Closure modeling is one of the key challenges in constructing stable and accurate Reduced-Order Models (ROMs) for nonlinear dynamical systems such as the viscous Burgers’ equation. In this work, the DARNet is presented, a Dissipation-Aligned Residual Neural Network, as a novel data-driven closure model for POD-Galerkin ROMs (GROM). The DARNet framework is designed to improve the energy behavior of ROMs by introducing a hybrid loss function that combines the standard closure term error with a dissipation alignment term and a regularization term. The model takes as input the modal coefficients, Reynolds number, and time, and predicts the closure contribution required to correct the ROM dynamics. The DARNet is trained on data from multiple Reynolds numbers and test its ability to predict physically compatible closure terms to correct system evolution. Our results show that DARNet significantly outperforms a standard ResNet(Residual Neural Network)-based closure model, especially in capturing the correct energy evolution and dissipation rate over time for a GROM evolving on a subspace built using POD. The proposed model improves the stability and physical consistency of the ROM without increasing model complexity. These findings demonstrate that incorporating physics-aware loss terms in neural network closures can lead to more reliable and generalizable ROMs.