Residual-Corrected Equivalent-Circuit Model with Universal Differential Equations for Robust Battery Voltage Prediction under Operating-Condition Shift

Abstract

Accurate terminal-voltage prediction underpins model-based battery management, yet low-order equivalent-circuit models (\ecm{}) lack expressiveness under transient conditions, whereas purely data-driven predictors sacrifice interpretability and may degrade under operating-condition shift. This paper introduces a residual-corrected hybrid formulation in which a first-order Thevenin \ecm{} (\ecmrc{}) provides the dominant voltage structure, and a compact neural network embedded as a universal differential equation (\ude{}) corrects only the latent polarization mismatch. The \ecmrc{} parameters identified by nonlinear least squares warm-start the hybrid model so that the learned component operates in a low-residual regime. Experiments on a public Panasonic 18650PF dataset compare the proposed \ecmude{} with standalone \ecmrc{} and Long Short-Term Memory (\lstm{}) baselines across four axes: matched-condition prediction on UDDS at \SI{25}{\celsius}, inference-time perturbation of the supplied state-of-charge (\SOC{}, denoted $z$) input, zero-shot temperature transfer (\SI{25}{\celsius} to \SI{-20}{\celsius}), and zero-shot drive-cycle transfer to US06, LA92, and HWFET. The proposed \ecmude{} achieves the lowest voltage error in every setting, reducing mean absolute error (\mae{}) by 48\% relative to the \lstm{} under matched conditions and showing an order-of-magnitude lower inter-seed variability (coefficient of variation: 0.44\% vs.\ 6.20\%). Substantial gains persist under challenging distribution shifts, indicating that the physical model anchors prediction where a purely learned model is most vulnerable. These results position residual-corrected \ecmude{} as a lightweight and interpretable enhancement of low-order circuit models for voltage prediction in battery management systems (\bms{}).