Machine Learning-Enhanced Prediction of Lunar Crescent Visibility for Unified Hijri Calendar Determination: A Global and Regional Framework

The lunar Hijri calendar governs religious observances for approximately 1.9 billion Muslims worldwide, yet disunity in crescent sighting criteria leads to inconsistent Ramadan and Eid dates across regions. Traditional visibility criteria (Yallop, Odeh) rely on simplified parametric approximations that inadequately capture complex atmospheric and geographical interactions. This study develops and validates a machine learning-enhanced framework for predicting lunar crescent visibility to support unified Hijri calendar determination through global and regionally-adapted models. A comprehensive dataset of 7,488 observations spanning 13 years (2013–2025) across 24 countries and five geographical regions was compiled. Feature engineering created 15 predictive parameters including interaction terms and composite indices. Eight supervised learning algorithms were evaluated with hyperparameter optimization using randomized search, genetic algorithms, and particle swarm optimization. Ensemble methods including voting, stacking, and hybrid configurations were developed and validated using 5-fold cross-validation. Findings: The hybrid ensemble model achieved superior performance (AUC 0.906, F1-score 0.888), outperforming traditional criteria by 17–19%. Engineered interaction features (elongation × altitude, lag time × altitude) demonstrated highest predictive importance. Regional analysis revealed visibility rate variations from 97.7% (Oceania) to 98.7% (Asia), supporting geographically-calibrated models. Long-term Ramadan predictions (2027–2075) confirmed the 33-year lunar cycle with mean interval of 354.37 days. Conclusion: Machine learning provides robust, evidence-based crescent visibility prediction that exceeds traditional criteria accuracy while capturing complex parameter interactions. The framework supports both global unification and region-specific applications. Recommendation: Religious authorities should adopt probabilistic, multi-model ensemble predictions with confidence scoring for calendar determination, supported by continuous validation against global observational networks.