Fourier Neural Operator for Fluid Flow in Small-Shape 2D Simulated Porous Media Dataset

Round 1

Reviewer 1 Report

The work seems to be good.  Authors should address the following comments

1. In the abstract the authors must highlight the motivation of this study.

2. Reference all the key equations.

3. Some references in this field (related to porous media) can enrich the introduction part such as

* https://doi.org/10.1166/jon.2018.1519

*  https://doi.org/10.1115/1.4041951

4. It is optional by my suggestion is to add nomenclature and list of abbreviations 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper is titled “Fourier Neural Operator for Fluid Flow in Small-shape 2D Simulated Porous Media Dataset” and the authors attempted to investigate and predict fluid flow in porous media using a deep learning approach. They have considered a Fourier Neural Operator (FNO) method to predict the pressure distribution for a small-shape data problem.

The authors need to clarify and specify some parts of the paper. Please find my comments and suggestions as follows:

1.       Line 48: could you please clarify “algorithms, sometimes requiring domain knowledge about a given problem.”?

2.       Line 52: Please clarify this sentence, the point of the sentence is not well expressed.

3. Lines  88 and 89: You mentioned the purpose of the paper in which to evaluate the FNO on small-shape data. When you described big-shape data, did you mean in situations where large input data are available? Please elaborate more on the details of the goal in this paper.

4.       Please provide literature on the research that has been done on small-shape data as well.

5.       The literature part looked like a book chapter while the introduction part should describe other research more specifically. The authors need to describe and mention other researchers’ studies.

6.       How do you demonstrate small-shape data versus big-shape data? What parameters need to be considered to evaluate that? We cannot just say small data or big data.

7.       Please change the title of section 2 “Problem to be solved using FNO and CNN models”. The title should not be like a sentence.

8.       Please describe the initial problem more specifically (like a schematic figure) after the introduction section and also explain it more thoroughly.

9.       The questions listed in line 91, need to be considered after describing the problem. Additionally, the problem description should be explained in a separate section after the introduction.

10.   Why authors considered “A 30*30 uniform mesh problem from the domain of petroleum engineering” as small-shape data? And was that the only case they investigated?

11.   Could you please describe in the paper, whether your method can be implemented in what conditions? like in what size domain?

12.   Section 2 should be titled something like governing equations. Shouldn’t be?

13.   Line 149: as mentioned before, the paper shouldn’t be like a book chapter. The methodology should be described by mostly referring to other researchers while explaining a few details.

14.   Authors need to put citations on the original formula and equations they put in section 2 of the paper.

15.   Need reference and citation in line 118 that why porous media should be included in all terms.

16.   No reference in line 171 about PyTorch and why they employed that?

17.   Need reference for all the equations in section 3.

18.   What did you mean by simple linear layer in line 160? And all the layers similar in Figure 1? Why do you need to consider the 4 Fourier layers? Please clarify it in the document.

19.   Please explain “Adam” in line 173. It requires reference as well.

20.   Line 178: “In preparing a CNN simulation involving a unit square, a 30*30 uniform mesh was selected.”. Please explain in more detail why you only consider 30*30 mesh and please justify that.

21.   Why modes 20 behaved differently than modes 15 and 10 in Figure 3? Should modes 15 and 20 looks similar? Although you mentioned that their behavior overlapped in line 224.

22.   It would be better if you describe the error you received for the pressure difference in Figure 4.

23.   The first sentence of the conclusion is quite vague in line 278. Please describe the problem in a simple and clear way at the beginning of the conclusion.

24.   The authors didn’t elaborate on what they have concluded in their investigation in the conclusion section. Please explain more details and significant findings you have had for the investigation.  

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

No further comments are needed. The authors responded to the previous comments.