Accurate State of Charge (SOC) and Time-to-Empty (TTE) predictions are critical for mobile power management, yet existing paradigms struggle to balance thermodynamic interpretability with computational efficiency. To address the limitations of traditional models under dynamic workloads and extreme thermal environments, this paper proposes a hybrid continuous-time dynamic prediction framework. We construct a continuous-time state evolution model that innovatively integrates an Arrhenius-based temperature compensation function with a cycle-driven State of Health (SOH) degradation factor, effectively capturing both transient thermal states and long-term capacity fading. Mechanistically, a decoupled multi-component power demand model—spanning display, processor, and network subsystems—is formulated and solved via a lightweight, second-order Improved Euler numerical scheme. Empirical benchmarking demonstrates high prediction fidelity, achieving a Root Mean Square Error (RMSE) of 2.84% and a Mean Absolute Percentage Error (MAPE) of 1.95%. Furthermore, multi-dimensional Response Surface Methodology (RSM) and sensitivity analyses identify ambient temperature (index -0.482) and CPU utilization (index -0.314) as the primary depletion drivers. Crucially, the analysis reveals a significant non-linear voltage collapse below the 20% SOC threshold. Ultimately, this framework delivers a scientifically grounded, Pareto-optimal power scheduling roadmap for next-generation mobile operating systems, holistically balancing predictive thermal-modulated control with user behavioral constraints.
