Paper: BatteryML: An Open-source Platform for Machine Learning on Battery Degradation (ICLR-2024)

Reviewer comment (Novelty):
The technical and theoretical contribution of the toolkit itself is limited.

Author response:
Thank you for acknowledging the strengths of our work. In response to your concern about the toolkit's limited technical and theoretical contributions, we'd like to offer further insight into the platform's design and utility.

Our toolkit, while not introducing groundbreaking machine learning algorithms or theories, plays a crucial role as a comprehensive and open-source resource for battery degradation modeling. The platform's core value lies in its ability to streamline the complex process of applying machine learning to battery degradation data, making it more accessible and efficient for researchers and engineers in the field.

**Key features of the platform** include:

- **Unified Interface**: The toolkit offers a cohesive interface for data preprocessing, feature extraction, and model building, significantly reducing the time and effort traditionally required in this research area.
- **Reproducibility and Comparison**: By standardizing these processes, the platform facilitates reproducibility and enables more straightforward comparison of results across different studies, a crucial aspect in advancing scientific research.
- **Extensibility**: Recognizing the dynamic nature of machine learning and battery science, we have designed the platform to be easily extendable. Users can integrate new data preprocessors, feature extractors, and models, as elaborated in the Appendix of our revised paper. This adaptability ensures that our platform remains relevant and useful as new techniques and research needs emerge.

Looking ahead, we are committed to enriching the technical and theoretical aspects of the toolkit. We plan to actively collaborate with the data science and battery science communities to incorporate cutting-edge advancements and insights, thereby continuously enhancing the toolkit's capabilities and contributions to the field.

Reviewer comment (Novelty):
While this paper provides a practical software tool for battery data research, it does not provide novel insights or modeling techniques that advance the state of the art in battery SOH or RUL prediction.

Author response:
We appreciate your feedback regarding the lack of contributions on the model aspect. Our primary objective is to establish a robust foundation of classical baselines and allow in-depth analyses, which we believe will catalyze future research and innovations in battery degradation modeling. By furnishing researchers with a diverse array of datasets and a thorough benchmark for existing models, our tool aims to foster further exploration and development in the field. We envision our work as a stepping stone, enabling the community to build upon these foundational aspects and contribute novel approaches and methodologies in battery SOC, SOH, RUL prediction and beyond.

Reviewer comment (Evaluation):
While RMSE numbers for the RUL task are presented in table 2, the results are not discussed in the text nor are the advantages/disadvantages of each method.

Author response:
We appreciate your feedback calling for an expanded discussion on the performance of various models and datasets for the RUL task. Recognizing the importance of this analysis, we have broadened our discussion to include comprehensive performance analysis and explanations for the differing performances of the models.

It is essential to note that **there is no singular method that consistently achieves competitive performance across all datasets**. Most methods display a lack of robustness, leading to substantial prediction errors in certain datasets, even when they demonstrate top accuracy in others.

The Variance, Discharge, and Full models, which fit linear regression on features designed by domain experts for LiFePO4 (LFP) batteries, delivered commendable results on datasets such as *MATR2*, *HUST*, and *CLO*. These datasets utilize the same type of LFP batteries, suggesting that manually constructed features based on domain knowledge can be particularly effective for LFP batteries, demonstrating a strong linear relationship with the Remaining Useful Life (RUL).

Traditional statistical models that utilize low-level *QdLinear* features yield significant results. Ridge Regression's consistent, albeit modest, performance across datasets confirms a strong linear relationship between the *QdLinear* feature and battery cycle life. However, its limitations on *HUST*, *CRUSH*, and *MIX* datasets underscore the challenges in maintaining this linear correlation under varying aging conditions. PCR and PLSR, which incorporate principal component analysis before linear regression, excel on *MATR1*, *CRUH*, and *SNL* datasets. This indicates a linear relationship of the QdLinear feature with battery life in different subspaces. Gaussian Process Regression (GPR) outperforms PCR and PLSR on the *MIX* dataset, due to its non-linear fitting ability, which is critical for capturing diverse battery degradation patterns. XGBoost and Random Forest demonstrate strong performance on *CRUSH* and *MIX* datasets, underscoring the effectiveness of tree-based models in modeling complex battery aging patterns.

