A Physics-Constrained Method for the Precise Spatiotemporal Prediction of Rock-Damage Evolution

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Language:

1. Page 1 and 2, Paragraph 2:"Recent studies have reported encouraging progress: deep models for surrounding-rock deformation in high-speed railway tunnels [4], hybrid constitutive modeling and deformation prediction for sandy limestone [5], transfer-learning-enhanced" . This sentence should be: This is a sentence fragment. It should be rephrased, e.g., "Recent studies have reported encouraging progress in areas such as..."
2. Page 3, Section 2.1: "The measurements record the full process from initial damage to macroscopic failure over 18 time steps, and the raw data are stored on a 100×100×100 regular grid in “.mat” format." This is Awkward phrasing.

This sentence should be: "The measurements, recorded over 18 time steps from initial damage to macroscopic failure, are stored as raw data on a 100×100×100 regular grid in .mat format."

3. Page 6, Section 2.4:"The design of the physical constraint loss not only considers the spatial continuity and smoothness of the predicted results but also incorporates the classical theories of rock mechanics." -> Redundant. Suggest: "The physical constraint loss is designed to incorporate classical rock mechanics theories, ensuring spatial continuity and smoothness."
4. Page 11, Ablation Section:"The recall and point-cloud coverage of the complete model are lower than those of the simplified models... This reflects an over-prediction tendency in the simplified models".  The logic is correct, but the phrasing is slightly confusing. Clarify: "While the simplified models achieve higher recall and coverage, this is a result of their tendency to over-predict the damaged area, which artificially inflates these metrics at the cost of precision."
5. Page 12, Discussion:"Performance in context: Compared with 3D CNN, ConvLSTM and UNet3D baselines...".  Avoid using headings or bullet points within a paragraph. Integrate smoothly: "In the context of performance, our model compares favorably against 3D CNN, ConvLSTM, and UNet3D baselines..."
6. Recommendation:A thorough proofreading by a native English speaker or a professional editing service is strongly recommended to correct grammatical errors, improve sentence flow, and ensure consistent use of technical terms (e.g., "point-cloud" vs. "point cloud").

Abstract 

1. The phrase "predictions that deviate from mechanical laws" could be slightly more specific (e.g., "...deviate from fundamental fracture mechanics principles").

      Suggestion: It would be beneficial to briefly mention the data source (uniaxial compression-        acoustic emission tests) earlier in the abstract to provide immediate context.

 Research Methodology

• The description of the "sliding window" mechanism in Section 2.1 is somewhat vague. A brief formula or clearer explanation of how the two-time steps are used to predict the next would be helpful.
• While the composite loss is well-described, more detail on how the weighting parameters () were chosen (e.g., through grid search, validation performance) would strengthen the methodology.
• The methodology is consistent with the research process and is rigorously presented. Minor clarifications on parameter selection and data sequencing would make it even stronger.

 Results Analysis

• The manuscript would benefit from a statistical significance test (e.g., a p-value) for the performance metrics in Table 2 to confirm that the improvements are not due to random chance.
• The discussion of Figure 6 and 7 correctly identifies error locations at boundaries and multi-damage intersections, but it could more deeply link these specific errors to the limitations of the physical constraints or the voxel resolution in these complex regions.
• Recommendation:The results are sound and directly address the research questions. Adding statistical validation and a more in-depth error analysis would enhance the section.

Conclusion Assessment

• The conclusion could be more critical by briefly reiterating the main limitation (e.g., boundary errors) and how the proposed future work aims to address it.
• There is a minor discrepancy: the abstract reports an F1-score of 0.947, while the conclusion reports 0.947 (correct) but Table 2 shows 0.950. This inconsistency should be resolved.

 Literature Review Evaluation

• While recent, the review could be more comprehensive. For instance, the discussion of Physics-Informed Neural Networks (PINNs) [16,17] is good, but it could more explicitly contrast the "hard constraint" approach of PINNs with the "soft constraint" (loss function) approach used in this paper.
• Some highly relevant and recent works on physics-constrained learning for geomechanics (beyond the cited ones) might be missing, but this is difficult to assess without a broader literature search.

Reference Section Check

Formatting Inconsistencies:

• Reference 1 has a DOI ending with "107844" while the text says "107822".
• Reference 6, 7, 12 use "https://doi.org/..." while others use "DOI: ...". A uniform format should be applied.
• Some references are incomplete (e.g., [11] PointNet++ cites the arXiv number but not the final conference proceeding).
• Citing a recent review paper on "Sparse 3D Deep Learning" or "Theory-Guided Data Science in Geomechanics" could further strengthen the background.
• The reference section is complete enough but requires careful formatting checks to ensure consistency and accuracy across all entries, following the journal's specific guidelines.

 Review of Tables

Table 1. Experimental Setup

• Clarity & Content:The table is clear but suffers from a misleading title and incomplete information.

1. Title Inaccuracy:The title "Experimental Setup" is incorrect. The content describes Data Preprocessing and Training Hyperparameters, not the physical laboratory experimental setup (e.g., load frame specifications, AE sensor details). The title must be changed to reflect the actual content.
2. Missing Rationale:The "Purpose" column is helpful, but the "Value/Setting" column lacks justification. Why was a sliding window of 2 chosen? Why do these specific weights loss (λ_s = 0.7, etc.)? A brief note on how these values were determined (e.g., "empirically tuned on validation set" or "via grid search") would add scientific rigor.
3. Inconsistent Terminology:It uses "Voxel resolution" while the rest of the paper focuses on "adaptive voxelization." This should be clarified (e.g., "Base grid for adaptive voxelization").
4. Integration with Text:Mentioned in Section 2.1, but the text does not elaborate on the choices made for these parameters.

