In recent decades, the intensification of meteorological droughts has significantly impacted semi-arid and arid regions, including Iran. This study aims to develop a high-accuracy simulation framework for the Standardized Precipitation Index (SPI) at 1-, 3-, and 6-month timescales (SPI-1, SPI-3, and SPI-6), using 40 years (1980-2019) of ERA5 precipitation data. Fourteen climatic predictors were employed to simulate SPI values using two machine learning approaches: a Deep Neural Network (DNN) and a hybrid model combining DNN with the Discrete Wavelet Transform (DNN-Wavelet). Evaluation across multiple metrics confirmed that the DNN-Wavelet model consistently outperformed the standalone DNN model by effectively capturing both temporal and frequency-domain features. Predictor importance analysis using Shapley Additive Explanations (SHAP) identified dew point temperature, mean sea level pressure, and evaporation rate as the primary drivers of SPI variations. In addition, multiscale wavelet analysis and Bivariate Wavelet Coherence (BWC) revealed strong time-frequency correlations between SPI drought indices and key climatic variables. The proposed DNN-Wavelet model shows strong potential as a reliable approach for simulating drought conditions, particularly in data-scarce and drought-prone regions such as Iran. Its application can enhance understanding of drought dynamics and support strategic and sustainable water resource planning.