Wavelet-Enhanced Neural ODE and Graph Attention for Interpretable Energy Forecasting

Usman Gani Joy

REVIEW 5 major objections 7 minor 55 references

Wavelet-Enhanced Neural ODE and Graph Attention for Interpretable Energy Forecasting

T0 review · 5 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A hybrid neural network that fuses Neural ODEs, graph attention, and wavelet transforms reports state-of-the-art forecasting accuracy across seven energy datasets, with SHAP-based interpretability.

desk verdict A reasonable multi-path fusion idea is undermined by internally inconsistent reported metrics and a lopsided baseline comparison, so the central claim does not stand. read the letter →

arxiv 2507.10132 v1 pith:W5EVSBHQ submitted 2025-07-14 cs.LG cs.AIstat.ML

Usman Gani Joy This is my paper · ORCID

classification cs.LGcs.AIstat.ML

keywords neuralordinarydifferentialequationsgraphattentionwavelettransformenergyloadforecastingtimeseriesSHAPinterpretabilityadaptivefrequencyfusionmultivariate

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that one architecture can handle the messy reality of energy time series — irregular sampling, multi-scale seasonality, and feature interactions — by combining continuous-time Neural ODEs with graph attention and wavelet-style transforms. Evaluated on four electricity transformer temperature datasets (ETTh1, ETTh2, ETTm1, ETTm2) and three renewable energy datasets (Waste, Hydro, Solar), it reports lower errors and higher R-squared than baselines like N-BEATS, N-HiTS, TCN, XGBoost, and Informer in nearly every setting. The abstract frames the result as consistent state-of-the-art performance, though the paper's own Solar results show a simple attention model scoring better on RMSE, R-squared, and MAE. SHAP analysis is used to identify which engineered features drive predictions, making the model more interpretable for energy planning and grid operations. If the claims hold under fair comparison, the architecture would be a practical general forecaster for sustainable energy systems.

What carries the argument

The load-bearing mechanism is a multi-path fusion pipeline: a Neural ODE with graph attention (state dynamics $dh/dt = f_\theta(h, A)$ using a dynamic adjacency matrix $A$ built from thresholded Pearson correlations, solved by one RK4 step), a Daubechies-inspired 1D convolution with global average pooling, a parametric transform using learnable frequency, amplitude, and phase, and a direct dense path. The concatenated feature vector is refined by dense layers with dropout and a residual connection, and the entire model is trained on mean squared error with Bayesian hyperparameter tuning and early stopping. What this machinery is doing is letting the model simultaneously represent continuous temporal dynamics, feature interdependencies, multi-scale transients, and periodic patterns, then merge them into a single scalar prediction.

What would settle it

Re-run the benchmark with the adjacency matrix computed only from the training portion, hand the same 51 engineered features to N-BEATS, N-HiTS, and TCN, and tune them with the same hyperparameter budget; if their RMSE and MAE approach or beat the reported values on ETTh1 and ETTm1, the claimed consistency would be an artifact of the evaluation setup.

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Extended reading notes

Core claim

The central claim is that fusing four parallel feature-extraction paths — a Neural ODE path with graph attention, a Daubechies-inspired wavelet convolution path, a learnable parametric frequency path, and a direct dense path — produces a forecaster that outperforms established baselines across diverse energy datasets. The adjacency matrix for the graph attention is built from thresholded Pearson correlations among features, allowing the model to learn inter-feature dependencies directly from data. The ODE state is evolved with a single fourth-order Runge-Kutta step at dt = 0.01, and all paths are concatenated and refined through dense layers with dropout and a residual connection. On the ETT datasets the model reports the best RMSE and MAE in 22 of 23 windowed settings, and on Waste and Hydro it achieves R-squared values above 0.98. The paper also argues through an ablation study that each path contributes, with the full model reaching R-squared 0.9606 on ETTh1 versus 0.7447 for the ODE-only configuration.

