用物理约束神经网络实现高精度三维磁场重建
3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks
- 将麦克斯韦方程组融入损失函数，强制满足无散和无旋条件
- 仿真精度达10⁻⁴，实验达千分之一以内，较现有方法提升十倍
- 适合复杂环境中的传感器受限场景，如高能物理实验
在许多高精度物理实验中，对不可达区域的磁场精确重构至关重要。传统方法如球谐展开常受截断误差限制，精度不足。本文提出一种先进的物理信息神经网络（PINN）框架，用于高精度三维磁场映射。与常规数据驱动模型不同，该方法将麦克斯韦方程组直接嵌入损失函数，强制在整个域上满足无散和无旋条件。关键创新在于在测量点显式引入物理残差损失，确保物理一致性超越随机采样。仿真验证显示重建精度达10⁻⁴，较现有PINN基准提升十倍；使用自研线圈装置的实验验证表明，在环境条件下实现亚百分之一相对精度，达到10⁻³水平。该人工智能驱动方法为复杂实验环境中传感器受限的场监测与测量提供了鲁棒、高精度解决方案。
原文摘要 · Abstract (English)
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.
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