Battery prognostics and health management predictive models are essential components of safety and reliability protocols in battery management system frameworks. Overall, developing a robust and efficient battery model that aligns with the current literature is a useful step in ensuring the safety of battery function. For this purpose, a multi-physics, multi-scale deterministic data-driven prognosis (DDP) is proposed that only relies on in situ measurements of data and estimates the failure based on the curvature information extracted from the system. Unlike traditional applications that require explicit expression of conservation principle, the proposed method devices a local conservation functional in the neighborhood of each data point which is represented as the minimization of curvature in the system. By eliminating the need for offline training, the method can predict the onset of instability for a variety of systems over a prediction horizon. The prediction horizon to prognosticate the instability, alternatively, is considered as the remaining useful life (RUL) metric. The framework is then employed to analyze the health status of Li-ion batteries. Based on the results, it has demonstrated that the DDP technique can accurately predict the onset of failure of Li-ion batteries.