Selective laser melting (SLM) additive manufacturing (AM) is widely used due to its significant advantages in designing and manufacturing special-shaped complex components. The process parameters of SLM determine the quality of as-built parts, but it is difficult to establish an accurate and reliable mathematical model to connect process parameters with the quality of as-built parts. However, data-driven machine learning can effectively solve the analysis and prediction problem of complex process. Therefore, a machine learning (ML) prediction method based on dimensionality augmentation and physical information is proposed, which connects the process parameters (laser power, hatching space, scanning speed, and layer thickness) of SLM with the quality characteristics (top layer surface roughness and relative density) of as-built parts. The four process parameter features (4-dimensional features) are expanded to high-dimensional features through feature engineering to characterize the quality of as-built parts. In addition, the physical information of powder melting forming in SLM process is fused with ML algorithm, the theory-guided ML is used to improve the prediction accuracy of the model. In this paper, the CoCrFeNiMn high-entropy alloy as-built samples dataset is used for network training of four ML algorithms, and three assessment indexes are used to evaluate the prediction model. The results show that dimensionally augmented and physics-informed ML model has better prediction accuracy and generalization ability. The proposed method can also provide guidance for optimizing process parameters.