The versatility across engineering applications, low production costs, and environmental sustainability position 3D printing as one of the most promising manufacturing technologies. Process parameters directly govern the quality of printed parts, making their optimization essential for performance enhancement. This paper explores how tensile strength and surface roughness of FDM-printed parts of thermoplastic polyurethane (TPU) can be optimized and predicted using Taguchi, RSM and ANN Models. Taguchi L27 orthogonal array design and ANOVA were used to test the effects of layer thickness (0.16, 0.2, 0.24 mm), infill density (40,60,80%), and infill pattern (Gyroid, Grid, Line) to achieve higher-the-better UTS and lower-the-better (Ra) per the ASTM D638 Type IV test. Optimal settings (LT 0.24 mm, ID 80%, IP Line) had a maximum UTS of 38.463 MPa, (LT 0.20 mm, ID 60, IP Grid) had a minimum RA of 1.88 µm, the infill pattern had the greatest effect on UTS (38.1 percent, p=0.043), and layer thickness had the greatest effect on RA (47.4 percent, p=0.010). The prediction was done using Response Surface Methodology (RSM) and Artificial Neural Network (ANN) model. ANN performed better than RSM with maximum prediction errors of 6.90 (UTS) and 6.49 (Ra) compared to the higher values of RSM, lower values of MSE, and an outstanding correlation coefficient of R = 0.99997. The validation of ANN on the experimental data indicated the high accuracy (MAE 0.011 UTS, 0.032 Ra) was achieved with the training of Levenberg-Marquardt (70-15-15 split), and the standard errors were low among all the runs. This combination of Taguchi design, RSM, ANOVA, and interpretable ANN modeling is a powerful scheme of optimization of the parameters of the FDM process when printing TPU, which improves the mechanical performance and the surface quality of the material in flexible engineering tasks.