In this work, we present different deep learning-based digital pre-distorters and compare them based on their performance towards improving the linearity of highly non-linear power amplifiers. The simulation results show that BiLSTM based DPDs work the best in terms of improving the linearity performance. We also compare two methodologies of direct learning and indirect learning to develop deep learning-based digital pre-distorters (DL-DPDs) models and evaluate their improvement on the linearity of Power Amplifiers (PA). We carry out a theoretical analysis on the differences between these training methodologies and verify their performance with simulation results on class-AB and class-F⁻¹ PAs. The simulation results show that both the learning methods lead to an improvement of more than 12 dB and 11dB in the linearity of class-AB and class-F⁻¹ PAs respectively, with indirect learning DL-DPD offering marginally better performance. Moreover, we compare the DL-DPD with memory polynomial models and show that using the former gives a significant improvement over the memory polynomials. Furthermore, we discuss the advantages of exploiting a BiLSTM based neural network architecture for designing direct/indirect DPDs. We demonstrate that BiLSTM DPD can be used to pre distort signals of any size without the drop in linearity. Moreover, based on the insights we develop a frequency domain loss using which further increased the linearity of the PA.