GAETS: A Graph Autoencoder Time Series Approach Towards Battery Parameter Estimation
Authors: Edward Elson Kosasih
Rucha Bhalchandra Joshi
Janamejaya Channegowda
Venue: ICLR 2022 Submitted (2022)

Abstract:  Lithium-ion batteries are powering the ongoing transportation electrification revolution. Lithium-ion batteries possess higher energy density and favourable electrochemical properties which make it a preferable energy source for electric vehicles. Precise estimation of battery parameters (Charge capacity, voltage etc) is vital to estimate the available range in an electric vehicle. Graph-based estimation techniques enable us to understand the variable dependencies underpinning them to improve estimates. In this paper we employ Graph Neural Networks for battery parameter estimation, we introduce a unique graph autoencoder time series estimation approach. Variables in battery measurements are known to have an underlying relationship with each other in a certain causal structure. Therefore, we include ideas from the field of causal structure learning as a regularisation to our learned adjacency matrix technique. We use graph autoencoder based on a non-linear version of NOTEARS Zheng et al. (2018) as this allowed us to perform gradient-descent in learning the structure (instead of treating it as a combinatorial optimisation problem). The proposed architecture outperforms the state-of-the-art Graph Time Series  (GTS) Shang et al. (2021a)   architecture for battery parameter estimation. We call our method GAETS (Graph AutoEncoder Time Series).

Under review as a conference paper at ICLR 2022
GAETS: A GRAPH AUTOENCODER TIME SERIES APPROACH TOWARDS BATTERY PARAMETER ESTIMATION
Anonymous authors Paper under double-bling review
ABSTRACT
Lithium-ion batteries are powering the ongoing transportation electrification rev- olution. Lithium-ion batteries possess higher energy density and favourable elec- trochemical properties which make it preferable energy source for electric ve- hicles. Precise estimation of battery parameters (Charge capacity, voltage etc) is vital to estimate the available range in an electric vehicle. Graph-based estima- tion techniques enable us understand the variable dependencies underpinning them to improve estimates. In this paper we employ Graph Neural Networks for battery parameter estimation, we introduce a unique graph autoencoder time se- ries estimation approach. Variables in battery measurements underlying relationship with each other in a certain causal structure. Therefore, include ideas from the field of causal structure learning as regularisation our learned adjacency matrix technique. We use graph autoencoder based on a non-linear version NOTEARS Zheng et al. (2018) as this allowed us perform gradient-descen in learning the structure (instead of treating it as combinatorial optimisation problem). The proposed architecture outperforms the state-of-the ahe Graph Time Series (GTS) Shang et al.] (2021a) architecture for battery parameter estimation. We call our method GAETS (Graph AutoEncoder Time Series).
known to have
INTRODUCTION AND LITERATURE REVIEW
Energy dense Lithium-ion batteries (LiB) are driving the current electrification revolution in the transportation sector Balasingam & Pattipati (202I). Rapid advancements in battery material science have enabled inexpensive and long-running LiBs. However, capacity degradation leading to poor performance are some of the drawbacks of these batteries Zhou et al. (021). Development of accurate State-of- Charge estimation algorithms have garnered attention over the past decade as these metrics translate to available range in an Electric Vehicle Herle et al. (2020).
Battery degradation capacity fade occurs due to repetitive charge/discharge cycles. Decreased battery capacity over its usage is an indicator of poor health of the battery MMohtat et al.] (2021). Present battery models available in literature suffer from reliable battery capacity fade predictions Hinz (2019). This uncertainty in prediction is chiefly due to the non-linear behaviour of battery discharge characteristics with increased battery age.
Battery Ageing has also been a topic of considerable interest in the energy storage domain Ning
& Popov )2004); ; Ning et al. (2006): Peterson al.] (2010); Barré al. (2013). Empirical battery
models have been used for Remaining Useful Life prediction of batteries Saha & Goebel (2009);
Daigle & Kulkarni (2016): Nuhie et (2018): Andre et al. (2013). Simple estimators from Kalman
Filter Andre et al. 2013); :) Bole et al. (2014) to Reinforcement Learning techniques Unagar et al.
2020 have been employed for battery parameter estimation.