Load-bearing premise

The reported margin of improvement depends on the baselines being given the same engineered inputs, the same data split, and comparable tuning effort, but the paper does not document that, and the correlation graph is built on the full dataset before the train/test split.

Editorial extensions

If this is right

If the reported results are reproducible, the architecture offers a single model that works across hourly, 15-minute, and monthly energy data without changing its core design.
The claimed margins on ETT datasets — for example MSE of 0.0135 on ETTh1 versus 0.2970 for the best baseline — would make the model a new benchmark for transformer-temperature forecasting.
The ablation study indicates that removing any path degrades accuracy, with the ODE-only version performing far worse, which suggests the multi-path fusion itself is the source of the reported gains.
SHAP analysis points to a small set of features — oil-temperature differences and lags on ETT data, rolling means and lags on renewable data — that could guide cheaper feature engineering in practical deployments.
The paper's own Solar results, where a simple attention model beats the proposed model on RMSE, R-squared, and MAE, imply the architecture does not yet handle irregular high-variance renewable patterns as well as it handles smoother series.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct extension the paper leaves implicit: recompute the adjacency matrix from sliding windows or learn it end-to-end, since the static full-series correlation used here cannot adapt to regime shifts in energy data.
The single RK4 step with a fixed tiny dt makes the continuous-time claim largely symbolic; a meaningful test would feed irregular timestamps and allow variable integration steps to see whether the ODE path actually buys accuracy for unevenly sampled sensors.
The claimed state-of-the-art status would be much stronger if tested against modern transformer-based forecasters such as PatchTST, iTransformer, or TimesNet, which are absent from the baseline set.
The SHAP analysis is applied to engineered features rather than raw sensor channels, so its practical value depends on whether those engineered features are available at deployment time; otherwise the interpretability finding would not transfer to operational settings.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is not in a state where its claims survive contact with its own tables. The core idea—combine a Neural ODE (one RK4 step), graph attention on a correlation-derived adjacency matrix, a wavelet-inspired conv, and a parametric frequency transform—is a legitimate architectural experiment. The writing is clear, the complexity analysis is fine, and the SHAP section is a real attempt at interpretability. I also give the author credit for openly reporting that the model loses to a plain Attention baseline on the Solar dataset and for listing limitations in Section 10.

The problems are in the evaluation. Table 9, the ablation study, is mathematically impossible. RMSE is defined as sqrt(MSE), but several rows violate that: No ODE gives MSE=0.0143 and RMSE=0.1155 (sqrt=0.1196), No Daubechies gives 0.0172/0.1059 (sqrt=0.1311), and No Dense gives 0.0268/0.1827 (sqrt=0.1637). Squaring the RMSEs gives different numbers than the reported MSEs. Additionally, the Full model's reported ME=0.0498 and SDE=0.1416 imply an RMSE near 0.150, not the 0.1161 in the same table. That is not rounding; those rows cannot describe the same test set. When a paper's own numbers contradict each other, the claim of "consistently outperforms state-of-the-art" loses its evidentiary base.

The comparison is also lopsided. N-BEATS, N-HiTS, and TCN are not current state-of-the-art on ETT, and the paper never shows that those baselines received the same 51 engineered features the proposed model uses. The adjacency matrix is computed on the full dataset before the 80/20 split, which leaks test information into the graph. The "dynamic" graph is static; the "Daubechies" is an ordinary Conv1D; the ODE is a single step.

What is worth keeping: the multi-path fusion concept is not crazy, and the paper specifies every component well enough to reimplement. If the author re-runs the experiments with proper baselines, a clean data split, and self-consistent metrics, there might be a modest empirical contribution for energy forecasting. As it stands, the evidence does not support the abstract's claims.

For you: a useful case study in how evaluation details can sink a paper. I would not cite it, and I would not send it to a serious referee in this form. The author should revise with a corrected protocol and re-submit.

