## 1 Introduction  
The safety issues of a lithium battery highlight the importance of monitoring the health of lithium-ion batteries throughout their lifecycle. The continuous monitoring of key parameters like the current, voltage, and internal resistance is crucial for safe operation, as they provide essential information on the battery's state of charge (SOC) and state of health (SOH) [1, 2, 3, 4]. Due to the difficulty of monitoring the operation parameters physically, many researchers focus on simulating a lithium battery response using electrochemical models or an equivalent circuit model (ECM) [5, 6, 7]. However, ECMs may become imprecise under dynamic load conditions due to their limited ability to capture the intricate relationship between the battery's internal electrochemical properties, resulting in a less accurate SOC estimation. These limitations have prompted researchers to explore data-driven approaches like machine learning (ML) [8, 9, 10, 11, 12, 13, 14, 15, 16]. [PERSON] et al. [17] proposed an adaptive ML framework based on a deep temporal convolutional network (TCN) and Coulomb counting for SOC estimation across different battery chemistries. [PERSON] et al. [18] successfully employed a particle-swarm-optimized Long Short-Term Memory (LSTM) network to achieve SOC estimation errors below 0.5% and demonstrated the model's robustness under noisy conditions. [PERSON] et al. [19] applied unscented Kalman filtering (UKF) for SOC smoothing before using LSTM for prediction, achieving root-mean-square errors below 1.1% across temperatures ranging from 0 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, with average errors below 1%. The LSTM methods excel at handling time-series data, leading to high accuracy and efficiency in the SOC prediction. But, traditional LSTM networks may be influenced by operating conditions from various time scales, thus they sometimes struggle with long-term dependencies in battery degradation. [PERSON] et al. (2020) developed an adaptive self-attention LSTM (SA-LSTM) model that significantly enhanced the capture of degradation information in lithium batteries. With the assistance of the attention mechanism, the model could better identify and utilize relevant historical patterns, leading to improved accuracy in both SOC and SOH predictions. They further proposed a bidirectional LSTM with attention mechanisms (AM-BiLSTM) for predicting the remaining useful life (RUL). The new model processes the time series data in both forward and backward directions while using attention to focus on critical degradation indicators, achieving remarkable prediction accuracy with errors within 1%. Meanwhile, these data-driven approaches typically require extensive cycling data for effective training, making the data collection process time-consuming and resource-intensive. To overcome this, recent studies combine physical models with data-driven methods ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). Although physical models provide fundamental electrochemical principles and domain knowledge, their simplicity often results in limited accuracy under complex operating conditions. For example, ECMs struggle to capture the nonlinear behavior of a battery's internal dynamics under dynamic load conditions, affecting the accuracy of SOC estimation ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2020). Moreover, they heavily rely on large amounts of cycling data, making the data collection process slow and resource-intensive. Additionally, most existing studies fail to deeply explore the complex correlations among various battery parameters, leading to low accuracy and significant errors in the battery state prediction ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). Furthermore, the current research primarily focuses on predicting the battery state at the next time step rather than over an extended period ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020).