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Abstract Artificial intelligence and machine learning frameworks have become powerful tools for establishing computationally efficient mappings between inputs and outputs in engineering problems. These mappings have enabled optimization and analysis routines, leading to innovative designs, advanced material systems, and optimized manufacturing processes. In such modeling efforts, it is common to encounter multiple information (data) sources, each varying in specifications. Data fusion frameworks offer the capability to integrate these diverse sources into unified models, enhancing predictive accuracy and enabling knowledge transfer. However, challenges arise when these sources are heterogeneous, i.e., they do not share the same input parameter space. Such scenarios occur when domains differentiated by complexity such as fidelity, operating conditions, experimental setup, and scale, require distinct parametrizations. To address this challenge, a two-stage heterogeneous multi-source data fusion framework based on the input mapping calibration (IMC) and the latent variable Gaussian process (LVGP) is proposed. In the first stage, the IMC algorithm transforms the heterogeneous input parameter spaces into a unified reference parameter space. In the second stage, an LVGP-enabled multi-source data fusion model constructs a single-source-aware surrogate model on the unified reference space. The framework is demonstrated and analyzed through three engineering modeling case studies with distinct challenges: cantilever beams with varying design parametrizations, ellipsoidal voids with varying complexities and fidelities, and Ti6Al4V alloys with varying manufacturing modalities. The results demonstrate that the proposed framework achieves higher predictive accuracy compared to both independent single-source and source-unaware data fusion models.