Table 2. Comparison Results

• This is a crucial and well-presented table. It clearly shows the proposed model's superiority across key metrics.

1. Missing Context:The table lacks a caption that defines the experimental context (e.g., "Single-step prediction performance on the test set").
2. Statistical Significance:As noted in the main review, there is no indication of the statistical significance of the improvements. Adding standard deviations (from multiple runs or cross-validation) would greatly strengthen the claim.

• Integration with Text:The results are discussed in Section 3.6. The discussion is good, correctly interpreting the trade-off between Recall and Precision for ConvLSTM.

Table 3. Comparison Results (Ablation Study)

• This table is problematic and confusingin its current state.

1. Poor Layout:The header "Fixed voxel | Only use MSE | Complete model" is ambiguous. It's unclear if these are column headers or row labels. The use of checkmarks (√) in the rows below is non-standard and difficult to interpret quickly.
2. Suggested Revision:The table should be restructured for clarity. Example:

Model Configuration	Accuracy	Recall	F1 Score	PC-Coverage
STConvLSTM (Fixed Voxel + Composite Loss)	0.868	0.991	0.925	0.991
STConvLSTM (Adaptive Voxel + MSE Only)	0.853	0.996	0.906	0.966
STConvLSTM (Complete Model)	0.924	0.970	0.947	0.970

3. Caption:The caption "Comparison results" is too generic. It should be "Ablation study results evaluating the contribution of adaptive voxelization and the composite loss function."
4. Integration with Text:The accompanying text in Section 3.7 does a good job of explaining the trends seen in the table, but the poor table design makes this unnecessarily difficult for the reader.

Scientific Significance

• Clarity on "Physics-Constrained" vs. "Physics-Informed":The manuscript would benefit from a clearer discussion in the introduction or methodology differentiating its "physics-constrained" approach (using physics in the loss function to guide a data-driven model) from "physics-informed" approaches like PINNs (which embed the PDEs directly into the network). This would more sharply define its conceptual novelty.
• Justification of Hyperparameters:The choice of loss function weights (λ_s = 0.7, λ_p = 0.2, γ_o = 0.1) is critical to the model's performance. The authors should briefly explain how these values were determined (e.g., via hyperparameter optimization on a validation set). Their sensitivity could also be discussed.
• Scalability and Computational Cost:A brief discussion on the computational cost of the adaptive voxelization and the STConvLSTM network compared to the baselines would be valuable for practitioners considering adoption. Is the performance gain worth the potential increase in training time or memory?

Overall Conclusion on Novelty and Significance

This manuscript presents a significant and novel advancement in the field of computational geomechanics. It moves the state-of-the-art beyond purely data-driven or purely physics-based models by creating a powerful hybrid framework. The proposed method is not an incremental improvement but a substantial step towards building predictive models that are both highly accurate and physically credible.

The work is of immediate interest to researchers and engineers in rock mechanics, geotechnical engineering, and broader communities working on spatiotemporal prediction of physical phenomena. After addressing all issues, this manuscript will be a strong candidate for publication in a high-impact journal.

 

Comments on the Quality of English Language

See previous section.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript “A Physics-Constrained Method for Precise Spatiotemporal Pre-2 diction of Rock-Damage Evolution is a very interesting topic that should be explored by the scientific community. However, the following comments need to be considered to meet Applied Sciences standard

Abstract

• The structure of the Abstract is week and it did not cover the main purpose of it which supposed to cover the following:
• A brief introduction to the topic that you're investigating.
• Explanation of why the topic is important in your field/s.
• Statement about what the gap is in the research.
• Your research question/s / aim/s.
• An indication of your research methods and approach.
• Your key message.
• A summary of your key findings.
• An explanation of why your findings and key message contribute to the field/s.

Thus, the abstract need to be revised based on the above structure

Introduction

Lines 64-85, this section of the introduction reads more like a technical report rather than a journal-style background. It is highly procedural and focuses on listing methods and technical steps rather than establishing the broader scientific motivation, research gap, and contribution. The introduction should be revised to provide a clearer narrative flow, highlight the problem context, summarise key prior work, and position the novelty of the study without going into detailed model components. The technical descriptions in points (1) to (3) should be moved to the Methodology section.

Method

Well presented

Results

Section 3.6 The comparative study is useful, but the authors do not cite any references for the baseline models (3D CNN, ConvLSTM, UNet3D). Please include appropriate citations to support the selection and implementation of these benchmark methods.

Section 3.7 Clear section, but some sentences are long and could be tightened. Boundary-error explanation needs a bit more clarity, especially on temporal uncertainty. Metrics are strong but could briefly state their practical significance.

Figure 5. Eight consecutive stages. Some image are repetitive (a-f), (e,h) (a-c).. Justify

The ablation study is useful, but the explanation is too lengthy. Please summarise the key findings more concisely.

Some descriptions are repetitive; streamline the discussion of accuracy, F1-score, recall, and precision.

Improve clarity when discussing over-prediction in simplified models and its impact on practical reliability

Replace “physical rationality” with a clearer term such as “physical consistency” or “mechanical plausibility.”

Formatting needs attention (spacing, punctuation, consistent numeric formatting).

the benefits of adaptive voxelization could be strengthened by adding brief quantitative evidence, if available

 

Conclusion

The conclusion is clear but overly long and somewhat repetitive. It would benefit from tightening, reducing methodological detail, and focusing more concisely on the key findings, practical implications, and future work.

 

Comments on the Quality of English Language

Can be improved  

Author Response

Please see the attachment.

Author Response File: Author Response.pdf