Neural network models, with the *QdLinear* feature, showed potential and instability. While their best performance under different seed settings might surpass some linear models (see the table below for CNN on *MATR1*), they also demonstrated a large variance, indicating poor model stability. Among them, the Transformer model exhibited better stability and achieved the best result on the mixed dataset *CRUSH*. This suggests that neural network models have significant potential in RUL prediction tasks, but the challenge of improving model stability persists.

||seed 0 | seed 1| seed 2| seed 3| seed 4| seed 5| seed 6| seed 7| seed 8| seed 9|
| ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | 
|CNN | 76 | 67 | 64 | 74| 60 | 82 | 65 | 79| 367 | 78 | 

In the revised version of the paper, we have provided a more detailed analysis of the RUL, SOH, and SOC results. This includes a comparative evaluation of diverse models on all battery datasets. Our aim with this enriched discussion is to illuminate the performance of each model under varying conditions, clearly highlighting their respective strengths and limitations.

Reviewer comment (Presentation):
Table 2 has bolded results for the top set of rows (MATR1, MATR2, HUST, SNL), but not the second set. Could you bold the results in the second set of rows as well to highlight the best performing models on those datasets?

Author response:
Thank you for pointing out the displaying issue in Table 2. We have adjusted this part in the revised version to ensure that the top-performing models in the different cases are all highlighted in bold.

Reviewer comment (Evaluation):
While BatteryML puts a lot of effort into standardizing publicly available datasets and making them accessible to work with, for the wider community, I'm curious how much of the detailed battery science gets communicated to the end-user, or whether the layer of abstraction necessary to standardize the framework obfuscates the nuances to a large degree. The reason this is important is to enable the development of models that actively support/engage with physical phenomena in the correct fashion (physically plausible explanations).

Author response:
**Response to Weakness 1 and Question 1**

Thanks so much for pointing out such insightful and visionary comments. We hope the following clarifications and explanations can help to address your concerns.

Firstly, we would like to clarify that our unified data representation does not obstruct the communication between the nuances of battery science (e.g., electro-chemical processes) and the development of machine learning methods. On the contrary, this unified data layer is indispensable to facilitating such communication as it alleviates the burden of handling various data sources, thereby forming the data foundation for both training and evaluation processes. Our tool includes various vital and interpretable features such as incremental capacity, differential capacity, and coulomb efficiency, etc. These classical features, which incorporate essential physical insights about detailed electro-chemical processes, can be easily derived from our unified data representation. Furthermore, by accommodating different datasets, our tool enables rapid verification of the effectiveness of these features across diverse data scenarios.

Additionally, we concur with your observation that there is significant room for enhancing the communication between battery science and data science. While there are many challenges to overcome, we envision BatteryML serving as a platform to facilitate these interactions and drive co-innovation among battery scientists and machine learning experts.

One interesting case you have mentioned is to develop physics-informed methods, holding both data-driven flexibility and physically plausible explanations. Without doubt, BatteryML can effortlessly support the implementation of these methods due to its extensible interfaces across data, feature, and model modules. However, developing such methods can be challenging and requires either battery researchers equipped with professional ML skills or data scientists with a deep understanding of electro-chemical processes. We believe BatteryML can greatly contribute in this regard by handling most of the complex and repetitive work, facilitating focus on the modeling aspect, and providing a comprehensive benchmark for verification.

Finally, your comments have inspired us to develop proactive mechanisms to foster communication between battery science and data science. For instance, we could incorporate visualizations or simulation examples to intuitively illustrate the details of battery science and inherent electro-chemical processes, which may inspire data scientists to incorporate proper insights into their models. Simultaneously, we could develop high-level interfaces to enable quick coding and verification for battery experts with limited programming skills.

Reviewer comment (Presentation):
There seems to be a mismatch between the keywords used in Figure 1 (Normalization) and subsequent descriptions, which use Data Preprocessing.

