The Modulated Grating Y-branch (MG-Y) tunable semiconductor laser stands out due to its short tuning time, wide tuning range, and high output power, making it a core device in the field of optical fiber sensing. However, achieving rapid and accurate quasi-continuous wavelength tuning within the tuning range of MG-Y lasers poses challenges, particularly in terms of the efficiency and accuracy of generating control parameter tables. Traditional wavelength tuning methods rely on spectrometers for wavelength acquisition, which are time-consuming and costly, failing to meet the demands of high-precision optical fiber sensing applications.To address these issues, this paper proposes a rapid quasi-continuous wavelength tuning method for MG-Y lasers based on the Deep Residual Shrinkage Network (DRSN). This method aims to collect optical power through Photodiodes (PD) instead of spectrometers for wavelength acquisition, combined with the DRSN model to rapidly generate high-precision control parameter tables, thereby realizing fast and accurate tuning of MG-Y lasers to meet the high-precision requirements of optical fiber sensing demodulation applications.The proposed method improves the process of control parameter table generation for MG-Y lasers. Instead of using wavelength meters, we employ photodiodes for collecting output optical power data, drastically reducing the data acquisition time from minutes to mere seconds. This significant speedup paves the way for more efficient subsequent processing steps. At the heart of our approach lies the DRSN model, which is specifically designed to rapidly classify the current tuning regions of the MG-Y laser. The model is trained on an extensive dataset comprising control currents, output optical power measurements, and precisely labeled tuning regions. The DRSN architecture incorporates residual modules, which alleviate the degradation problem commonly encountered in deep neural networks, ensuring that the model's performance remains stable as it grows deeper. Furthermore, the introduction of Residual Shrinkage Building Units (RSBUs) within the DRSN model effectively suppresses noise and enhances the model's generalization capabilities, resulting in more robust classifications. Once the tuning regions are classified, we employ the Lagrange interpolation method to generate high-precision control parameter tables. This approach ensures that the resulting tables enable precise and stable wavelength tuning across the entire tuning range of the MG-Y laser.To validate the effectiveness of the MG-Y laser control parameter table constructed using the DRSN model in practical engineering applications, accuracy experiments were conducted first. The stability and accuracy of the laser output wavelength under the control of this parameter table were verified using an ATLS7503 laser and an AQ6151 wavelength meter with a measurement accuracy of 0.3 pm. The deviation between actual and target wavelengths was within 1 pm, with a standard deviation of 0.28 pm. Subsequently, a Fabry-Perot (F-P) etalon wavelength demodulation experiment was performed to verify the effectiveness of the control parameter table in a laboratory environment. The wavelength standard deviation of the 51 transmission peaks of the F-P etalon was within 1.8 pm. Finally, strain demodulation experiments were conducted on two strain FBGs, with errors consistently below 1 με across 21 different strain conditions, and the standard deviation was consistently below 0.6 με. The result has been demonstrated that the control parameter table generated using the proposed method can be effectively applied to fiber optic sensing systems, showing excellent practical utility. The proposed method excels in improving control parameter table generation efficiency and accuracy, meeting the high-precision requirements of optical fiber sensing demodulation applications. In the future, this method is expected to be further promoted and applied in a broader range of optical fiber sensing fields.