LSA-PINN: A new method based on Physics-Informed Neural Network with lightweight self-attention for solving modified Bloch equation

The Spin-Exchange Relaxation-Free (SERF) atomic magnetometers play an increasingly significant roles in cardiac and brain magnetometry fields, etc. For the SERF atomic magnetometer, the evolution and interaction with the magnetic field of atomic spins can be described by the Bloch equation. However, the traditional Bloch equation does not take into account the transport phenomena caused by the atomic density gradient within the vapor cell, which makes it unable to accurately reflect the polarization distribution in the vapor cell, thereby reducing the accuracy of magnetic field measurement. To achieve a more accurate representation of the evolution characteristics of the spatial distribution of the atomic ensemble, a diffusion term for the polarization strength is introduced into the Bloch equation. Furthermore, a new unsupervised Physics-Informed Neural Network (PINN) model with lightweight self-attention (LSA) module is proposed to solve the modified nonlinear equation. The introduction of LSA enhances the adaptive representational capability of PINN, enabling it to more effectively extract global features and consequently obtain more accurate numerical solutions of the Bloch equation. The experimental results show that LSA-PINN achieves a minimum loss value of 3.98×10^-2, which is 62 % lower than the traditional PINN. This study provides new insights and methods to address the limitations of traditional Bloch equation and gain a deeper understanding of system behavior.