🤖 AI Summary
This work addresses the truncation errors inherent in conventional methods for three-dimensional magnetic field reconstruction in inaccessible regions by proposing a physics-informed neural network (PINN) framework that integrates Maxwell’s equations. The approach embeds the divergence-free and curl-free conditions of the magnetic field directly into the loss function, enforcing global physical consistency. Innovatively, explicit physical residual losses are introduced at measurement points, replacing traditional random collocation sampling and substantially enhancing model accuracy. Numerical simulations demonstrate reconstruction errors on the order of 10⁻⁴, representing a tenfold improvement over existing PINN-based methods. Experimental validation further confirms a relative accuracy better than 0.1% (approximately 10⁻³) under ambient conditions, meeting the stringent requirements of high-precision physical experiments.
📝 Abstract
Accurate reconstruction of magnetic fields in inaccessible regions is vital for many high-precision experiments in physics. Traditional methods, such as spherical harmonic expansion, often suffer from truncation errors that limit their precision. This study proposes an advanced Physics-Informed Neural Network (PINN) framework for high-precision 3D magnetic field mapping. Unlike conventional data-driven models, the proposed PINN integrates Maxwell's equations directly into the loss function, enforcing divergence-free and curl-free conditions across the entire domain. A key innovation is the inclusion of explicit physics-residual losses at measurement locations, ensuring rigorous physical consistency beyond random collocation sampling. Validation using simulated data achieves a reconstruction accuracy of $10^{-4}$, a tenfold improvement over existing PINN benchmarks. Furthermore, experimental validation using a custom coil assembly demonstrates robust reconstruction with sub-percent relative accuracy, reaching the $10^{-3}$ level under ambient conditions. This AI-driven methodology provides a robust, high-precision solution for field monitoring and measurement in complex experimental environments where direct sensor placement is restricted.