Referee Report

5 major / 7 minor

Summary. The paper proposes a hybrid time-series forecasting architecture that combines a Neural ODE (solved by one RK4 step with dt=0.01), graph attention over a Pearson-correlation adjacency matrix, a learnable 'Daubechies-inspired' convolution path, a parametric frequency transform, and a dense path, with SHAP used for interpretability. The model is evaluated on four ETT datasets and three monthly EIA energy datasets against baselines such as N-BEATS, N-HiTS, TCN, XGBoost, RandomForest, LSTM-Attention, and Informer. The paper claims consistent state-of-the-art performance, reports an ablation study on ETTh1, and provides execution-time, memory, and SHAP analyses.

Significance. If the reported results were reliable, the architecture would be a useful contribution to energy time-series forecasting, and the paper does provide a detailed architecture description, complexity analysis, and SHAP-based feature interpretation. However, the evaluation is the load-bearing part of the claim, and it is not internally consistent: the ablation table contains metric values that cannot be reconciled, the correlation-based graph is built on the full dataset before the train/test split, and the baseline comparison is lopsided and omits current state-of-the-art methods. These problems mean that the central claim of consistent superiority is not supported by the manuscript as written.

major comments (5)

[Section 8, Tables 9 and 10] The ablation table is internally inconsistent, so the paper's own numbers undermine the conclusion that each architectural component contributes. In Table 9, the Full Model reports MSE=0.0135 and RMSE=0.1161, which are consistent (0.1161^2=0.0135), but the other rows are not: No ODE has MSE=0.0143 and RMSE=0.1155, whose square is 0.0133; No Daubechies has MSE=0.0172 and RMSE=0.1059, whose square is 0.0112; No Dense has MSE=0.0268 and RMSE=0.1827, whose square is 0.0334. Additionally, for the Full Model, Table 8 reports ME=0.0498 and SDE=0.1416, which would imply RMSE=sqrt(ME^2+SDE^2)=0.150, not the 0.1161 reported in Table 9. These discrepancies are far too large to be rounding artifacts, and since the ablation is the primary evidence for the contribution of each path, the evaluation cannot be regarded as valid.
[Section 2.2, Eq. (1), and Section 5] The adjacency matrix A is computed from Pearson correlations over the full dataset X before the 80/20 train/test split described in Section 5. Algorithm 1, line 1, repeats this full-data computation. This means that test-set information is used to construct the graph that guides the attention mechanism during training and evaluation, which is a form of test leakage. A valid protocol would estimate the correlations and threshold on the training portion only, or use a rolling-window graph, and then freeze A before scoring the test set. As written, the reported margins may be inflated by this leakage.
[Section 5.1 and Section 6, Tables 2 and 3] The claim that the proposed model 'consistently outperforms state-of-the-art baselines' is not supported by the baseline selection or by the feature-setting symmetry. For the ETT datasets, N-BEATS, N-HiTS, and TCN are not current state-of-the-art; well-known stronger baselines such as PatchTST, iTransformer, TimesNet, and DLinear are absent. More importantly, the paper does not state whether those baselines received the 51 engineered features that the proposed model uses, or only raw windows. The hyperparameter description in Section 5.2 for the Darts models (input chunk length, layer widths, number of filters) suggests they do not receive the same engineered features. If the baselines were not given the same inputs, the comparison is not on the same forecasting task, and the large error gaps reported in Tables 2 and 3 are not meaningful.
[Section 6.1.1, Tables 4 and 5] The paper's summary claim of consistent wins is contradicted by its own Table 4. The text in Section 6.1.1 states that for the Solar dataset the Attention-based model outperforms the proposed model in RMSE, R2, and MAE (7.2984 vs 7.8372, 0.8886 vs 0.8716, and 5.4474 vs 5.4902). Yet Table 5 reports that the proposed model wins 22 of 23 RMSE settings and 22 of 23 MAE settings. If the Solar result is included in those counts, the table is wrong; if it is excluded, the counting basis is not stated. Either way, the 'consistently outperforms' claim in the abstract and Section 6 is not supported by the paper's own results.
[Section 2.3, Eq. (2)-(7)] The Neural ODE path as implemented performs a single RK4 step with dt=0.01 from the projected input, which is equivalent to a fixed residual update rather than an integration over a continuous interval. The text further claims that the framework can evaluate the state at arbitrary time points for irregularly sampled data, but no experiment or procedure demonstrates this capability. The contribution would be better framed as a residual-style ODE-inspired block than as a continuous-time model, and the claim of flexible handling of irregular sampling should be removed unless it is actually exercised and tested.

