Multi-physics computational models based on finite element analysis, offer detailed insights into the dynamics and metrics in the weld pool formed by laser welding. Conversely, data-driven surrogate models provide a cost-effective means to predict desired responses. These models establish statistical or mathematical correlations with input–output data, eliminating the need for additional simulations during design optimization. This study proposes a data-driven surrogate model, employing the Gaussian process regression network (GPRN), to predict weld pool metrics, such as weld width and depth of penetration in laser welding of aluminum alloy. A 3D computational fluid dynamics-based numerical model is initially constructed and experimentally validated to predict weld pool metrics. Subsequent experimental runs, guided by the design of experiments, include various configurations of process parameter settings. The developed numerical model computes weld pool metrics for each experimental run, forming a dataset for training and testing the GPRN model. The GPRN model is evaluated against simulated data, showing adequacy with a mean square error of 1.7 µm and mean absolute percentage error of 10−7, with experimental validation further confirming its accuracy, revealing a minimum error of 1.7%, a maximum error of 8%, and an average error of 3%. The key contribution and novelty of this study lie in the development of the hybrid data-driven model, which accurately predicts weld pool metrics while minimizing experimental and computational efforts.