Studying Inverse Problem of Microscale Droplets Squeeze Flow Using Convolutional Neural Network

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a novel residual convolutional neural network architecture (CNN-TTR) to address the inverse problem of microscale droplet squeeze flow. The application of deep learning techniques to this specific fluid dynamics problem is innovative and provides new ideas and methods for research in this field. Compared to traditional physics-based solvers, the proposed CNN-TTR model can predict droplet distribution patterns more efficiently, reducing the need for customized templates and lowering manufacturing costs. This has potential applications in the semiconductor manufacturing and packaging industries.

 

1. Although comparisons with a simple baseline model were made, it is recommended to conduct experiments comparing the proposed model with more existing methods to highlight the uniqueness and superiority of CNN-TTR in terms of physical constraints.
2. The dataset has certain limitations, as it includes only a specific range of liquid film thicknesses. It would be helpful to add a discussion on the effects of changes in viscosity and surface tension.
3. Adding diagrams or illustrations could clarify the connection between convolutional layers and the refinement mechanism. Additionally, the output of the function approximators (f1-f7) and its quantitative relationship with convolution block weights could be visualized through feature map changes.
4. A comparison with 3D CFD simulation results (e.g., using COMSOL) could be beneficial for quantifying model errors, especially during the droplet merging phase.
5. The analysis of the minimum resolvable feature size and the relationship curve between resolution and droplet volume has not been discussed.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1) Many papers are already published on the same concept, what is the difference; here it should be clearly mentioned in the revised manuscript.
2) Objective of the study is not clear. Indicate the novelty of this work.
3) The originality points and the practical applications of this work must be added in the introduction section.
4) The introduction section is not clear and it is very poor. It lists a few investigators research work, but it does not impress on readers the importance of this work, what isnot solved in this field and why is it important. Therefore, as a reader, it is difficult to draw the conclusion from them as to why this study has been carried out. The authors need to discuss the previous work instead of only mentioning that author `A' did this and author `B' did this. Update the introduction section with recent and relevant literature. It is recommended the authors try to explain the novelty of the paper as clear as possible and explain the research gap they are trying to fill.
5) There were many errors in writing mechanics and grammar. There are many mistakes in the sentence formation, no proper meaning of the sentences and sub-sentences; continuity is missing in the sentence formation.
6) The mathematical model and solutions presented in the manuscript are not new and the authors did not explain the contribution this work can bring to the existing literature.
7) What new terms are studied in the governing equations
8) Explain the boundary condition physically.
9) What are the merits and demerits of the applied method?
10) What about an error estimator of order?
11) Please include the comparison table or graph to validate your results.
12) Need more discussion about the results? In the results section, authors need to analyse the finding by giving reasons for each fact. Explain physical interpretation?
13) The quality of figures should be improved.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript introduces a residual convolutional neural network to determine the initial positions of droplets corresponding to the imprint pattern. The proposed method successfully transforms high-resolution imprint images with a specific liquid film thickness into low-resolution droplet distribution images that generate the given imprint, and this transformation is validated through numerical simulations. The results demonstrate that the residual convolutional neural network is feasible, accurate, and practical for solving inverse problems in microdroplet squeezing flows. The idea is intriguing, and the manuscript is rich in content. If the authors can fully address the following comments, the manuscript may be considered for publication.

1. The first two sentences of the abstract are somewhat repetitive and should be simplified.
2. Section 1.1 is a bit verbose and needs to be streamlined. Additionally, more content should be added to highlight the significance of inverse problem research.
3. Is setting the size of each computational unit to one-eighth of the nozzle array pitch sufficient to capture the characteristics of the droplet distribution? Would a smaller computational unit size be necessary?
4. Some labels in Figure 5 are incorrect and need to be revised.
5. “In average, only about 3% of pixels of dp images are ‘on.’” Is this statement a conclusion or merely an observation? Please provide a detailed discussion.
6. The discussion about AUC-PR and AUC-ROC is confusing and requires supporting data or figures.
7. Are spread time and film thickness incorporated into the residual convolutional neural network? If so, how are they integrated? How does the method obtain the initial droplet positions from the imprint images and liquid film thickness? Is it possible to also determine the spread time?
8. The results are all based on simulation data; is there any experimental data available to validate them?

