This work proposes a physics-informed feature engineering approach to improve the predictive accuracy of surrogate models for problems in solid mechanics. The prediction of the maximum deflection of a thin square plate under a uniform load is considered as a case study. A dataset of 5000 samples was generated using the finite element method in Ansys Mechanical. This was followed by a physical validation based on the theory of small deflections, and invalid samples were discarded. A random forest regressor algorithm was used for the surrogate model, and its hyperparameters were optimized using RandomizedSearchCV. Two input feature architectures were compared: a baseline architecture (using fundamental physical parameters) and a physics-informed architecture (using complex engineering features, specifically relative flexibility K1 and cylindrical rigidity D). The results showed a significant increase in accuracy when using physics-informed features compared to the baseline approach. An analysis of feature importance confirmed the dominant role of K1 and the load p, which is fully consistent with theoretical mechanics. The obtained results demonstrate that feature engineering based on physical principles improves both the accuracy and interpretability of machine learning surrogate models.