<p>Hybrid models often referred to as gray-box models offer a promising approach by combining the flexibility of data-driven techniques with the accuracy and physical interpretability of first-principles models. This study evaluates a range of mathematical modeling techniques in the context of chemical reaction engineering, with a focus on the production of dimethyl ether (DME) from bio-methanol in a fixed-bed reactor. A comprehensive case study was conducted, beginning with the development of a first-principles model to solve a system of governing equations and generate 7,000 synthetic data points with added noise. Three black-box machine learning algorithms, including K-Nearest Neighbors (KNN), Gradient Boosting Regressor (GBR), and Extreme Gradient Boosting (XGB), were employed for predictive modeling. In parallel, hybrid modeling approaches were developed to estimate reaction rates and correct reactor outputs. Model performance was assessed using metrics such as mean squared error (MSE) and the coefficient of determination (R²), using key variables including the inlet molar flow rate, initial temperature, pressure, and the outlet concentrations of methanol, dimethyl ether, and water, as well as overall conversion. Results indicated that the data-driven models performed exceptionally well, with hybrid models offering comparable accuracy while maintaining interpretability. Finally, process optimization was performed using the Extreme Gradient Boosting model integrated with a Differential Evolution algorithm. The optimized operational conditions achieved a high dimethyl ether conversion rate of 84.3%, with a minimal temperature rise of 84.9&#xa0;K.</p>