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Extreme heat waves (HWs), defined here as periods when daily maximum temperature exceeds the 98th percentile for three or more consecutive days, pose a significant threat to public health. The extreme heat risk is particularly relevant to urban residents due to the urban heat island (UHI) effect and its synergistic interactions with HWs in some cities. Previous research on the interactions between UHI and HWs has focused on a single city or region, and both positive and negative interactions have been reported. The global patterns of interactions between UHI and HWs across various climate backgrounds, as well as their underlying mechanisms, remain unclear. Here, we simulate the global urban heat island intensity (UHII) from 1985 to 2013 using the Community Land Model (CLM). By conducting a global-scale analysis of interactions between UHII and HWs, we diagnose their spatial and diurnal patterns across different regions and climate zones. To identify and explain the key contributors to the UHI-HW interactions, we employ machine learning models (CatBoost) and the SHapley Additive exPlanations (SHAP) framework to quantify the contributions of local energy flux, climate background, and land surface characteristics. UHI-HW interaction is quantified as the difference between UHII during heatwave (HW) days and non-heatwave (NHW) periods. We find that the UHI-HW interaction, which peaks at 6 AM local solar time (LT), is more positive at night than during the day. We identify net longwave radiation as a strong indicator of the interaction, while humidity emerges as a key driver, alongside contributions from sensible heat flux and wind speed. However, the influence of these factors varies across different Köppen-Geiger climate zones. Our study provides new insights into the complex interaction between UHIs and heat waves, with implications for urban climate adaptation strategies in a warming world. The machine learning-based approach offers a novel method for attributing the spatial variability in UHI heat wave interactions to specific biophysical variables.