The increasing deployment of inspection drones for monitoring remote and critical infrastructure presents new opportunities and challenges in asset management. These drones operate in demanding environments, where ensuring operational reliability is essential. Among the various subsystems, battery health plays a central role in determining mission success and safety. This chapter presents a physics-aware probabilistic approach for battery health management, integrating data-driven techniques with physics-based models to improve the predictability of battery performance. At the core of this methodology lies a probabilistic machine learning model that provides uncertainty quantification, enabling more informed and robust decision-making. By incorporating this uncertainty-aware perspective into battery discharge forecasting, the approach supports advanced digital maintenance strategies. The methodology is demonstrated to drone-based inspections of offshore wind energy infrastructure, highlighting its contribution to enhancing asset reliability and enabling condition-aware maintenance strategies.