Melt track monitoring in the laser powder bed fusion (LPBF) process is crucial for preventing internal defects in as-printed parts. Uncontrollable melt pool dynamic behavior easily leads to melt track morphology defects. Existing monitoring methods face challenges in balancing modeling accuracy and physical interpretability. Specifically, traditional physics-based models typically require complex monitoring equipment, extensive simulation data, and empirical formulas, resulting in high costs and limited applicability. Meanwhile, conventional data-driven models lack physical constraints, leading to insufficient interpretability, process parameter sensitivity, and poor generalization. To address these challenges, this article proposes a deep Gaussian process-based method for LPBF melt track morphology prediction. The proposed model employs kernel functions in the first layer to learn melt pool evolution patterns and embeds the Rosenthal equation into the second-layer kernel function as a physical constraint, constructing a physically interpretable multilayer Gaussian process framework. Finally, a softmax classifier based on melt track geometric deviation achieves five-category melt track morphology recognition. Multi-condition experimental results demonstrated that the proposed method achieved root mean square errors of 0.069, 0.020, and 0.039 for melt track geometry, outperforming traditional data-driven models in prediction accuracy. The classification accuracy reached 90.76%. Furthermore, the influence of different features on melt track morphology is quantified through time-lagged mutual information analysis and other visualization methods. This study provides an effective solution for achieving quality monitoring and defect prediction in the LPBF process.