Integrating physics into data-driven modeling allows utilizing validated engineering knowledge in machine learning (ML) regression tasks to enhance physical consistency and data efficiency. This study presents a hybrid framework that combines an inaccurate physics-based process model for friction surfacing (FS)—a friction stir-based solid state layer deposition technique for metals—with an ML correction model. While the physics-based model provides an initial prediction based on a representation of fundamental physical relationships, inherent simplifications and assumptions introduce errors compared to experimental results. The ML model corrects these discrepancies, requiring fewer data points than using only a data-driven model without a physics-based model where fundamental physical relationships are already embedded. This approach reduces the number of required experiments, necessitating resources such as materials, energy, and time. The correction model is implemented with dimensionless inputs based on the Buckingham Pi theorem to reduce prediction inaccuracies and increase model generalization. The hybrid framework is applied to the FS process to predict the deposited layer geometry, specifically thickness and width. Key process parameters, that include force, rotation speed, traverse speed, maximum process temperature, and feed rate, serve as dimensionless inputs for training the ML model. A Smoothed-Particle Hydrodynamics model functions as the physics-based model, while a scarce experimental dataset provides the desired reference solutions for training. The values for thickness and width of the deposited layer from both experiments and simulations are used to compute a correction factor k which is the target solution of the ML model. The corrected simulation results, i.e. the predicted hybrid solutions, show excellent agreement with experimental measurements. Furthermore, the proposed hybrid model predicts results with enhanced prediction performance when compared with a purely data-driven model.