field images. Our method is based on neural networks with physically inferred loss functions to efficiently eliminate common numerical artefacts. We report on a significant improvement in reconstruction over traditional methods and we show that our approach is robust to different magnetisation directions, both in- and out-of-plane, and to variations of the magnetic field measurement axis orientation. While we showcase the performance of our method using magnetometry with Nitrogen Vacancy centre spins in diamond, our neural-network-based approach to solving inverse problems is agnostic to the measurement technique and thus is applicable beyond the specific use-case demonstrated in this work.