Long-horizon Forecasting of Sodium-ion Battery Charge-profile Evolution and Degradation using Autoregressive Deep Sequence Models

Abstract

Accurate long-horizon battery ageing prediction remains challenging because degradation alters not only scalar health indicators but also the shape and duration of electrochemical cycling profiles. Here, we introduce an autoregressive deep sequence-learning framework to forecast voltage-current profiles and state-of-health (SOH) evolution in NVPF/hard-carbon sodium-ion batteries. Stacked LSTM (Batt-LSTM) and hybrid CNN-LSTM (Batt-LSTM-C) models learn from voltage, current, and cycle-index sequences to generate future cycling profiles iteratively from measured data. Scheduled sampling mitigates the training-inference mismatch during autoregressive rollout, extending stable forecasting horizons from a few tens of cycles to as many as 600 cycles while preserving local waveform fidelity. Horizon-dependent benchmarking against classical machine-learning models evaluates voltage mean absolute error (MAE), global and local dynamic time warping (DTW), and SOH MAE across five forecasting horizons. Batt-LSTM with scheduled sampling achieves the lowest voltage MAE at horizons from 5,000 to 20,000 time steps. The predicted profiles also enable extraction of capacity-, resistance-, and energy-based SOH indicators, together with internal-resistance evolution. Monte Carlo dropout and deep ensembles estimate predictive spread at local profile and global degradation-trajectory scales. Fine-tuning on an independent ageing dataset improves cross-cell adaptation, with rolling-horizon updates reducing SOH prediction error to 3.844 percentage points for a 200-cycle horizon. These results show that curve-level forecasting retains diagnostically relevant electrochemical information beyond scalar SOH regression and offers a route toward uncertainty-aware, adaptive battery-health monitoring.