This study introduces a novel control framework for adaptive cruise control (ACC) in automated driving, leveraging Long Short-Term Memory (LSTM) networks and physics-informed constraints. As automated vehicles (AVs) adopt advanced features like ACC, transportation systems are becoming increasingly intelligent and efficient. However, existing AV control strategies primarily focus on optimizing the performance of individual vehicles or platoons, often neglecting their interactions with human-driven vehicles (HVs) and the broader impact on traffic flow. This oversight can exacerbate congestion and reduce overall system efficiency. To address this critical research gap, we propose a neural network-based, socially compliant AV control framework that incorporates social value orientation (SVO). This framework enables AVs to account for their influence on HVs and traffic dynamics. By leveraging AVs as mobile traffic regulators, the proposed approach promotes adaptive driving behaviors that reduce congestion, improve traffic efficiency, and lower energy consumption. Within this framework, we define utility functions for both AVs and HVs, which are optimized based on the SVO of each AV to balance its own control objectives with broader traffic flow considerations. Numerical results demonstrate the effectiveness of the proposed method in adapting to varying traffic conditions, thereby enhancing system-wide efficiency. Specifically, when the AV's control mode shifts from prioritizing energy consumption to optimizing traffic flow efficiency, vehicles in the following platoon experience at least a 58.99% increase in individual energy consumption alongside at least a 38.39% improvement in individual average speed, indicating significant enhancements in traffic dynamics.