Decoding the Drain: A Physics-Based Continuous-Time Model for Smartphone Battery Life Prediction

Summary

Can we mathematically predict smartphone battery life and identify the most effective power-saving interventions? Despite over 6 billion smartphones in daily use, battery runtime remains frustratingly unpredictable—lasting a full workday under certain conditions yet draining before lunch under others. This study develops a rigorous physics-based framework to answer this question.

Model Architecture. This study formulated a continuous-time model based on coupled ordinary differential equations governing smartphone’s lithium-ion battery state of charge (SoC) dynamics. The framework integrates three subsystems: (1) electrochemical battery dynamics derived from lithium intercalation principles, (2) componentwise power decomposition modeling five subsystems (screen , CPU , network, GPS, and background processes) using intensity factor matrices, and (3) thermal-aging coupling incorporating Arrhenius degradation kinetics and SEI film growth. Meanwhile, time-to-empty is the zero point of the time equation with respect to SOC.

Key Findings. Model validation across typical scenarios (gaming, navigation, video watching) demonstrates strong predictive accuracy with relative errors under 8%. Sensitivity analysis reveals screen brightness and processor intensity as dominant drain factors, contributing 40-60% of total consumption in high-load scenarios. Critical insights include: (1) internal resistance surge below 20% SOC causes nonlinear performance degradation; (2) temperature elevation above 40°C doubles aging rate; (3) background tasks account for 15-25% consumption even during standby.

Strategic Recommendations

For Users: Scenario-specific optimization includes reducing screen brightness by 30% during gaming (extending runtime 25%), pre-downloading offline maps for navigation (50% improvement), and selecting 720p video resolution (25% decoder power reduction). Long-term maintenance requires maintaining 20-80% SOC windows and avoiding charging above 30°C ambient temperature.

For System Designers: Implement adaptive power scheduling below 20% SOC, temperature-aware CPU throttling above 40°C, and machine learning-based usage pattern prediction for proactive resource allocation. Our model generalizes to laptops and power tools with subsystem reconfiguration.

Keywords

battery depletion model; SOC dynamics; multi-subsystem analysis; predictive power management

Award

Honorable Mention | 2026 Mathematical Contest in Modeling

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