Interpretable physics-based hybrid modeling with improved BPNN and transfer learning for prediction and optimization of melt pool morphology in laser cladding

• An interpretable physics-informed hybrid model coupling Rosenthal–Gaussian theory with an improved BPNN. • A hybrid GSABO optimizer tunes the BPNN to model residuals, improving predictive accuracy and robustness. • The SHAP-based analysis quantifies parameter contributions and elucidates the physical sources of prediction errors. • A physics-guided transfer learning with L2-SP enables reliable cross-domain modeling in limited data regimes. • An NSGA-II-based multi-objective framework enables inverse design toward target melt pool morphology. In laser cladding, the morphology of the melt pool is a critical determinant of the geometric accuracy and metallurgical quality of the clad layer, making its prediction and optimization essential for process design and quality control. To overcome the limitations of conventional data-driven models, including low accuracy and poor interpretability under small-sample conditions, this study proposes an interpretable hybrid modeling approach that integrates a physical model with an improved back-propagation neural network (BPNN). First, a physical model combining a Rosenthal point heat source and a Gaussian surface heat source is established to derive analytical relationships between process parameters (laser power, scanning speed, and powder feed rate) and melt pool morphologies (width, depth, and height), with energy balance constraints ensuring physical consistency. Second, a hybrid Golden sine and Subtraction Average-Based Optimizer (GSABO) optimization strategy is applied to enhance the BPNN, enabling effective correction of residuals between the physical model predictions and experimental data. The SHapley Additive exPlanations (SHAP) method is further employed to interpret the contribution of each process parameter to prediction errors. Additionally, a transfer learning strategy is adopted to facilitate small-sample modeling across different materials and equipment, substantially improving the model’s generalization capability. Finally, a multi-objective optimization framework based on NSGA II is constructed to inversely optimize process parameters according to target melt pool morphologies. Experimental results demonstrate that the proposed physics-improved BPNN hybrid model outperforms traditional methods in prediction accuracy, interpretability, and transferability, offering an efficient and reliable solution for intelligent modeling and optimization of the laser cladding process.