Intraventricular vector flow mapping (iVFM) seeks to enhance and quantify color Doppler in cardiac imaging. In this study, we propose novel alternatives to the traditional iVFM optimization scheme using physics-informed neural networks (PINNs) and a physics-guided nnU-Net-based supervised approach. When evaluated on simulated color Doppler images derived from a patient-specific computational fluid dynamics (CFD) model and in vivo Doppler acquisitions, both the approaches demonstrate comparable reconstruction performance to the original iVFM algorithm. The efficiency of PINNs is boosted through dual-stage optimization and pre-optimized weights. On the other hand, the nnU-Net method excels in generalizability and real-time capabilities. Notably, nnU-Net shows superior robustness on sparse and truncated Doppler data while maintaining independence from explicit boundary conditions. Overall, our results highlight the effectiveness of these methods in reconstructing intraventricular vector blood flow. The study also suggests potential applications of PINNs in ultrafast color Doppler imaging and the incorporation of fluid dynamics equations to derive biomarkers for cardiovascular diseases based on blood flow.