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

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.This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Copyright (c) the Developers. See the COPYRIGHT.txt file at the top-level directory of this distribution. **For the sake of clarity and the rights carried by this license, Qnami AG grants to the user a non-exclusive, free and non-commercial license on all patents filed in its name relating to the open-source code (the "Patents") for the sole purpose of evaluation, development, research, prototyping and experimentation.** If you wanna collaborate or have questions please contact one of the contributors. For AI related questions: Adrien Dubois. For physics related questions: David Broadway. For (commercial) license related question: Alexander Stark