Full Waveform Inversion (FWI) reconstructs high-resolution subsurface models via multi-variate optimization but faces challenges with solver selection and data availability. Deep Learning (DL) offers a promising alternative, bridging data-driven and physics-based methods. While FWI in DL has been explored in the time domain, the pseudo-spectral approach remains underutilized, despite its success in classical FWI. This thesis integrates pseudo-spectral FWI into DL, formulating both data-driven and theory-guided approaches using Deep Neural Networks (DNNs) and Recurrent Neural Networks (RNNs). These methods were theoretically derived, tested on synthetic and Marmousi datasets, and compared with deterministic and time-domain approaches. Results show that data-driven pseudo-spectral DNNs outperform classical FWI in deeper and over-thrust regions due to their global approximation capability. Theory-guided RNNs yield greater accuracy, with lower error and better fault identification. While DNNs excel in velocity contrast recovery, RNNs provide superior edge definition and stability in shallow and deep sections. Beyond enhancing FWI performance, this research identifies broader applications of DL-based inversion and outlines future directions for these frameworks.