All the current battery parameter estimation techniques available in literature can be broadly classi-
fied as follows:
Physics- based modeling which employs Partial Differential Equations (PDEs) to compute equivalent battery parameters Wang et al. (201))

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Under review as a conference paper at ICLR 2022
2. Phenomenological battery modeling, achieved by focused computation of battery capacity changes corresponding to specific charge/discharge cycles Goebel et al. (2008)
3. Data-driven estimation models, which provide meaningful insights from historical battery data and do not involve computation of complex electrochemical models [Svvesson et al. (2019)
In the present work we use Graph-based data-driven technique to gain meaningful insights from battery datasets to improve estimate accuracy. The paper is organised as follows, brief review of graph based forecasting techniques is covered in Section 2 the architecture of the proposed Graph- based estimation technique is presented in Section
[ details about experimentation are covered in Section 4 followed by conclusion in Section
GRAPH-BASED TIME SERIES ESTIMATION: RELATED WORK
Battery datasets typically consist of time series Voltage, Current, Temperature and State-of-Charee values as shown in Fig. Statistical Time series based estimation techniques have heen popular
Bhatnagar al. 2021 for typical time series datasets.
Voltage
Current
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3.5
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Time (s)
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Figure 1: Typical battery discharge characteristics of 18650 cells Herle et al. (2000)
In Multivariate time series scenarios variable dependencies have been investigated improve esti- mations Yu et al.) (2018). Traffic datasets are one of the prime examples wherein variation in speed and traffic density insights are useful accurately predict vehicular traffic other nodes of the net- work. There are numerous Graph Neural Network (GNN) based techniques which exploit the graph structure of datasets to improve prediction accuracy Seo et al. (2016). Li al. (2018) and Zhao al. 2020).
All Graph-based forecasting and estimation approaches available in literature have been validated using traffic datasets. A more recent variant of Graph Neural Network dubbed GTS (Graph for Time Series) has been successfully employed to learn specific graph structures to improve prediction accuracy (Shang et al. (2021b). In this paper we build upon the GTS architecture specifically for battery datasets. Following section elucidates the proposed architecture in greater detail.
3 GAETS ARCHITECTURE
2

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Battery
Decoder
Bettery
A = H'
sampled graph
Encoder
link predictor
sampling
learned
6
recurrent graph convolution
recurrent graph convolution
recurrent graph
recurrent graph
c+1
2 windowed data
t+T
t+
Forecasted Values 7+
Figure 2: Graph AutoEncoder Time Series (GAETS) architecture
3.1
THE METHOD
The architecture of GAETS is as depicted in The objective of the method is fore- cast X14I+14+7+7 given the observations X1+1+++T where X denotes training data and con- sists of multiple charge/discharge cycles of battery measurements. The model is denoted as X++r+1=47=+ f(A, w. Xx+1++)), where A is the graph structure and is parameterized by T the input window duration, our goal to predict future data from time i T + I to & + + T, here is the output prediction window length. The graph structure represented by adjacency matrix A 1001]"mn is to be parameterized as it is exclusively not available to the forecasting model. GTS (Saang al. (2021b) parameterizes the graph structure by considering the adjacency matrix A to be random variable on matrix Bernoulli distribution and is learned as part of the task. We use Gumbel reparameterization trick is used in [Shang al. (022b) because the gradients fail to flow through A in Bernoulli sampling.
3.1.1 RICODER-DECODERS
The encoder-decoo decoder architecture is used in order to reconstruct the original time series data and to learn the intermediate represetations. The model assumes inherent nonlinear Structural Equation Model (SEM) that connects the node features to the adjacency matrix. The SEM was first proposed NOTEARS Zheng et al. (2018).
x = f(x() =2
- (x(())
(1)
where and G2 are neural networks, encoder and decoder respectively while j represents the node id. This can be seen as graph autoencoder. The encoder extracts the features from the original time series data, by applying fully connected layer the convolved original features.
h FC (vec (Conv (X)))
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where h' is the features extracted in the lower dimensional space. X' is the ith series of features. The matrix H of representations h's generated by the encoders are used in the graph autoencoder well as in the link predictor. In this scenario the vector representations are fed as input to the link predictor which spits out a scalar. The output scalar decides the existance of a link. These are represented h; and hy, the vectors concatenated and passed through two fully connected layers to finally get the scalar.
The extracted features along with the sampled graph adjacency matrix is passed through the decoder. We make use of an MLP as the decoder. The loss incurred by the autoencoder also adds up to the final loss to be optimized.