Author response:
**Response to Questions 2, 3**

Thanks for your proofreading. In the updated manuscript, the term `Data Preprocessing` will be consistently employed throughout the document. Additionally, we will ensure that all acronyms are clearly defined prior to their initial usage within the text.

Reviewer comment (Reproducibility):
Could the authors clarify how much communication, about the details of battery science and the nuances of various electro-chemical processes involved in battery science is effectively relayed to the end-user, to help formulate models that match physical phenomena? In case this is limited, could the authors justify how the framework could help machine learning researchers effectively collaborate with battery science researchers?

Author response:
**Response to Weakness 1 and Question 1**

Thanks so much for pointing out such insightful and visionary comments. We hope the following clarifications and explanations can help to address your concerns.

Firstly, we would like to clarify that our unified data representation does not obstruct the communication between the nuances of battery science (e.g., electro-chemical processes) and the development of machine learning methods. On the contrary, this unified data layer is indispensable to facilitating such communication as it alleviates the burden of handling various data sources, thereby forming the data foundation for both training and evaluation processes. Our tool includes various vital and interpretable features such as incremental capacity, differential capacity, and coulomb efficiency, etc. These classical features, which incorporate essential physical insights about detailed electro-chemical processes, can be easily derived from our unified data representation. Furthermore, by accommodating different datasets, our tool enables rapid verification of the effectiveness of these features across diverse data scenarios.

Additionally, we concur with your observation that there is significant room for enhancing the communication between battery science and data science. While there are many challenges to overcome, we envision BatteryML serving as a platform to facilitate these interactions and drive co-innovation among battery scientists and machine learning experts.

One interesting case you have mentioned is to develop physics-informed methods, holding both data-driven flexibility and physically plausible explanations. Without doubt, BatteryML can effortlessly support the implementation of these methods due to its extensible interfaces across data, feature, and model modules. However, developing such methods can be challenging and requires either battery researchers equipped with professional ML skills or data scientists with a deep understanding of electro-chemical processes. We believe BatteryML can greatly contribute in this regard by handling most of the complex and repetitive work, facilitating focus on the modeling aspect, and providing a comprehensive benchmark for verification.

Finally, your comments have inspired us to develop proactive mechanisms to foster communication between battery science and data science. For instance, we could incorporate visualizations or simulation examples to intuitively illustrate the details of battery science and inherent electro-chemical processes, which may inspire data scientists to incorporate proper insights into their models. Simultaneously, we could develop high-level interfaces to enable quick coding and verification for battery experts with limited programming skills.

Reviewer comment (Writing):
Could the authors clarify which among Normalization or Data preprocessing is the correct nomenclature, and update the manuscript to maintain consistency?

Author response:
**Response to Questions 2, 3**

Thanks for your proofreading. In the updated manuscript, the term `Data Preprocessing` will be consistently employed throughout the document. Additionally, we will ensure that all acronyms are clearly defined prior to their initial usage within the text.

Reviewer comment (Writing):
In addition, please make sure that all acronyms remain well defined prior to their usage.

Author response:
**Response to Questions 2, 3**

Thanks for your proofreading. In the updated manuscript, the term `Data Preprocessing` will be consistently employed throughout the document. Additionally, we will ensure that all acronyms are clearly defined prior to their initial usage within the text.

Reviewer comment (Experiments):
The addition of an example detailing a custom data preprocessing/feature extraction technique would highlight the flexibility of the framework even further.

Author response:
**Response to Question 4**

As requested, we have included examples in the revised manuscript's appendix to illustrate the implementation of customized data preprocessing, feature engineering, and model development. For your convenience, an example of a customized data preprocessing step is detailed below.

**Example of Adding New Data Preprocessor**  
Integrating a new data preprocessor into BatteryML involves two primary steps:  
1. Define a new preprocessor class:  
The class definitions for data preprocessors are organized within  `batteryml/data/transformation`. To introduce a new data preprocessor, it is essential to implement interfaces such as `fit`, `transform`, and `inverse_transform`, closely resembles the design pattern of `scikit-learn`.  
2. Import data preprocessor class in `__init__.py`:  
Our system employs automatic builders for the instantiation of BatteryML components. These builders register all declared classes in the registry for subsequent construction during the initial import of batteryml.  

