A Novel Neural Network with the Ability to Express the Extreme Points Distribution Features of Higher Derivatives of Physical Processes
Round 1
Reviewer 1 Report
This is a very difficult manuscript to read. A typical reader will have a difficult time getting beyond the first few sentences of the abstract and introduction, if not the title itself. It's not the grammar, it's just they don't mean anything or are ambiguous. Other parts are just jargon that will not be understandable to anyone not familiar with sub neural networks like “extreme feature calculation”. Even the term higher order derivative has a double meaning. I believe the authors are referring to dn/dtn, where n is large if not infinite! While this has its place in a Taylor series expansion, it is not appropriate for data as the manuscript suggests. Then higher-order would refer to the error of finite difference approximations such as central-differences being higher order than forward- or backward-differencing. The first few references (also badly written) refer to large n Taylor Series expansions and do not motivate the problem. There might be a reason to go to n=4 for an elastica problem, for instance. But since the concept and motivation are not there, I could not get a foothold to proceed deeply into the ideas of the paper.
While grammatically correct in most cases, the authors need help in writing their ideas cogently.
Author Response
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Author Response File: 
Author Response.docx
Reviewer 2 Report
1) Numeric result is missing in Abstract. It is good. Mention the best-performing results (Quantitative values).
2) The novelty of this paper is not presented well. Please add. Contribution is missing.
3) Introduction should provide more background on the work with scope of the work
4) Contribution should be clearly identified and presented under the Introduction.
5) The paper, does not link well with recent literature on top-tier journals and research gap should be clearly identified.
6) A high-level block diagram of the entire technical work can be added at the beginning of Section 3.
7) Further discussion on Figure 6 part a) Cylinder pressures and errors can be included.
8) A performance/advantages comparison with existing related works should be added at the end of the result section to validate the proposed method’s capability.
9) Results section should be updated by adding the strength, limitation and impact/significance of this work in real-life scenarios.
10) Specific Future research directions are missing. Please add those at the end of the conclusions.
Minor correction is required.
Author Response
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Author Response File: Author Response.docx
Reviewer 3 Report
In this paper, the authors investigate the research on the error's influence on higher-order derivatives and the typical functions' extreme points distribution, which demonstrates the necessity and feasibility of adopting extreme points distribution features in neural networks. A list of points that appears to deserve to be better clarified in the paper together with some suggestions follows.
§ More details are needed to clarify the structure of the EDNN network
§ The data set which is used for training the proposed EDNN should be described in more detail.
§ The optimization criterion and the stopping criterion of the EDNN should be clearly clarified.
§ In section 4.3, the comment regarding “And the errors between the noise reduced signal and the measured signal in Figure 6.b are all less than 400Pa, which satisfies the accuracy requirements.” should be better explained.
§ The authors should refer in more detail and in clearly way to the advantages of their methodology and summarize possible limitations.
§ The reader of this article will be interested in the articles:
- Zainab Mohammed Alwan, "Solution Non Linear Partial Differential Equations By ZMA Decomposition Method," WSEAS Transactions on Mathematics, vol. 20, pp. 712-716, 2021.
- Abdallah Al-Habahbeh, "Numerical Solution of a System of Fractional Ordinary Differential Equations by a Modified Variational Iteration Procedure," WSEAS Transactions on Mathematics, vol. 21, pp. 309-318, 2022.
- Hewa Selman Faris, Raad Noori Butris, "Existence, Uniqueness, and Stability of Solutions of Systems of Complex Integrodifferential Equations on Complex Planes," WSEAS Transactions on Mathematics, vol. 21, pp. 90-97, 2022.
Author Response
Please see the attachment
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
I would like to thank the authors for addressing my comments. I have no other comments.
Reviewer 3 Report
The manuscript can be published in its present form.
