Magnetic field mapping of inaccessible regions using physics-informed neural networks

Abstract

A difficult problem concerns the determination of magnetic field components within an experimentally inaccessible region when direct field measurements are not feasible. In this paper, we propose a new method of accessing magnetic field components using non-disruptive magnetic field measurements on a surface enclosing the experimental region. Magnetic field components in the experimental region are predicted by solving a set of partial differential equations (Ampere’s law and Gauss’ law for magnetism) numerically with the aid of physics-informed neural networks (PINNs). Prediction errors due to noisy magnetic field measurements and small number of magnetic field measurements are regularized by the physics information term in the loss function. We benchmark our model by comparing it with an older method. The new method we present will be of broad interest to experiments requiring precise determination of magnetic field components, such as searches for the neutron electric dipole moment.

Magnetic field regression using artificial neural networks for cold atom experiments

“…3 indicates a strong relation between the NN and Maxwell's equations, strengthening the claim that training the NN is equivalent to bringing the NN closer to the ideal hyperplane calculated from Maxwell's equations. Our observation is consistent with another early work, [30] which demonstrated that the solution of the Maxwell's equation can be approximated by the NN trained with sufficient amount of data around the target point. On the other hand, however, it is crucial to notice the NN can only approximate the ideal hyperplane but never reach it since their mathematical forms are fundamentally different.…”

“…Moreover, we systematically investigate the impact of the number of three-axis sensors at surrounding positions and the magnitude of the magnetic field on the performance of the method providing a practical guide for implementation. In contrast to previous works, [26][27][28][29][30] which predict the magnetic field vector across a wide experimental region, our goal in this work is to extrapolate the magnetic field vector at a specific position within an inaccessible region. Our approach provides a simple method for monitoring magnetic fields without requiring any prior knowledge of the solution of the Maxwell equation.…”

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

“…Conventional approaches can reduce the number of SC calculations by utilizing particle-in-cell methods, but state-of-the-art 3D CSR calculations still rely on point-to-point calculations 33 . Machine learning (ML) methods have demonstrated to be useful in non-invasive measurements and diagnostics of charged beams 34 and in the simulations of magnetic fields through physics-informed neural networks 35 . They have also been found to speed up lattice quantum Monte Carlo simulations 36 , the design and simulation of fin field‑effect transistors 37 , the simulation of spin dynamical systems 38 and finding the optimal ramp up for the production of Bose–Einstein condensates 39 .…”