Once these steps are completed, you can configure the parameters for feature and label transformations in the configuration file. BatteryML's `Pipeline` API is designed to streamline the learning and evaluation processes.

Reviewer comment (Writing):
One of the potential improvements of this work is to include more discussions on the compared algorithms, which would help people using this framework to get to know the existing approaches better, along with their advantages and limitations for different tasks, thus making this work more impactful.

Author response:
Thanks so much for all your thorough reviews, insightful comments, and many constructive suggestions, based on which we will further enrich the technical and experiment content of this paper. Besides, we hope the following responses can help answer your questions and address your concerns.

**Response to Including More Discussions and Model Comparisons**

Thank you for your valuable comments and suggestions. We appreciate your insight and have further elaborated on the comparisons and discussions of different methods in our revised paper to better address your concerns.

Our comparative methods have been categorized into four types:
- **Dummy Regressor**, a baseline using the mean of the training label for prediction.
- **Linear models using handcrafted features**, such as Variance, Discharge, and Full Models, which employ linear regression on features devised by battery experts.
- **Statistical models** using raw *Qd(Vd)* features, encompassing methods like Ridge Regression, PCR, PLSR, Gaussian Process, XGBoost, and Random Forest.
- **Neural Network Models**, which include advanced models fitted to the *Qd(Vd)* feature, such as MLP, CNN, LSTM, and Transformer models.

We initially compare these methods from the feature perspective and subsequently provide a detailed analysis of their strengths and weaknesses.

**From a feature perspective**, Linear models, utilizing handcrafted features, have demonstrated satisfactory performance on datasets such as *MATR2*, *HUST*, and *CLO*, which solely consist of one battery type, LiFePO4 (LFP). This finding validates the efficacy of domain knowledge. However, these models appear to be less successful when applied to datasets that encompass a wider range of battery types and aging conditions, such as *CRUSH* and *MIX*. In these instances, models that are directly fitted on the *Qd(Vd)* curve have proven to be more effective than those using manually crafted features. This highlights a deficiency in domain-specific feature design and underscores the necessity for more versatile, generalizable features, emphasizing the potential advantages of automated representation learning.

**Strengths and limitations of the three types of methods:**
- Linear models using handcrafted features, such as the Discharge and Full model, offer relatively accurate predictions for LFP datasets. However, their performance diminishes on the *MIX* dataset, which features diverse aging conditions, due to the limited feature set and model capacity.

- Traditional statistical models, capable of discerning non-linear patterns from low-level features such as *Qd(Vd)* curves, employ specific modeling mechanisms. These include the decision tree ensemble approach in Random Forests and the use of kernel functions in Gaussian Processes. Despite their robust performance on datasets like *CRUH*, *CRUSH*, and *MIX*, their efficacy decreases on datasets such as *MATR2* and *SNL*, characterized by a scarcity of training samples. This finding indicates that these statistical models require a larger volume of training data to effectively learn and represent meaningful insights in RUL task.

- Neural networks, through automatic representation learning on low-level features, offer advancements, but face significant performance variations due to different random parameter initializations. For instance, our observations of CNN reveal its ability to make accurate predictions with many random seeds (as exemplified by the results on MATR1, shown below). However, certain seeds can lead to a surprising increase in error, causing significant regression error variations. This highlights both the potential benefits and challenges of applying neural networks to RUL prediction tasks.

||seed 0 | seed 1| seed 2| seed 3| seed 4| seed 5| seed 6| seed 7| seed 8| seed 9|
| ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | 
|CNN | 76 | 67 | 64 | 74| 60 | 82 | 65 | 79| 367 | 78 | 

In conclusion, our analysis indicates that no single method is universally optimal across all datasets. Each method exhibits unique strengths and weaknesses, suggesting the need for continued research in this domain.

