Data-Driven Prediction of Polymer Nanocomposite Tensile Strength Through Gaussian Process Regression and Monte Carlo Simulation with Enhanced Model Reliability

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, a machine learning framework based on Gaussian Process Regression (GPR) was developed to predict the tensile strength of polymer nanocomposites. Before the manuscript can be considered for publication, the following issues should be addressed:

1. This manuscript mentions a “curated database”, but does not explain how data was selected, validated, or preprocessed.
2. In Figure 1, some of the text is displayed as garbled characters, please check it carefully.
3. In the abstract, the model is said to achieve RMSE = 12.14 MPa, MAE = 7.56 MPa, and MAPE = 31.73%. However, later sections report lower RMSE and MAE. This confuses the readers and undermines confidence in the results.
4. The analysis in Figures 13-14 reports error distribution, but does not explore why these errors occur.

Author Response

Reviewer 1

“We sincerely thank the Academic Editor and the reviewers for their constructive and insightful comments on our manuscript. We greatly appreciate the time and effort invested in evaluating our work. The feedback has been invaluable in improving the technical depth, clarity, and overall quality of the manuscript. We have addressed all comments in a point-by-point manner below, and the corresponding revisions have been incorporated into the manuscript as suggested.”

In this manuscript, a machine learning framework based on Gaussian Process Regression (GPR) was developed to predict the tensile strength of polymer nanocomposites. Before the manuscript can be considered for publication, the following issues should be addressed:

1. This manuscript mentions a “curated database”, but does not explain how data was selected, validated, or preprocessed.

Response: We thank the reviewer for highlighting this important point. In response, we have revised Section 3.1 of the manuscript to clearly describe the data collection, selection, validation, and preprocessing procedures. The updated text explains that the database was compiled from approximately 100 peer-reviewed studies, with 125 records selected based on completeness, experimental validation, and clarity of reported processing and mechanical parameters. We have also added details about how categorical and numerical variables were encoded and normalized prior to model training. This clarification strengthens the transparency and reproducibility of our methodology.

 

 

1. In Figure 1, some of the text is displayed as garbled characters, please check it carefully.

Response: We thank the reviewer for pointing this out. Figure 1 has been carefully reviewed and the garbled characters have been corrected. The revised version now includes properly rendered text, ensuring full clarity and readability. The updated figure has been included in the revised manuscript.

 

 

1. In the abstract, the model is said to achieve RMSE = 12.14 MPa, MAE = 7.56 MPa, and MAPE = 31.73%. However, later sections report lower RMSE and MAE. This confuses the readers and undermines confidence in the results.

Response: We thank the reviewer for highlighting this important inconsistency. Upon review, we found that the values reported in the abstract were derived from the performance summary averaged over 2000 Monte Carlo simulations, whereas certain later sections presented the best-case or single-run values. To maintain consistency and avoid confusion, we have now updated the abstract to explicitly state that these are average values across 2000 randomized trials. We have also ensured that the same values are consistently reported throughout the manuscript and clearly labeled as “mean performance” to avoid ambiguity.

 

 

1. The analysis in Figures 13-14 reports error distribution, but does not explore why these errors occur.

Response: We thank the reviewer for this thoughtful comment. In response, we have added a new paragraph in the Results and Discussion section (following Figures 13–14) to provide a deeper analysis of the observed error distributions. This addition discusses possible causes for error variations across material categories, including dataset imbalance, property overlap among polymer types, and nonlinearity in CNT-matrix interactions. This explanation enhances the interpretability of the error behavior and supports the robustness of our probabilistic modeling approach.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

This manuscript discusses the application of GPR and Monte Carlo Simulation for predicting the tensile strength of polymer nanocomposites. In general, the results are suitable for publication. However, there are several issues that need to be addressed:

1. Please clearly describe the data used for regression, such as sample dimensions, testing standards, testing machines, and the manufacturing process of the samples.
2. Figure 1: Please clarify the target of Phase 1. Currently, only the inputs are shown—what about the outputs?
3. Figure 1: How is the Monte Carlo method integrated into the process?
4. Please provide a discussion explaining the rationale for using both the GPR and Monte Carlo methods.
5. The regression performance and estimation indices appear satisfactory. However, it would be helpful if you could briefly explain how these results are applied or used in the context of your paper.