minor comments (7)

[Abstract] The abstract contains grammar errors, including 'This paper introduce' instead of 'This paper introduces', and 'proving its robustness' should be softened to 'demonstrating robustness' or similar. Please proofread the entire text.
[Section 2.5, Eq. (10)] The concatenated feature dimension is h + h/2 + h/2 + h/4 = 2.25h, not 'approximately 2h' as stated; the text should either correct the formula or the stated total.
[Figure 3] Figure 3 is captioned 'Adams-Bashforth ODE Solver Workflow' and shows Euler and Adams-Bashforth equations, but the text refers to Figure 3 as the proposed Neural ODE with graph attention and RK4. The figure and caption do not match the described architecture.
[Table 3] The ETTm2 rows for N-BEATS, N-HiTS, and TCN are identical to the corresponding ETTh1 rows for windows 96, 120, 336, and 720 (e.g., ETTm2 Window 96 N-BEATS RMSE=0.6334, MAE=0.4962, exactly as ETTh1 Window 96). This looks like a copy-paste error and should be corrected.
[Table 6] The Solar non-windowed hyperparameter row lists only four values ('96, 8, 63, 0.0001') whereas other rows list five; the dropout rate is missing and should be specified.
[Section 2.4.2] Calling the learnable Conv1D path a 'Daubechies transform' is misleading because the kernel is learned and not constrained to a Daubechies wavelet basis; the text should consistently say 'wavelet-inspired convolutional path' to avoid overclaiming.
[References] References [34] and [52] are duplicates of the same Informer paper; please merge them and cite the published version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the model is empirical and no prediction reduces to a fitted input or self-citation; the noted issues are evaluation-integrity concerns, not circularity.

full rationale

This is an empirical forecasting paper: the proposed multi-path network is trained to minimize MSE and evaluated on held-out test metrics, with no derived constants, no fitted parameter later renamed as a prediction, and no load-bearing self-citation or imported uniqueness theorem that would force a particular architectural choice. The graph-construction step in Eq. (1) is computed on the full dataset X before the 80/20 split described in Section 5, and Section 8's Table 9 is internally inconsistent with the definitional identity RMSE = sqrt(MSE) (e.g., Full Model MSE=0.0135/RMSE=0.1161 is consistent, but No ODE MSE=0.0143/RMSE=0.1155 and No Daubechies MSE=0.0172/RMSE=0.1059 are not), so the reported ablation and claim of consistent state-of-the-art performance are not reliable as stated. These are serious benchmark-integrity and internal-consistency problems, but they are not cases where a claimed prediction or first-principles result is equivalent to its inputs by construction, nor do the model's equations reduce to a self-citation chain. Accordingly, no circularity step is identified.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical or theoretical entities. The 'dynamic graph' and 'adaptive frequency transform' are algorithmic constructs built from standard operations. The central claims rest on hand-chosen hyperparameters, the adequacy of engineered features, and the correctness of the evaluation protocol, several of which are unvalidated or ad hoc to this paper.

free parameters (6)