3.1.2 RECURRENT NETWORKS
In order to estimate the time series predictions based on graphs. make use of diffusion convolu- tional GRU as in DCRNN Li et al. (0018) and GTS /Shan et al. (2021b).
Re (WRIA (Xe Hr-1] bR). Ce tanh (Wa.A [Xp (Ry Hy-1)) bc), Up (Wo.A (Xe He-1] bb),
H = Up @ Hy-1 + (1 Uv) @ Cv.
where
K Wo = -0 k,1 R=0
AD) + 6 (D7 (DF
where all W's are corresponding weight matrices, Dy and Do are in-degree and out-degree matrix respectively. o and 2x, and bq are the model parameters and K is the hyperparameter corre- sponding to the degree of diffusion.
3.2 TRAINING
The time series forecasting loss the base loss which is the loss between the values forecasted by the models and the ground truth. Hence the first objective is given in 2
4T++ Σ
min Mase (X4T+)
X - X
t'=+T++1
The autoencoder compares the reconstructed data against the input data. The autoencoder loss, the second objective is given in
1x (2 91
min lautoencoder
where, n is the number of samples, and min lautoencoder acts as regularizer to the original GTS (Shang al. (2021a)) loss. The original GTS loss given
The final loss comprises of the loss incurred by the autoencoder and the base loss. It is given in
loss Ihase (SUTHLLTT4e) + lautoencoder
(4)
Finally, we arrive at the expression 5 that we need to minimize.
loss 1 t+T47
Σ
X Xx
(x()
(A 91 (1
(5)
7 (=t-T41
2n
4

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4 EXPERIMENTS
To validate the GAETS architecture we used Lithium-ion Battery Data 2018). All the batteries listed in the dataset had multiple charge/discharge cycles. We trained the model on two sets of mea- surement values logged from two separate channels. The data consists of 6 measurements namely: Voltage, Current, Charge Capacity, Discharge Capacity, Charge Energy and Discharge Energy. Each measurement treated as a node and the task is to learn the structure that represents relationship between variables well as forecasting the battery parameter of interest. We fix the input horizon to be 80 and test the data on three different forecasting window horizons of 40, 80 and 120.
In terms of tensor size, the training data is made of (Xtrains Ytrai)) where Xtrain is 1497 signals with dimension
(for each measurement) and horizon as 80, while Ytrain is 1497 signals with dimension of 6 and 40/80/120 horizon values. Validation is done 213 signals. Meanwhile, testing data is made of (Xtest. Yeest) where Xrest is 1497 signals with a dimension of 6 (for each measure- ment) and 80 window ticks, while Yreat 1497 signals with dimension of 6 and 40/80/120 12 horizon values. These datasets are obtained by continuous moving window average across the original long time series data.
We follow the code implementation in GTS Shang et al. (202 using the same setting for the graph neural network architecture and optimiser. We train each model for 200 epochs, obtain the best model for validation dataset and test it. Each model is trained from different random initialisations. The performance result and confidence interval shown in the chart. Performance is measured through MAE, RMSE and MAPE values shown in Fig. 6 following GTS Shang et al. (2021a) paper. Visual comparison Battery Voltage, Current and Charge Energy is presented Fig. 3,4 and 5.
GAFTS Prediction
Prediction
07
05
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03
125
175
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(b)
Figure 3: Battery Voltage predictions using GAETS (this work) and GTS Shang et al. (2021a)
Prediction
GTS Prediction
05
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2.0
-25
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25
200
(b)
Figure 4: Battery Current predictions using GAETS (this work) and GTS Shang et al. 2021ab

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GAETS Prediction
GTS Prediction
2.0
10
1.0
05
0.5
(a)
(b)
Figure 5: Battery Energy predictions using GAETS (this work) and GTS Shang et al. 202
Model
Model
0.6
Modell
GAFTS
GAFTS
GIFTSS
0.25
0.5
0.5
MAE
0.20
MAPE
0.4
RMSE
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0.3
0.2
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0.1
40
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8D Horizon
100
12
40
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8D Hoftzon
100
120
40
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8D
100
120
Hofizon
(a) MAE
(b) MAPE
(c) RMSE
Figure 6: Evaluation metrics comparing the proposed GAETS architecture with GTS
5 CONCLUSION
Battery parameter estimation remains to be challenging and topic of relevance due to the burgeon- ing number Electric Vehicles the past decade. Accurate battery capacity estimation also helps to predict remaining usage time in battery powered consumer electronics. In this paper introduce a Graph AutoEncoder Time Series (GAETS) architccture which exploits the dependencies between battery parameters (charge capacity, voltage, current etc) to provide precise estimates. We compare our architecture with the existing Graph Time Series architecture to highlight the effectiveness of our approach.
