The application of additive manufacturing technologies for producing parts from polymer composite materials has gained significant attention due to the ability to create fully functional components that leverage the advantages of both polymer matrices and fiber reinforcements while maintaining the benefits of additive technology. Polymer composites are among the most advanced and widely used composite materials, offering high strength and stiffness with low mass and variable resistance to different media. This study aims to experimentally investigate the impact of selected process parameters, namely, wall thickness, raster angle, printing temperature, and build plate temperature, on the flexural properties of carbon fiber reinforced polyamide (CFrPA) fused deposition modeling (FDM) printed samples, as per ISO 178 standards. Additionally, regression and artificial neural network (ANN) models have been developed to predict these flexural properties. ANN models are developed for both normal and augmented inputs, with the architecture and hyperparameters optimized using random search technique. Response surface methodology (RSM), which is based on face centered composite design, is employed to analyze the effects of process parameters. The RSM results indicate that the raster angle and build plate temperature have the greatest impact on the flexural properties, resulting in an increase of 51% in the flexural modulus. The performance metrics of the optimized RSM and ANN models, characterized by low MSE, RMSE, MAE, and MAPE values and high R2 values, suggest that these models provide highly accurate and reliable predictions of flexural strength and modulus for the CFrPA material. The study revealed that ANN models with augmented inputs outperform both RSM models and ANN models with normal inputs in predicting these properties.