Correlation threshold tau = 0.3
Used in Eq. (1) to threshold the adjacency matrix; chosen by hand and not tuned per dataset or justified empirically.
RK4 step size dt = 0.01
Section 2.3 states dt=0.01 was selected based on preliminary experiments; no sensitivity analysis is provided.
Per-dataset hidden dimension h = Varies per dataset, e.g., 64, 128, 48, 446, 96 in Table 6
Tuned via Bayesian optimization per dataset; the final performance depends on these dataset-specific settings.
Per-dataset dropout rate, learning rate, batch size, epochs = Varies per dataset, e.g., dropout 0.1-0.5, lr 1e-4 to 1e-2
Tuned with Optuna and listed in Table 6; no unified protocol.
Number of features after RFE = 8
Eq. (22) fixes |S|=8 for all datasets; this is an arbitrary choice that defines the model input.
Feature engineering window sizes and lag sets = EIA: window 3, lags 1-6; ETT: windows 5/10/20, lags 1-28
Hand-selected in Section 4; these features largely determine the forecasting performance, so the hand choices are load-bearing.

assumptions (5)

domain assumption The future target value is a function of the engineered feature vector, so a feedforward network on lags, rolling statistics, and calendar features suffices for forecasting.
The model input x is a feature vector, not a raw sequence; this is assumed throughout Section 4 and is never validated against a sequence-based model with the same data.
ad hoc to paper A thresholded Pearson correlation matrix computed on the full dataset is a valid graph structure for feature interactions and does not leak test information.
Section 2.2 defines A from X in R^(n x d) before the 80/20 split in Section 5, so the graph may encode test-period correlations; no train-only recomputation is stated.
ad hoc to paper One RK4 step with dt=0.01 captures the continuous-time dynamics needed for forecasting.
Section 2.3 uses a single ODE step, which reduces the Neural ODE to a residual block; the choice is justified only by preliminary experiments.
ad hoc to paper A learnable Conv1D with random initialization behaves like a Daubechies wavelet transform.
Section 2.4.2 calls the convolution a Daubechies transform, but the kernel is learned and is not constrained to satisfy wavelet properties.
domain assumption The 80/20 data split preserves temporal order and avoids lookahead in lag and rolling features.
Section 5 specifies an 80/20 split without stating whether it is chronological or random; unless features are computed causally, lag and rolling features at train time could include future information.

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Cite this review

Pith. "Pith review of Wavelet-Enhanced Neural ODE and Graph Attention for Interpretable Energy Forecasting." pith.science (2026). https://pith.science/paper/W5EVSBHQ

@misc{pith2026250710132,
  author       = {Pith},
  title        = {Pith review of: Wavelet-Enhanced Neural ODE and Graph Attention for Interpretable Energy Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5EVSBHQ}},
  note         = {Machine review of arXiv:2507.10132}
}

read the original abstract

Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework that integrates continuous-time Neural Ordinary Differential Equations (Neural ODEs), graph attention, multi-resolution wavelet transformations, and adaptive learning of frequencies to address the issues of time series prediction. The model employs a robust ODE solver, using the Runge-Kutta method, paired with graph-based attention and residual connections to better understand both structural and temporal patterns. Through wavelet-based feature extraction and adaptive frequency modulation, it adeptly captures and models diverse, multi-scale temporal dynamics. When evaluated across seven diverse datasets: ETTh1, ETTh2, ETTm1, ETTm2 (electricity transformer temperature), and Waste, Solar, and Hydro (renewable energy), this architecture consistently outperforms state-of-the-art baselines in various forecasting metrics, proving its robustness in capturing complex temporal dependencies. Furthermore, the model enhances interpretability through SHAP analysis, making it suitable for sustainable energy applications.

Figures

Figures reproduced from arXiv: 2507.10132 by the authors.

