Electric water heaters (EWHs) provide a flexible and widely distributed resource for demand response (DR) programs due to their controllable thermal storage capacity and high residential penetration. To fully exploit their flexibility in grid services, dynamic EWH models must be both accurate and computationally efficient to enable large-scale, real-time control for effective market participation. This paper introduces a Sobolev-trained neural network reduced-order model (STNN-ROM) for predicting EWH thermal dynamics, while preserving key stratification behavior under reduced spatial dimensionality. The model incorporates physics-driven features from a multi-zone differential equation model (MZ-DEM) for EWHs and employs derivative-informed Sobolev training with a recursive approach to enhance physical consistency, mitigate error accumulation, and improve generalization. The STNN-ROM is trained on simulation data generated by MZ-DEM and validated against real-world measurements, achieving acceptable accuracy while reducing computational cost by over 69% compared to the full-order MZ-DEM. These results demonstrate the proposed model’s potential for real-time DR implementation and the coordination of aggregated EWHs’ flexibility through scalable control frameworks for demand-side management.