Accurate prediction of the Remaining Useful Life (RUL) is essential for enabling timely maintenance of lithium-ion batteries, impacting the operational efficiency of electric applications that rely on them. This paper proposes a RUL prediction approach that leverages data from recent charge-discharge cycles to estimate the number of remaining usable cycles. The approach introduces both a novel signal processing pipeline and a deep learning prediction model. In the signal preprocessing pipeline, a derived capacity feature $\dot{Q}(I, Q)$ is computed based on current and capacity signals. Alongside original capacity, voltage and current, these features are denoised and enhanced using statistical metrics and a delta-based method to capture differences between the current and previous cycles. In the prediction model, the processed features are then fed into a hybrid deep learning architecture composed of 1D Convolutional Neural Networks (CNN), Attentional Long Short-Term Memory (A-LSTM), and Ordinary Differential Equation-based LSTM (ODE-LSTM) blocks. This architecture is designed to capture both local signal characteristics and long-range temporal dependencies while modeling the continuous-time dynamics of battery degradation. The model is further evaluated using transfer learning across different learning strategies and target data partitioning scenarios. Results indicate that the model maintains robust performance, even when fine-tuned on limited target data. Experimental results on two publicly available large-scale datasets demonstrate that the proposed method outperforms a baseline deep learning approach and machine learning techniques, achieving an RMSE of 101.59, highlighting its strong potential for real-world RUL prediction applications.

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that similar to standard RNNs, the underlying reason for this issue is the vanishing or exploding of the gradient during training. This phenomenon is expressed by the ordinary differential equation (ODE) representation of the hidden state, regardless of the ODE solver's choice. We provide a solution by designing a new algorithm based on the long short-term memory (LSTM) that separates its memory from its time-continuous state. This way, we encode a continuous-time dynamical flow within the RNN, allowing it to respond to inputs arriving at arbitrary time-lags while ensuring a constant error propagation through the memory path. We call these RNN models ODE-LSTMs. We experimentally show that ODE-LSTMs outperform advanced RNN-based counterparts on non-uniformly sampled data with long-term dependencies. All code and data is available at https://github.com/mlech26l/learning-long-term-irregular-ts.