PONE-D-25-12306HYDRODYNAMIC MODELING USING PHYSICS INFORMED MACHINE LEARNING METHODPLOS ONE

Dear Dr. Mumtaz,

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Divyesh Varade, PhD

Academic Editor

PLOS ONE

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Additional Editor Comments:

I have received the reviewer reports and based on these and my own evaluation of the manuscript, I invite the authors to revise the manuscript in accordance with the comments.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: N/A

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I enjoy reading the paper. Some specific comments are as follow:

1. What is meant by: This approach can improve the accuracy of predictions, especially when data are limited, noisy, or missing.

2. The training setup is described in 3.0.2. Is the additional description in 4.0 redundant or for a different purpose?

3. How are the number of layers and neuron decided a priori?

4. The distinction between the PINN, HNN and DDNN is not entirely clear for me.

(a) For PINN, what is the training input?

(b) For HNN, what is the training input? What is done in t ∈ (0, 0.4) and t ∈ (0.4, 1) for each/both the approach?

(c) For DDNN, what is the training input?

Perhaps a graphical summary/ flow chart will greatly help the reader.

Note: Meaning of the term "unseen data" is not clear. Care should be taken to differentiate "data", "input", "numerical results (data?)"

5. Please provide detail on: the loss function formulation differs for each of the networks.

6. Statistical justification for: outperforming traditional numerical methods in terms of generalization and computational efficiency.

7. Please clarify statement in Abstract: This study emphasizes PINNs scalability and versatility for hydrodynamic modeling,

Other area to improve:

1. Paragraph 1 is too lengthy and should be split accordingly.

2. The figures quality is not adequate for viewing the results in detail and the legend

Reviewer #2: 1. In the introduction section, the sentence beginning with "In recent years, … of hydrological applications" lacks clarity. Please rephrase it to convey a more precise meaning.

2. The manuscript currently cites only a few references ([1], [2], [3]) and lacks an in-depth comparison of related work involving PINNs in hydrology or fluid mechanics. A more comprehensive literature review is needed to establish the novelty and context of your work.

3. The manuscript contains several repetitive sentences, especially in the introduction and methodology sections. Consider revising for conciseness and clarity.

4. In Section 1.1 (State of the Art), phrases like "[4] is employed..." should be rewritten using author names, e.g., "Kader et al., 2020 [4]." Please ensure that all references throughout the manuscript follow this format for clarity and readability.

5. Figures 7, 9, 11, 13, and 15 are labeled as showing both training and testing loss, but only one curve is plotted, which appears to be the training loss. Moreover, these figures are not cited or discussed in the main text. Please correct the figures and provide a proper interpretation in the results section.

6. The purpose and content of Figures 4 and 6 are unclear. Please elaborate on what these figures represent and how they contribute to the findings.

7. The manuscript does not explain how the models were trained. What portions of the data were used for training and testing? What were the input features and target variables? This information is critical and must be included.

8. There is no discussion of how model performance was validated. Please include quantitative evaluation metrics such as RMSE, MAE, MSE, or R² to assess and compare the model predictions.

9. The results section lacks detailed explanation and interpretation of the figures. Each figure should be properly described and analyzed to highlight key insights and outcomes.

10. A discussion section is completely missing from the manuscript. Please add a dedicated section that critically interprets the findings, compares them with previous studies, discusses limitations, and highlights the implications of your results.

Reviewer #3: This study proposed a Physics-Informed Neural Network (PINN) framework to solve 1D and 2D SWEs for dam-break problems. While some of their results are interesting, the study has low novelty regarding methods and applications. Some papers, such as 10.1016/j.jhydrol.2024.131263, 10.1029/2023WR036589, 10.48550/arXiv.2406.16236, etc., all trained the PINN without precomputed numerical data.

The main comments are:

1. The paper is only an application of PINN with no new idea or approach. The contribution of this paper is unclear.

2. The test cases are very simple. No friction or varying topography is considered. Besides, I do not appreciate that the wet-dry problem is ignored in the study. I would recommend the paper to consider at least one of these issues.

3. The comparison between PINN and other numerical methods is unfair. In this study, PINN is compared with a FD scheme, which is well known to struggle with shock wave modelling and has been considered suboptimal for such water problems for over a decade. To strengthen the evaluation, I recommend comparing PINN with more advanced numerical methods, such as FV and FE schemes, which are more robust in handling discontinuities and complex flow dynamics.

Other comments are:

1. Introduction: Shallow water modelling belongs to the hydraulic study instead of the hydrological study. More references for flood review should be cited.

2. The review of using PINN to solve SWEs is limited. The study of PINN for SWEs is recently a very active field. Many papers can be cited. More examples such as doi.org/10.3389/fcpxs.2024.1508091, 10.1029/2024WR037490, 10.1016/j.scitotenv.2023.168814, 1016/j.jcp.2022.111024.

3. The paper could include a table summarising all the PINN training configurations.

4. Some experiments for the model design and trials can be added as the appendix.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes: Xin Qi

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Attachments

Attachment

Submitted filename: Review_PlosOne.docx

Investigating the use of physics informed neural networks for dam-break scenarios

PONE-D-25-12306R1

Dear Dr. Mumtaz,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Divyesh Varade, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

The reviewers have recommended consideration of the revised manuscript for publication and I am in agreement with their comments. Reviewer-3 has mentioned including some review literature to be incorporated, which is optional.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #3: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #3: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #3: N/A

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #3: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: (No Response)

Reviewer #3: I have reviewed all the responses and the whole paper. The authors may not want to do any extra tests. Thus, I will leave it to the editors to decide.

I would still recommend that authors have more references to support their discussion. Some studies have attempted to address issues, such as the wet-dry front or changing topography (https://doi.org/10.1016/j.jhydrol.2024.131263, https://doi.org/10.3390/w17081239, https://doi.org/10.3390/w17081239, https://doi.org/10.1016/j.ocemod.2025.102601 etc). I would encourage the authors to further improve the manuscript by enriching the reviewed papers.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #3: No

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