This paper introduces an innovative approach for the efficient analysis of composites manufacturing processes and phenomena. The method combines low- and high-fidelity simulation schemes with limited amounts of experimental data to train surrogate machine learning (ML) models. Guided by a novel approach, Spatially Weighted Gaussian Process Regression (SWGPR), a predictive model is efficiently constructed and calibrated by assigning datapoint-dependent noise levels to simulation points, establishing a multi-scale data-driven uncertainty structure. This study demonstrates the effectiveness of the method in accurately predicting process-induced deformations (PIDs) for L-shaped cross-ply laminates using minimal experimental efforts. The presented method aims to provide a cost-effective and broadly applicable framework for understanding and improving the design, development, and manufacturing of composites.