## 3 Proposed Work
### Model Development and Training
#### 3.3.4 Long Short-Term Memory (LSTM)  
The Long Short-Term Memory (LSTM) is a type of recurrent neural network (RNN) that is well-known for making and processing predictions from sequential data. Its architecture is also used for time series algorithm analysis and natural language sequencing. The design of the LSTM algorithm is crucial for addressing the problem of capturing long-term dependencies in sequential data, which typical RNNs have a limited ability to do. While Transformer-based models and hybrid physics-informed approaches have shown strong potential in recent RUL prediction studies, our focus remains on maintaining a balance between performance and practicality. LSTMs provide reliable results with lower computational demands, making them more suitable for real-world, resource-constrained settings. Given the scale of our dataset and the application context, we opted for a simpler, proven architecture. That said, we acknowledge the value of newer methods and plan to explore them in future work. The choice of an LSTM architecture in this work is motivated by its established strength in modeling temporal dependencies and sequential patterns in battery degradation data. This is particularly important in RUL prediction, where the state of a battery evolves over time through charge-discharge cycles. [PERSON] et al. (2018) demonstrated the effectiveness of LSTM networks for lithium-ion battery RUL estimation in their study on the NASA dataset. These findings support the adoption of LSTM in this work as a reliable architecture for capturing the nonlinear and time-dependent dynamics of battery degradation. Now how the LSTM works is very interesting, we utilized all the features but excluding the cycle counts to see how it will perform and after which we included all features including the cycle count and compared both performance metrics, first an initial decision-making process calculates if the information received from the previous timestamp will be kept or seen as irrelevant and removed. In the subsequent part, the cell makes sure it gets new insights from the received input. Lastly, during the third phase, the cell transfers the updated information from the current timestamp to the subsequent timestamp. Note that a single LSTM cycle is called a one-time step, while the three parts that make up an LSTM unit are called gates. These gates in turn regulate how information is moved into and out of the memory cell in an efficient and effective manner. The initial gate is called the forget gate, the subsequent gate is known as the input gate, whereas the final gate is the output gate. For a provided input sequence \(x_{t}\) at time step t, the LSTM updates its cell state \(C_{t}\) and hidden state \(h_{t}\) as follows:  
Figure 12: Training and validation loss over epochs for the ANN model after hyperparameter tuning. Forget Gate: Determines which information to discard from the cell state. \[\text{f}_{\text{t}}=\sigma(\text{W}_{\text{f}}\times[\text{h}_{\text{t}-1},\text{ x}_{\text{t}}]+\text{b}_{\text{f}})\]
2. Input Gate: Decides which new information to store in the cell state. \[i_{t}=\sigma(W_{i}\times[h_{t-1},x_{t}]+b_{i})\] \[\widetilde{C}_{t}=tanh(W_{\text{C}}\times[h_{t-1},x_{t}]+b_{\text{C}})\]
3. Cell state update: Combine the forget and input operations to update the cell state. \[C_{t}=F_{t}\times C_{t-1}+i_{t}\times\widetilde{C}_{t}\]
4. Output Gate: Determines the output of the LSTM cell. \[o_{t}=\sigma(W_{o}\times[h_{t-1},x_{t}]+b_{\text{C}})\]  
\[h_{t}=o_{t}\times\tanh(C_{t})\]  
Here, sigma represents the sigmoid activation function, and tanh signifies the hyperbolic tangent function. weights (W) and biases (b) are learned during training. In this study, LSTM networks are employed to predict the Remaining Useful Life (RUL) of lithium-ion batteries by learning from sequential patterns in the features. Unlike traditional models, LSTMs can effectively model the temporal dependencies in the data, making them highly suited for this task.