MINN+VPA: magnetic field inversion neural network embedded volume-preserving algorithm

The magnetic inversion problem described by differential equations is an important research direction in plasma physics. Recently, neural networks have emerged as a widely used tool to address this problem. However, in the process of solving forward problem, structure-preserving algorithms have not been considered. In this study, we develop a framework of magnetic field inversion neural network embedded volume-preserving algorithm (MINN+VPA) by applying the volume-preserving algorithms to the forward problem, which is expressed by the charged particle dynamics. The divergence-free constraint of the magnetic field is also incorporated into the loss function to enhance the physical realism of the trained model. To evaluate the effectiveness and robustness of the MINN+VPA method, we apply it to three numerical experiments. For comparison, magnetic field inversion neural network embedded Runge-Kutta algorithm (MINN+RK) is implemented, and the numerical results confirm the superiority of MINN+VPA. Moreover, the framework of embedding structure-preserving algorithms in forward problems to construct neural networks can be extended to other types of inversion problems.