RUL Prediction in LFP Batteries: Comparison of Gompertz, LSTM and Gompertz-Informed LSTM Models for Interpretability and Accuracy

Lithium iron phosphate batteries have seen a recent rise in usage in electric vehicles and battery energy storage systems. For these applications, reliability is of paramount importance, influences long-term adoption and high return on investment, especially regarding battery replacement. Remaining Useful Life (RUL) prediction is at the core of avoiding unexpected failure and enabling proactive battery maintenance. Physics-based and data-driven methods have been explored by researchers, whilst Physics-Informed Neural Networks (PINNs) can combine their strengths in estimating battery RUL. This paper investigates the integration of the Gompertz function, an inherently interpretable white-box model, into Long Short-Term Memory (LSTM) networks to follow the physical laws of degradation, capture downward monotonic behavior and long-term dependencies from data resulting in Gompertz-Informed LSTMs (GILSTMs). Pure LSTMs are regarded as black box systems and critical infrastructure operators such as battery energy storage system (BESS) operators may refrain from using such systems. Gray-box models such as GILSTMs may get over this hurdle by increasing model interpretability and helping industry adopters know when they will benefit from data-driven modeling. This study explores two GILSTM architectures. The first uses an LSTM to predict Gompertz parameters, which are then converted into RUL via the inverse Gompertz equation. The second uses the inverse Gompertz equation as a verification step to cross-check the RUL values generated by the LSTM. The first type of GILSTM was constrained by both a physics loss and an inverse Gompertz layer to predict RUL while the second verified the results of an LSTM, despite that the GILSTMs failed to generalize. The first type of GILSTM achieved an average RMSE of 22.97%, while the second type achieved an average RMSE of 26.99%. The models in this paper are also benchmarked on the first 100 cycles, a current state of art for battery degradation testing. The best overall implementation was an LSTM that predicted RUL by recursively predicting SoH achieving an average RMSE per cycle of 9.18% and a 100th cycle RMSE of 17.02%. This study evaluates the trade-off between the predictive accuracy of black-box LSTMs and physical interpretability of Gompertz models. While pure LSTMs provide superior accuracy, the Gompertz parameters stabilize by 85% SoH. This 85% threshold serves as an interpretable confidence trigger, informing BESS operators when to rely on LSTM RUL forecasts.