Prior-guided learning for ordered battery degradation trajectory prediction from partial charging observations under variable protocols

Battery lifetime prediction under variable operating conditions is constrained by incomplete charging records, yet most partial-curve methods return only a scalar capacity or state-of-health estimate. This work proposes a prior-guided teacher–student framework that predicts an ordered degradation trajectory comprising knee-start, knee-point, knee-end, and end of life (EOL) from fixed state-of-charge segments. A split-local tabular model supplies a deployable prior, while a teacher with richer early-cycle observations guides a partial-observation student to learn order-preserving residual corrections. Under repeated five-fold evaluation with nested inner validation on the Severson dataset, the fixed guided two-student ensemble achieves a four-event mean absolute error (MAE) of 56.00 cycles in the cell-level setting and 58.74 cycles under protocol-grouped evaluation. In the cell-level setting, the ensemble improves on the strict partial prior by 15.99 cycles, while the matched teacher/no-teacher comparison isolates an additional 6.23-cycle reduction from privileged teacher guidance (95% bootstrap CI: 3.85–8.77 cycles). Its point estimate is comparable with that of the full-domain teacher, while event chronology is enforced by the ordered output parameterization. These results support privileged-to-partial learning as a deployable strategy for joint knee-to-EOL prediction under restricted charging observations.