用高斯过程回归快速估算无线充电磁场，实现交互式设计。

Wireless power transfer (WPT) with coupled resonators offers a promising solution for the seamless powering of electronic devices. Interactive design approaches that visualize the magnetic field and power transfer efficiency based on system geometry adjustments can facilitate the understanding and exploration of the behavior of these systems for dynamic applications. However, typical electromagnetic field simulation methods, such as the Method of Moments (MoM), require significant computational resources, limiting the rate at which computation can be performed for acceptable interactivity. Furthermore, the system's sensitivity to positional and geometrical changes necessitates a large number of simulations, and structures such as ferromagnetic shields further complicate these simulations. Here, we introduce a machine learning approach using Gaussian Process Regression (GPR), demonstrating for the first time the rapid estimation of the entire magnetic field and power transfer efficiency for near-field coupled systems. To achieve quick and accurate estimation, we develop 3D adaptive grid systems and an active learning strategy to effectively capture the nonlinear interactions between complex system geometries and magnetic fields. By training a regression model, our approach achieves magnetic field computation with sub-second latency and with an average error of less than 6% when validated against independent electromagnetic simulation results.