**Figure 2.** Dynamic adjacency matrix construction, showing feature connections based on correlation threshold [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Visualization of the Neural ODE component with graph attention, showing [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (24 more)

**Figure 4.** Figure 4: Process flow of the parametric transform, showing the learnable frequency matrix [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Illustration of the Daubechies transform, depicting convolution with kernel [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: EIA Datasets: Energy Consumption with Rolling Mean (2015-2020) for Waste, Hydro, and Solar. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: ETTh1 and ETTh2: Oil Temperature Difference with Rolling Mean (Jul 1-7, 2016). 4.1. Feature Selection Methodology Feature selection follows a two-stage process to optimize feature relevance [44]. First, an initial ranking of features is performed based on their importa…

**Figure 8.** Figure 8: ETTm1 and ETTm2: Oil Temperature Difference with Daily Lag (Jul 1-7, 2016). 5.1. Baseline Model Comparison The performance of the proposed model was evaluated through a comparative analysis against established baseline models. In the experiments with the ETT datasets, …

**Figure 9.** Figure 9: Actual vs. Predicted Values for the ETTm1 Dataset (First 500 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

**Figure 10.** Figure 10: Actual vs. Predicted Values for the ETTh1 Dataset (First 500 Samples). The orange bars represent the [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

**Figure 11.** Figure 11: Actual vs. Predicted Values for the ETTh2 Dataset (First 500 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

**Figure 12.** Figure 12: Actual vs. Predicted Values for the ETTm2 Dataset (First 500 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]

**Figure 13.** Figure 13: Actual vs. Predicted Values for the Waste Dataset (First 124 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

**Figure 14.** Figure 14: Actual vs. Predicted Values for the Hydro Dataset (First 124 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]

**Figure 15.** Figure 15: Actual vs. Predicted Values for the Solar Dataset (First 97 Samples). The blue line represents the actual [PITH_FULL_IMAGE:figures/full_fig_p025_15.png]

**Figure 16.** Figure 16: ETTh1 - Global SHAP Visualizations [PITH_FULL_IMAGE:figures/full_fig_p031_16.png]

**Figure 17.** Figure 17: ETTh1 - SHAP Dependence Plot for OT diff [PITH_FULL_IMAGE:figures/full_fig_p032_17.png]

**Figure 18.** Figure 18: ETTh1 - SHAP Waterfall Plot for Instance 0 [PITH_FULL_IMAGE:figures/full_fig_p032_18.png]

**Figure 19.** Figure 19: ETTm1 - Global SHAP Visualizations [PITH_FULL_IMAGE:figures/full_fig_p033_19.png]

**Figure 20.** Figure 20: ETTm1 - SHAP Dependence Plot for OT diff [PITH_FULL_IMAGE:figures/full_fig_p034_20.png]

**Figure 21.** Figure 21: ETTm1 - SHAP Waterfall Plot for Instance 0 [PITH_FULL_IMAGE:figures/full_fig_p034_21.png]

**Figure 22.** Figure 22: Waste - Global SHAP Visualizations 9.4. Hydroelectric Dataset Analysis For the hydroelectric dataset, the SHAP bar plot (Figure 24a) highlights hydro rolling mean 3 as the most impactful feature, with an average SHAP value exceeding 15, followed by hydro lag 1 and hy…

**Figure 23.** Figure 23: Waste - SHAP Waterfall Plot for Instance 0 [PITH_FULL_IMAGE:figures/full_fig_p036_23.png]

**Figure 24.** Figure 24: Hydro - Global SHAP Visualizations 36 [PITH_FULL_IMAGE:figures/full_fig_p036_24.png]

**Figure 25.** Figure 25: Hydro - SHAP Waterfall Plot for Instance 0 [PITH_FULL_IMAGE:figures/full_fig_p037_25.png]

**Figure 26.** Figure 26: Solar - Global SHAP Visualizations [PITH_FULL_IMAGE:figures/full_fig_p038_26.png]

**Figure 27.** Figure 27: Solar - SHAP Waterfall Plot for Instance 0 [PITH_FULL_IMAGE:figures/full_fig_p038_27.png]

Discussion (0). Continue with ORCID to comment.

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