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Reviews:
[{"review_id": "sB0VAyc4mJ9", "reviewer": "Reviewer_LsgQ", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Pros:\n1. The problem is meaningful. Lithium-ion batteries are driving the current electrification revolution. Studying the time-series battery estimations is impactful.\n2. The method achieves good results on the real-world battery dataset and outperforms the compared SOTA method.\n\nCons:\n1. The proposed method, GAETS, essentially adds a graph autoencoding module on top of the previous GTS method. The autoencoding module acts as a regularizer. But overall this added module is only incrementally novel. The paper lacks enough evidence to support why this autoencoding is necessary.\n2. The experiment is thin. There are many existing temporal graph neural networks for time-series forecasting [1]. It is not very convincing when you only compare with 1 other method. Also, as you mentioned in the introduction, there also exist physics-based modeling and phenomenological battery modeling. As an application specific paper, it makes more sense to include those models in comparison.\n3. The method looks quite general. Could you also validate its performance on other time-series scenarios?\n4. Some descriptions are not very clear. In sec 3.1, when the graph structure $A$ is first introduced, there is no prior descriptions about what is this A. I understand you inherit many setups from GTS paper. But you really need to make sure your paper is self-contained and provide all necessary details. Also, you mentioned $A$ is sampled. How is it sampled should be clarified? Do you sample one $A$ for all timestamps, or sample one $A$ for each timestamp?\n5. In your problem, you have the index for different time series sources and the timestamp index for sequence data. You should better clarify the notations and be more consistent. For instance, In sec 3.1.1, you have $X^{(j)}$ and $X^i$. It is confusing whether they denote different things. \n6. You only give brief introductions for the recurrent networks. Given its importance in your work, you should elaborate on this section and expand it (even it is from previous works). \n7. When you first introduce $A$ is $n\\times n$ in sec 3.1, you didn't specify what $n$ is. $R, C, U$ from sec 3.1.2 are not well explained either.\n\n\n[1] Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting. Cao, D., Wang, Y., Duan, J., Zhang, C., Zhu, X., Huang, C., Tong, Y., Xu, B., Bai, J., Tong, J. and Zhang, Q. NeurIPS 2020.", "summary_of_the_paper": "This work proposes a new method based on graph neural network for Lithium-ion batteries parameters estimation. In a typical time-series data, one is given some past timestamps and is asked to predict some future timestamps. In this problem, you have multiple time series of battery parameters. The goal is to predict multiple future states for all the time series data. Since the time series data could be correlated, this work introduces a graph neural network where each time series source is a node on the graph, and the node relations are learnt through training. The graph is used in the recurrent graph convolution and graph autoencoding. The loss function has a future prediction component, and an autoencoding reconstruction component to regularize the learning. The method is validated on a Lithium-ion battery dataset. It outperforms the compared state-of-the-art method.", "summary_of_the_review": "This paper is an application paper, on Lithium-ion battery parameter estimations. While I generally appreciate the application, I think the paper is thin. Method-wise, it is incrementally novel compared to the prior work GTS. Experiment-wise, given this is an application paper, authors are expected to show more experiments and give more analyses, including more datasets and compared methods. Even the given experiment shows the proposed method is only marginally better than the only compared method. The paper is neither well-organized nor self-contained. The authors should keep improving the paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "m9jxEqw3eav", "reviewer": "Reviewer_L9LB", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The graph auto encoder used in the paper forecasts the state of charge using an absolute error prediction loss. This part is based on an existing algorithm (Shang et al 2021a and 2021b). The neural network architecture is also based on the same paper. \n\nThe paper proposes adding a reconstruction loss (given by absolute error) to the prediction loss as a regularizer. This is a small addition to the algorithm. The resulting performance improvement is also marginal as seen by the prediction graphs between the proposed algorithm GAETS and existing algorithm GTS. \n\nTherefore, the paper does not meet the acceptance criteria for a top tier conference such as ICLR. \n\nThe paper can also benefit from analysis of the relationships learned by the graph network to inform the domain experts in the area.", "summary_of_the_paper": "The paper proposes a graph neural network based forecasting algorithm for battery state of charge. Building on prior work, the paper proposes a regularization based on reconstruction loss. Evaluation on a battery dataset shows improvements.", "summary_of_the_review": "The proposed algorithm is incremental over the existing ones and the corresponding impact on results is marginal.