Clinical investigations on atrial fibrillation, the most common cardiac arrhythmia, are based on computational models of the cardiac electrophysiology. Accurate high fidelity models are costly and have limited applicability in the clinical setting, where patient-specific in-silico assessments need to meet the practical time constraints. To speed up the computations, less accurate but faster low fidelity models could be employed. In this work, we develop two low fidelity models for atrial fibrillation that approximate the monodomain high fidelity model. One low fidelity model is based on the eikonal model, that we adapt to handle the re-entries that characterize atrial fibrillation. This model includes the restitution properties computed from the high fidelity model and handles anisotropy. The other low fidelity model is based on a coarser discretization of the computational domain. In this model the coarsening of the underlying atrial model is properly defined and the conduction velocity is adjusted. We assess the similarity of the low fidelity approximations to the high fidelity results in quantitative and qualitative studies and we explain the discrepancies. The accuracy of the low fidelity models depends on the considered metric. Here the main focus is on the inducibility of atrial fibrillation. The characterization of the atrial regions where the arrhythmia can be induced provides information for the evaluation and the design of the ablation treatment. Personalized inducibility maps can be obtained with a multi-fidelity method. The multi-fidelity approach, in which the high fidelity model and a correlated low fidelity model are combined, leads to a speed-up compared to single-fidelity approaches. The eikonal low fidelity model shows a poor agreement to the high fidelity model in terms of atrial fibrillation inducibility. However, its qualitative accuracy in simpler numerical experiments and its very low cost (potentially real-time) make it attractive. This motivates our future interest in optimizing the implementation and in reducing the discrepancies to the high fidelity model. Instead, the low fidelity model based on a coarser discretization highly agrees to the high fidelity model on the atrial fibrillation inducibility. Moreover, thanks to this high correlation, it performs well in the multi-fidelity framework.