The increasing demand for durable and sustainable asphalt pavements has led to the exploration of high-density polyethylene (HDPE) as a modifier in hot asphalt mixtures (HAMs). This study presents a comprehensive framework that integrates Deep Residual Neural Networks (DRNNs) and variance-based global sensitivity analysis (VBSA) to optimize HDPE-modified asphalt mixtures (HDPE-HAMs). By integrating experimental findings with well-documented research, the model’s accuracy and robustness were significantly enhanced, making it more reliable for predicting the performance of HDPE-HAMs across various settings. Preprocessing analysis, including statistical evaluation and correlation analysis, ensures the selection of the most relevant features, while postprocessing analysis using VBSA identifies dominant factors influencing performance. The proposed DRNNs model accurately predicted Marshall stability and flow with high reliability (R² = 0.94 and 0.91). The VBSA revealed that bitumen content, polymer additive percentage, and voids in mineral aggregate are the most influential parameters governing mixture performance. Laboratory results confirmed that incorporating 12% HDPE enhanced stability by 21%, reduced flow by 23%, and improved retained strength by 7% after moisture conditioning compared to the control mix. This data-driven approach not only advances asphalt mixture design but also provides a replicable framework for analyzing various pavement materials, promoting sustainable and cost-effective infrastructure development.