Solar chimneys represent an effective passive ventilation technology capable of improving indoor thermal comfort while reducing building energy consumption. In this study, the thermal and fluid dynamic performance of a solar chimney integrated into a residential building located in Bordj Bou Arréridj (Eastern Algeria) was investigated through a comprehensive numerical, predictive, and optimization framework. A transient mathematical model was developed to evaluate the influence of key geometric parameters, including chimney width and inlet opening width, as well as environmental factors such as solar radiation intensity and wind speed, on the system performance. The generated simulation database was subsequently employed to develop and compare four machine learning models, namely, Artificial Neural Networks with Bayesian Regularization (ANN-BR), Deep Neural Networks optimized by Improved Grey Wolf Optimization (DNN-IGWO), k-Nearest Neighbors (KNN), and Extreme Gradient Boosting (XGBoost), for predicting eight output parameters including glazing temperature, fluid temperature, absorber temperature, outlet temperature, thermal efficiency, air change rate (ACH), mass flow rate, and outlet velocity. The results demonstrated that increasing chimney and inlet widths significantly enhances ventilation performance by increasing airflow rate and ACH. Weather conditions and wind speed were also found to strongly affect thermal efficiency and buoyancy-driven airflow. Among the predictive models, XGBoost and DNN-IGWO exhibited the highest predictive accuracy, achieving coefficients of determination ($R^2$) close to unity and very low prediction errors for all output variables, confirming their robustness and generalization capability. The proposed methodology provides a reliable tool for rapid performance prediction and design optimization of solar chimney systems under different climatic and operating conditions, thereby supporting the development of energy-efficient passive ventilation strategies for residential buildings.