Reviewer comment (Experiments):
The paper would be more convincing if more discussion and comparison are included between the methods from different categories, such as conventional methods vs tree-based methods vs NN-based methods.

Author response:
Thanks so much for all your thorough reviews, insightful comments, and many constructive suggestions, based on which we will further enrich the technical and experiment content of this paper. Besides, we hope the following responses can help answer your questions and address your concerns.

**Response to Including More Discussions and Model Comparisons**

Thank you for your valuable comments and suggestions. We appreciate your insight and have further elaborated on the comparisons and discussions of different methods in our revised paper to better address your concerns.

Our comparative methods have been categorized into four types:
- **Dummy Regressor**, a baseline using the mean of the training label for prediction.
- **Linear models using handcrafted features**, such as Variance, Discharge, and Full Models, which employ linear regression on features devised by battery experts.
- **Statistical models** using raw *Qd(Vd)* features, encompassing methods like Ridge Regression, PCR, PLSR, Gaussian Process, XGBoost, and Random Forest.
- **Neural Network Models**, which include advanced models fitted to the *Qd(Vd)* feature, such as MLP, CNN, LSTM, and Transformer models.

We initially compare these methods from the feature perspective and subsequently provide a detailed analysis of their strengths and weaknesses.

**From a feature perspective**, Linear models, utilizing handcrafted features, have demonstrated satisfactory performance on datasets such as *MATR2*, *HUST*, and *CLO*, which solely consist of one battery type, LiFePO4 (LFP). This finding validates the efficacy of domain knowledge. However, these models appear to be less successful when applied to datasets that encompass a wider range of battery types and aging conditions, such as *CRUSH* and *MIX*. In these instances, models that are directly fitted on the *Qd(Vd)* curve have proven to be more effective than those using manually crafted features. This highlights a deficiency in domain-specific feature design and underscores the necessity for more versatile, generalizable features, emphasizing the potential advantages of automated representation learning.

**Strengths and limitations of the three types of methods:**
- Linear models using handcrafted features, such as the Discharge and Full model, offer relatively accurate predictions for LFP datasets. However, their performance diminishes on the *MIX* dataset, which features diverse aging conditions, due to the limited feature set and model capacity.

- Traditional statistical models, capable of discerning non-linear patterns from low-level features such as *Qd(Vd)* curves, employ specific modeling mechanisms. These include the decision tree ensemble approach in Random Forests and the use of kernel functions in Gaussian Processes. Despite their robust performance on datasets like *CRUH*, *CRUSH*, and *MIX*, their efficacy decreases on datasets such as *MATR2* and *SNL*, characterized by a scarcity of training samples. This finding indicates that these statistical models require a larger volume of training data to effectively learn and represent meaningful insights in RUL task.

- Neural networks, through automatic representation learning on low-level features, offer advancements, but face significant performance variations due to different random parameter initializations. For instance, our observations of CNN reveal its ability to make accurate predictions with many random seeds (as exemplified by the results on MATR1, shown below). However, certain seeds can lead to a surprising increase in error, causing significant regression error variations. This highlights both the potential benefits and challenges of applying neural networks to RUL prediction tasks.

||seed 0 | seed 1| seed 2| seed 3| seed 4| seed 5| seed 6| seed 7| seed 8| seed 9|
| ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | 
|CNN | 76 | 67 | 64 | 74| 60 | 82 | 65 | 79| 367 | 78 | 

In conclusion, our analysis indicates that no single method is universally optimal across all datasets. Each method exhibits unique strengths and weaknesses, suggesting the need for continued research in this domain.

Reviewer comment (Presentation):
Within each category, it would be helpful to show the comparison as well.

Author response:
**Response to the Request for Detailed Comparison Discussion within Each Category**

In response to your suggestion, we have included an in-depth discussion comparing the methods within each category, further elucidating the strengths and weaknesses of different group methodologies.

**Linear Models with Hand-Crafted Features**: The Variance model, which uses the variance of the incremental *Qd(Vd)* curve as a scalar feature, displays moderate prediction accuracy across various datasets but generally falls short when compared to the Discharge and Full models. Both the Discharge and Full models exhibit variable effectiveness with significant errors on certain datasets, indicating a need for enhancements in feature design to improve the accuracy of linear model fitting.

