Regional geomagnetic field modelling method based on a two-stage adaptive weight physics-informed neural network

SUMMARY Regional geomagnetic field models are used to delineate intricate details of the Earth’s magnetic field and have significant application value in precision navigation and geomagnetic exploration. However, traditional modelling methods often encounter challenges when applied to sparse data, leading to issues like low model resolution and accuracy, as well as limited generalizability. The recently developed physics-informed neural networks (PINNs), a powerful modelling tool, presents a viable alternative for regional geomagnetic field modelling. This study employed the PINNs method to construct a geomagnetic field model for satellite altitudes over the Chinese region, based on the Swarm satellite data set provided by the European Space Agency. An adaptive weight training method was used for the two-stage training process, involving an initial pre-training and subsequent fine-tuning of the model. Experimental verification shows that the proposed algorithm enhanced the model’s fidelity to physical laws, improved its resolution and prediction accuracy (reducing the root mean square errors for geomagnetic components to as low as 4 nT), and enhanced its generalizability, with the total field intensity F and the prediction accuracy of both the X- and Y-components demonstrating superiority over that of other traditional methods. Collectively, these advancements enable efficient regional geomagnetic field modelling while providing a foundation for more reliable and precise predictions.