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "UGxRaNJfv6b", "reviewer": "Reviewer_61UC", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n- The idea of incorporating causal structure learning with graph-based forecasting is interesting and, to the best of my knowledge, novel.\n\nWeaknesses:\n- The motivation of incorporating causal structure learning is unclear. The authors could provide more explanation, and also visualize the learned adjacency matrix to verify if the learned relationships are consistent with domain knowledge.\n- In Section 3, $A$ is not guaranteed to be acyclic, different from [1], since the author does not enforce the acyclicity constraint. In this case, how is it related to causality?\n- Apart from demonstrating that the proposed method works on the battery dataset, I would encourage the authors to compare it to standard traffic prediction dataset, as also mentioned in Section 2.\n\nOther comments:\n- A large part of Figure 2 seems to be similar to Figure 1 in [2] with a different color.\n- Also, Equation (1) seems to be similar to Equation (5) in [3] but is not referenced.\n\nReferences:\n\n[1] DAGs with NO TEARS: Continuous Optimization for Structure Learning, 2018.\n\n[2] Discrete Graph Structure Learning for Forecasting Multiple Time Series, 2021.\n\n[3] A Graph Autoencoder Approach to Causal Structure Learning, 2019.", "summary_of_the_paper": "The paper proposes to incorporate a graph-autoencoder method from the field of causal structure learning for improving graph-based forecasting, with a focus on battery parameter estimation. In particular, the authors include a regularization term based on graph-autoencoder in the forecasting model to learn the variable dependencies. The authors demonstrate empirically that the proposed method has an improved performance over the baseline considered.", "summary_of_the_review": "The idea of incorporating causal structure learning with graph-based forecasting is interesting and novel, but the motivation is unclear. Moreover, the adjacency matrix used is not guaranteed to be acyclic, and, in that case, the authors should explain how it is related to causality.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "P06KkeI1zql", "reviewer": "Reviewer_5kWi", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n1. The paper is easy to read. \n2. In terms of methodology, instead of learning graph structure directly, the method iteratively samples the graph with learned parameters for the encoder-decoder framework. The Gumbel reparameterization technique is used and enables the gradients to flow through A.\n3. Experiments outperform the SOTA method and achieve satisfactory results.\n\nWeaknesses:\nMy major concern of this paper:\n1. The technical contribution is limited. Considering that the architecture of RNN+GNN is not novel, the main contribution of this paper may come from the application of graph sampling for learning the relationship between variables. \n[KDD20] Wu, Zonghan, et al. \"Connecting the dots: Multivariate time series forecasting with graph neural networks.\" \n[AAAI21]Deng, Ailin, and Bryan Hooi. \"Graph neural network-based anomaly detection in multivariate time series.\" \n\n2. The necessity of graph structure learning needs to be proved. The dataset used in this paper has only six dimensions of variables, and the underlying relationships learned by the method are not explicitly shown in this paper.\n\n3. The experimental results are not enough. The proposed method is only compared with GTS, while more baseline methods need to be included. The authors may want to conduct an ablation study to show the effectiveness of each component in their method.\n[AAAI2021]Zhou, Haoyi, et al. \"Informer: Beyond efficient transformer for long sequence time-series forecasting.\" ", "summary_of_the_paper": "This paper studies a new problem of battery parameter estimation. The paper proposes a new graph autoencoder time series estimation approach that learns the underlying relationship between variables in battery measurements. Experimental results show that the new method outperforms the SOTA method and achieves satisfactory results.\n\n", "summary_of_the_review": "\nOther comments:\n\n- The functions of g_1 and g_2 are not explained.\n\n- In 3.1.2, the equation of W_(Q*A)Y is confusing. This function is not mentioned in the rest of the paper. \n\n- In Fig3,4,5, the results of the proposed method compared with the baseline seems not significant. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper proposes to apply graph neural networks to predict battery state of charge. The main concern is the lack of technical novelty, since the main work is a straightforward application of existing works. The work could be better suited for a more application-oriented venue.
Decision: Reject