Abstract: Electromagnetic wave propagation in magnetized plasma stands as a significant focal point in research. The effective formulation and precise resolution of equations to model electromagnetic plasma coupling within specific scenarios carry profound research significance and pose noteworthy challenges. These undertakings are pivotal in delving into the intricate mechanisms governing the nonlinear interaction between electromagnetic waves and plasma. This paper introduces a novel approach employing recurrent neural networks (RNNs) for both forward and backward modeling of electromagnetic plasma. The forward propagation process emulates the current density convolution finite difference time domain method (JEC-FDTD), accommodating arbitrary magnetic tilts. Consequently, it not only resolves targeted electromagnetic modeling issues but also offers the advantage of efficient computation through parallel processing. By establishing a forward-differentiable simulation process, our methodology adeptly leverages automatic differentiation techniques to precisely compute gradients. This enables us to effectively address inverse problems through network training. As a result, our approach harnesses observed time-domain scattered field signals to successfully deduce pivotal plasma parameters. Taking advantage of the optimization strategy and dedicated hardware support provided by deep learning, the method can be applied to electromagnetic modelling and plasma parameter inversion in various simulation scenarios.