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Overall the manuscript is of good quality, but there are a few comments and concerns that I would like to the authors to address before accepting.

1. While the authors gave an extensive introduction to the forward problem and SFIL overall, they did not provide enough background on the inverse problem. A brief introduction on (a) why this inverse problem is of interest and (b) what are the existing methods for solving or attempting to solve this problem would be great.
2. Many of the droplet pattern and imprint images have barely readable X/Y axis tick labels. Please make them larger if they are intended to be read by the readers, or remove them if they are unnecessary.
3. In Table 2, Category 2 and 3 are not used in training, validation or testing set. Please provide the reason for this in the manuscript. Additionally, instead of fraction, it might be easier for the reader to check for class imbalance if the table provides the number of samples from each category.
4. Please provide the information on the optimizer (with proper references), learning rate, batch size, regularization factor, number of epochs trained, estimated total wall time and hardware used for training in Section 6.2 for reproducibility purposes.
5. In Table 4, the authors mentioned comparison with a crude model with only max pooling layers and no trainable parameters. This might be too simplistic of a model to compare to. A more reasonable comparison model to demonstrate the advantage of tunable refinement would be a Resnet with 3 max pooling layers, similar number of trainable parameters and without the TR. For this comparison model, a reasonable input would be the element-wise multiplication of the vof image with corresponding h*, such that pixels with fluid will have the value h* and value 0 for those without fluid.
6. In Section 6.5, the authors stated that "the kernels of the earlier blocks act as a collection of various liquid-gas interface detectors. As moving higher, the kernels act more like a set of detectors for various local droplet patterns". Please explain how this conclusion was drawn in the manuscript.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

In this manuscript, the authors present a CNN architecture for the inverse learning of the imprint problem. They generate their training set by running forward simulations with an unsteady physical model—given a droplet image, the model predicts the corresponding high-resolution imprint image at discrete time steps. They then train a CNN to recover the low-resolution droplet image from the high-resolution imprint image and a normalized height input. The paper is well structured, and the results are impressive, but I have a fundamental concern about feasibility. Because the network does not explicitly incorporate the spread time, the same output droplet image can be produced by multiple imprint-image-and-height pairs; conversely, a single imprint image and height may correspond to more than one droplet shape. To validate their inverse-learning approach, the authors should therefore provide evidence that the forward mapping is one-to-one (i.e., invertible) or otherwise demonstrate that the inverse problem admits a unique solution.

Besides, I have a few minor issues:
1. What exactly does “Threshold” refer to in Figure 10 and in all subsequent mentions?
2. I’m not clear on how the authors reached the conclusion in Section 6.5. Please provide more details on how Figure 14 supports their interpretation. If this analysis isn’t central to the paper, consider moving it to an appendix or omitting it.
3. In the data pre-processing step, the authors select samples from different categories based on Table 2. What is the rationale behind this selection, and how might it affect training performance?
4. The term “function approximator” in Section 5.1 is too vague—this phrase generally describes any method for approximating functions. Please replace it with more specific terminology that conveys exactly what the authors intend.
5. Figure 5 spans three pages but is introduced by only a single sentence. What narrative or insight does this figure convey? If it is important, please add explanatory text; otherwise, consider removing it.
6. The phrase “system becomes slower” appears twice (lines 229 and 235). What do the authors mean by this, please elaborate on the underlying cause.
Overall, considering the innovation and integrity of the work, I recommend its publication in Fluids, provided that the authors address the issues outlined above.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The revised manuscript has addressed my concerns.

Reviewer 5 Report

Comments and Suggestions for Authors

I am satisfied with the revisions and recommend the manuscript for publication.