Continuous ageing trajectory representations across heterogeneous battery datasets: Knee analysis and protocol-held-out early-life prediction

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Accurate assessment of lithium-ion battery ageing is complicated by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven predictors. This study develops a continuous ageing-trajectory framework in which coordinate-based multilayer perceptron (MLP) and sinusoidal representation network (SIREN) models represent state-of-health and voltage–capacity trajectories as differentiable functions of normalized trajectory coordinates. The framework combines continuous reconstruction, derivative-based knee descriptors, equivalent-full-cycle (EFC) harmonization, protocol-held-out early-life prediction, perturbation analysis, and conformal uncertainty quantification. Early-life prediction was evaluated in four protocol-held-out folds, repeated for three random seeds, using the first 𝑁 ∈ { 5 , 1 0 , 2 0 } available degradation observations rather than assuming that one observation represented one physical cycle. The pooled association between robust consensus knee location and the first crossing of the 80% SOH threshold was strong ( 𝑛 = 1 7 2 , Spearman 𝜌 S = 0 . 8 3 4 , 95% bootstrap CI [ 0 . 7 3 8 , 0 . 9 0 7 ] , Holm-adjusted 𝑝 = 3 . 3 6 × 1 ⁢ 0 − 4 5 ). Raw adapted cINR predictions exhibited substantial architecture- and window-dependent bias. A leakage-safe bias-corrected MLP-protocol blend achieved MAEs of 113.57, 107.79, and 112.82 EFC for 𝑁 = 5 , 10, and 20, respectively, compared with 116.66, 115.57, and 125.02 EFC for the protocol-median baseline. These numerical reductions were not statistically significant after multiplicity correction, although the blend significantly improved over raw MLP cINR predictions for 𝑁 = 5 and 𝑁 = 1 0 . Fold-external conformal intervals at the nominal 90% level attained empirical coverages of 90.3%, 91.0%, and 95.5%, but remained wide, reflecting substantial inter-cell uncertainty. Knee detection was comparatively stable under missing observations but sensitive to aggressive downsampling and measurement noise. The results support continuous trajectory representations as useful differentiable descriptors and components of calibrated hybrid predictors, but do not establish a uniform predictive advantage over a strong protocol-informed baseline.

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