Sincerely yours,

Author Response

Reviewer 2

“We sincerely thank the Academic Editor and the reviewers for their constructive and insightful comments on our manuscript. We greatly appreciate the time and effort invested in evaluating our work. The feedback has been invaluable in improving the technical depth, clarity, and overall quality of the manuscript. We have addressed all comments in a point-by-point manner below, and the corresponding revisions have been incorporated into the manuscript as suggested.”

 

This manuscript discusses the application of GPR and Monte Carlo Simulation for predicting the tensile strength of polymer nanocomposites. In general, the results are suitable for publication. However, there are several issues that need to be addressed:

 

Comment: Please clearly describe the data used for regression, such as sample dimensions, testing standards, testing machines, and the manufacturing process of the samples.

Response: We thank the reviewer for this important suggestion. As our database was compiled from numerous published experimental studies, the sample dimensions, testing standards, machines, and fabrication methods varied across sources. In response, we have now included a summarizing paragraph in Section 3.1 to describe the typical ranges of these parameters as reported in the literature. Where available, we have noted adherence to standardized tensile testing protocols (e.g., ASTM D638, ISO 527) and common manufacturing techniques (e.g., melt mixing, solution casting, extrusion). This addition clarifies the nature and variability of the underlying experimental data used for model training.

 

Comment: Figure 1: Please clarify the target of Phase 1. Currently, only the inputs are shown—what about the outputs?

Response: We thank the reviewer for this helpful observation. In response, we have revised Figure 1 to clearly indicate the target output of Phase 1, namely the tensile strength of polymer nanocomposites. The revised flowchart now provides a clearer visual representation of the full research methodology, including both input parameters and the predicted output. The updated figure has been included in the revised manuscript.

 

Comment: Figure 1: How is the Monte Carlo method integrated into the process? Please provide a discussion explaining the rationale for using both the GPR and Monte Carlo methods.

Response: We thank the reviewer for this insightful comment. In response, we have revised Figure 1 to visually indicate where the Monte Carlo method is integrated in the workflow specifically during the model training and evaluation phase. Additionally, we have expanded the text in Section 3.3 to explain the rationale for using Monte Carlo simulation alongside GPR. This addition clarifies that while GPR provides point predictions and uncertainty estimates, Monte Carlo simulation was employed to perform repeated sampling and model validation, thereby assessing statistical robustness and variability across random data splits. This combination enhances the credibility and generalisability of the predictive model.

 

Comment: The regression performance and estimation indices appear satisfactory. However, it would be helpful if you could briefly explain how these results are applied or used in the context of your paper.

Response: We appreciate the reviewer’s positive assessment and constructive suggestion. In response, we have added a clarifying paragraph at the end of the Results and Discussion section. This addition explains how the regression outcomes and error metrics are used to assess model generalisability, identify dominant parameters, and guide potential design optimisation in CNT-polymer nanocomposites. It reinforces the broader applicability of the model beyond performance benchmarking.

 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This study presents a machine learning approach that integrates Gaussian Process Regression (GPR) with comprehensive Monte Carlo simulations to accurately predict the tensile strength of polymer nanocomposites. The paper is well-structured, easy to follow, and features clean and visually appealing plots. The paper effectively highlights its novelty in the background theory section, providing a clear and compelling foundation for the study's unique contributions. The methodology chart is well-designed and effectively enhances the presentation of the study's approach, making the process more comprehensible and visually engaging. However, there are some points that need to be checked listed below.

Please provide the expanded form of "CNT" as mentioned in the abstract.

There are problems with the methodology of the paper are listed below.

The sample data used in this study has been sourced from existing literature. However, nanocomposite manufacturing methods are inherently unstable, resulting in variability in mechanical behavior even among parts produced under identical conditions. How can the reliability of this data be ensured when developing a predictive model? Furthermore, how can this challenge be addressed, and how can the inherent deviations be effectively integrated into the predictive model to improve its accuracy and robustness?

It was mentioned that “In this database, 25 distinct polymer matrices have been considered, combined with 24 different processing methods and 22 surface modification strategies across various nanofiller types.” How can you ensure that the number of sample sets is sufficient to achieve accurate predictions?

