Multiscale analysis necessitates solving problems of the challenge of characterizing non-elastic microstructural behavior with a macroscopic material response. Traditionally, microstructural behaviors have been reduced to a few homogenized material properties, limiting their ability to model complex interactions. Recent machine learning approaches address this limitation but rely on predefined loading conditions and constitutive laws. Deep Material Networks (DMNs) offer an alternative reduced-order modeling approach, generalizing the model across diverse constitutive behaviors without retraining. However, conventional DMN training relies on microstructural homogenized linear properties, often neglecting rich local field data from direct numerical simulations. This study enhances the DMN framework by integrating local field data for offline training, improving predictive capabilities. By refining the network architecture, we leverage previously dropped information more effectively. A U-Net-based architecture efficiently captures and integrates linear local field data during the offline training, yielding a better refined microstructural representation. Results demonstrate improved predictive accuracy and model performance over traditional DMNs. By incorporating high-fidelity data, this approach advances DMNs as a robust tool for multiscale analysis, bridging high-fidelity simulations and computational efficiency.