**Traditional Statistical Models**: These models achieve significant results by fitting on low-level features, such as raw *QdLinear* curves. Ridge Regression displays consistent, albeit modest, performance across datasets, affirming a strong linear correlation between *Qd(Vd)* feature and battery cycle life. However, its underperformance on datasets like *HUST*, *CRUSH*, and *MIX* underscores the challenges in linear correlations under varying aging conditions. PCR and PLSR, which apply principal component analysis and project cells into different subspaces before fitting a linear regression, excel in *MATR1*, *CRUH*, and *SNL* datasets. This suggests that the *Qd(Vd)* feature exhibits a linear relationship in different subspaces with the battery life. Gaussian Process Regression (GPR) outperforms PCR and PLSR on *MIX*, demonstrating the importance of GPR's non-linear fitting ability in accurately capturing the diverse degradation patterns of batteries with different electrode chemistry and operating conditions. XGBoost and Random Forest, exhibiting strong performance on *CRUSH* and *MIX* datasets, indicate that tree-based models' non-linear capabilities are adept at effectively modeling complex battery aging patterns.

**Neural Network Models**: Neural network models, including Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Transformer architectures, display significant performance variability. MLP performs well on datasets such as *SNL*, *CLO*, and *CRUH*, while CNN shows high sensitivity to initial conditions. LSTM, exhibiting less variability, proves its robustness and superior performance on the MATR2 dataset among the neural network methods. The Transformer architecture, emerging as the most robust among deep models, achieves the best results on the *CRUSH* dataset across all models. These findings underscore both the potential of neural networks and the necessity for further refinement in learning methods and architectural designs to maximize their potential and possibly outperform traditional models.

Reviewer comment (Experiments):
It would be helpful to have a more detailed ablation study on the hyperparameter choices, feature selections, etc.

Author response:
**Response to the Request for Additional Ablation Studies.**

In response to your recommendation, we have incorporated ablation studies that delve into feature space and hyperparameter analysis. Below, we provide a brief overview of the principal results.

**Feature Ablations**

| |"Variance" features | "Discharge" features | "Full" features| *Qd(Vd)* Curve|
| ----- | ----- | ----- | ----- | ----- | 
|Linear Regression | 521 | 1743 | 331 | 395| 
|PCR | 521 | 1634 | 386 | 384 | 
|PLSR | 521 | 873 | 510 | 371 | 
|Gaussian Process | 521 | 341 | 287 | 257 | 
|Random Forest | 634 | 213 | 164 | 211 |

- The "Variance" feature refers to the log variance of $∆Q_{100−10}(V)$ during the discharge process.
- The "Discharge" feature encompasses multiple features extracted from the discharge process.
- The "Full" feature includes features extracted from both the charging and discharging processes.
- The *Qd(Vd)* Curve represents the *Q(V)* curve during the discharge process.

The predictive performance of the statistical models on the *MIX* dataset, using various features, offers distinct insights. The Variance feature, acting as a reliable baseline, provides consistent results across all models. Conversely, the Discharge feature demonstrates weaker performance with linear regression, PCR, and PLSR due to its non-linear characteristics in the *MIX* dataset, which includes diverse batteries and aging patterns. The Full feature displays a strong linear relationship with RUL, performing well across all models. Notably, both the Gaussian Process and Random Forest models yield effective results with the Discharge feature, underscoring its predictive prowess for RUL. The raw *Qd(Vd)* feature also performs commendably, demonstrating the models' capacity to learn directly from low-level data. However, a significant performance gap exists between the *Qd(Vd)* and Full features when using Random Forest, indicating a considerable scope for improvement in the models' ability to autonomously extract effective features from raw inputs.