Author Response

Reviewer 3

“We sincerely thank the Academic Editor and the reviewers for their constructive and insightful comments on our manuscript. We greatly appreciate the time and effort invested in evaluating our work. The feedback has been invaluable in improving the technical depth, clarity, and overall quality of the manuscript. We have addressed all comments in a point-by-point manner below, and the corresponding revisions have been incorporated into the manuscript as suggested.”

 

Comment: This study presents a machine learning approach that integrates Gaussian Process Regression (GPR) with comprehensive Monte Carlo simulations to accurately predict the tensile strength of polymer nanocomposites. The paper is well-structured, easy to follow, and features clean and visually appealing plots. The paper effectively highlights its novelty in the background theory section, providing a clear and compelling foundation for the study's unique contributions. The methodology chart is well-designed and effectively enhances the presentation of the study's approach, making the process more comprehensible and visually engaging. However, there are some points that need to be checked listed below.

Response: We sincerely thank the reviewer for the encouraging and detailed feedback. We are pleased to know that the structure, clarity, visual presentation, and methodological novelty of our work have been well received. We also appreciate the recognition of the effort invested in designing a clear and informative methodology chart. The reviewer’s comments are highly motivating and reinforce our commitment to delivering scientifically robust and well-communicated research.

 

Comment: Please provide the expanded form of "CNT" as mentioned in the abstract.

Response: We thank the reviewer for this observation. The abbreviation “CNT” has now been expanded to “carbon nanotube” at its first mention in the abstract for clarity and completeness.

 

Comment: There are problems with the methodology of the paper are listed below. The sample data used in this study has been sourced from existing literature. However, nanocomposite manufacturing methods are inherently unstable, resulting in variability in mechanical behavior even among parts produced under identical conditions. How can the reliability of this data be ensured when developing a predictive model? Furthermore, how can this challenge be addressed, and how can the inherent deviations be effectively integrated into the predictive model to improve its accuracy and robustness?

Response: We sincerely thank the reviewer for raising this important concern regarding data variability and model reliability. Indeed, nanocomposite manufacturing often involves microstructural inconsistencies, even under controlled conditions, which can introduce natural variability in mechanical responses. To address this, our methodology incorporates two key strategies:

• Literature-Based Screening: During data curation, we included only studies that reported tensile strength values obtained through standardized testing methods (e.g., ASTM D638, ISO 527) and well-documented processing conditions. Incomplete, ambiguous, or anomalous data entries were excluded to improve data consistency.
• Monte Carlo Simulation for Robustness: To account for the inherent uncertainty and variability in the sourced data, we employed Monte Carlo simulation over 2000 iterations. This allowed us to assess how the predictive performance of the GPR model behaves under repeated random sampling, simulating variability in real-world inputs. The use of probabilistic modeling, particularly through the GPR framework, further enables uncertainty-aware predictions, providing confidence intervals for each predicted output.

Additionally, we have now added (in section 3.3) a clarifying paragraph in the revised manuscript to explicitly discuss how manufacturing-induced variability was considered and how the model remains robust despite input heterogeneity.

 

Comment: It was mentioned that “In this database, 25 distinct polymer matrices have been considered, combined with 24 different processing methods and 22 surface modification strategies across various nanofiller types.” How can you ensure that the number of sample sets is sufficient to achieve accurate predictions?

Response: We thank the reviewer for this important comment regarding dataset size and model generalisability. While it is true that the total number of categorical combinations is large, the model does not rely on exhaustively sampling every possible combination. Instead, the GPR model identifies trends and relationships across the dataset through kernel-based learning, enabling generalisation even when only a subset of combinations is present.

Furthermore, we address dataset sufficiency in three ways:

1. Cross-validation: A 5-fold cross-validation scheme was used to evaluate the model’s stability and guard against overfitting.
2. Monte Carlo simulation: 2000 randomized iterations were performed to assess prediction consistency across varied data splits, providing confidence in the statistical robustness of the model even with moderate sample sizes.
3. Probabilistic prediction intervals: The GPR framework not only predicts output values but also quantifies uncertainty, offering reliable estimates even when data sparsity occurs in certain input regions.

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised version responds to all my concerns, in my opinion, it can be considered for acceptance.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you to authors. The paper is well adjusted and it can be published as is.