**Hyperparameter Analysis for Statistical Models**

|Numbers of principal components | 2| 4| 8|  16| 32| 
| ----- | ----- | -----| ----- | ----- | ----- | 
|RMSE of PLSR | 475 | 459 | 455 | 9262 | 29142 | 
|**Number of decision trees** | **8**|  **16** | **32**|  **64**| **128**| **256**|
|RMSE of Random Forest | 233 | 234 | 236 | 237 | 237 | 234 |
|**Number of boosters** | **8**|  **16** | **32**|  **64**| **128**| **256**|
|RMSE of XGBoost | 336 | 325 | 324 | 323 | 323 | 323 |

The hyperparameter analysis of traditional statistical methods offers valuable insights for practical applications. PLSR exhibits a trend towards overfitting with an increasing number of principal components, necessitating cross-validation to determine the optimal number of components. Random Forest shows stable effectiveness, indicating a preference for a moderate number of decision trees to balance performance and computational efficiency. In the case of XGBoost, an increase in the number of boosters improves effectiveness, with a convergence point observed beyond 64 boosters. This suggests the feasibility of employing a higher number of boosters while maintaining computational practicality.

**Hyperparameter Analysis for Deep Neural Network Models**

|Hidden dimension | 4| 8|  16| 32|  64| 128|256|512|
| ----- | ----- | -----| ----- | ----- | ----- |  ----- | --- | --- |
|MLP | - | 342 | 334 | 330 | 330 | 336 | - | - |
|CNN | 375 | 368 | 326 | 353 | 347 | 394 | - | - |
|LSTM | 337 | 310 | 319 | 287 | 282 | 270 | 248 | 257 |
|Transformer | 382 | 330 | 322 | 309 |277 | 259 | 278 | 302 |

The performance analysis of deep models reveals the influence of hidden dimensions on model robustness and accuracy. In the Multilayer Perceptron (MLP), an increase in hidden dimensions results in higher variance without a significant change in mean prediction value, suggesting reduced robustness for larger dimensions in the *MIX* data source. Convolutional Neural Networks (CNN) require an optimal hidden dimension size, as extremes in size lead to high variance; a dimension of 16 is found to be most effective. For sequence modeling approaches, such as LSTM and Transformer models, increased model capacity enhances performance, indicating the benefit of using larger model capacities in practical battery modeling scenarios.

Reviewer comment (Experiments):
It could be beneficial to include a transformer model as well for the NN-based method or explain why this is not a method considered in the paper.

Author response:
**Response to the Request for Incorporation of Transformer Model**

We appreciate your suggestion to incorporate the Transformer model into our research. Initially, we had reservations about its use due to the data-scarce nature of battery degradation modeling, which could potentially impede the effective pre-training of the Transformer model. However, following your recommendation, we conducted experiments with the Transformer model and found it to be rather competitive. We present these findings below for your consideration.

|Models | *MATR1* | *MATR2* | *HUST* | *SNL* |  *CLO* | *CRUH*| *CRUSH* | *MIX*|
| ----- | ----- | -----| ----- | ----- | ----- |  ----- | ----- |  ----- | 
|MLP  | 149 ± 3 | 275 ± 27 |  459 ± 9  | 370 ± 81 |  146 ± 5  | 86 ± 4  | 448 ± 10 |  455 ± 37 | 
|CNN  | 102 ± 94 |  228 ± 104 |  465 ± 75  | 924 ± 267  | >1000 |  162 ± 116  | 354 ± 37  | 261 ± 38 | 
|LSTM  | 119 ± 11 |  219 ± 33 |  443 ± 29 |  539 ± 40  | 222 ± 12 |  97 ± 7  | 337 ± 19 |  266 ± 11 | 
|Transformer | 135 ± 13  | 364 ± 25| 391 ± 11| 424 ± 23| 187 ± 14 | 93 ± 5  |  **239 ± 9** |  259 ± 27|


The Transformer model displayed consistent performance across various datasets, surpassing other neural network models. It notably achieved the best performance among all neural counterparts on the *CRUSH* dataset. Furthermore, our ablation study on neural network models shed light on the influence of increased hidden layer dimensions on prediction errors across all mixed datasets. These findings will be incorporated into the revised paper.