Bayesian Optimisation with Dimensionless Groups: A Synergy of Performance and Fundamental Understanding

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The study “Harnessing the power of dimensional analysis to accelerate experimental optimization” describes how machine learning algorithms can take advantage of dimensionless groups to accelerate experimental optimization and help the experimenter derive crucial information. Please consider the following observations:

1. I believe that the abstract does not contain the common elements needed to understand what and how the study was conducted and its main results. Therefore, I recommend rewriting it.
2. Please clearly state the objective of the study and how it differs from previous work on the subject.
3. In the materials and methods section, separate and describe the characteristics of materials such as soybean wax and canola oil.
4. Similarly, separate characterization methods such as TGA, rheometry, DLS, etc., indicate conditions, brand, model, and place of manufacture of the equipment.
5. Information on lines 165-173, page 4: decide whether to place in Table and/or combine with Tables 1 and 2.
6. Reorganize the experimental section, for example, Figure 2, which includes tables of poor quality.
7. The text in Figure 3 is very long.
8. Evaluate Table 5 with only one line of information.
9. In the title replace “optimization”

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The paper presents an interesting research on combining Bayesian optimisation and dimensionless groups for the system analysis.

However, the authors must clearly address the following issues in order to improve the manuscript:

• First, the authors must clearly demonstrate what is the novelty and scientific contribution of the proposed research.
• It is totally unclear why „intelligent manufacturing“ is selected as one of the key words. In the current form, the proposed research has almost no relevance to intelligent manufacturing. The authors must clearly elaborate how the proposed research directly addresses the intelligent manufacturing, or delete „intelligent manufacturing“ fro the list of key words.
• The authors presented the application of the proposed method on one use case. However, this is not sufficient to judge the effectiveness of the proposed method. The authors are requested to compare their results to the results of the methods typically used to address the considered problem/use case. The comparison with Regression Threes addresses only a part of the proposed method, so it could not be accepted as a benchmark with the overall proposed that is proposed.
• The practical implications of the obtained results on the considered problem/use case remain unclear. What does it mean for the considered problem/system? What exactly is the benefit of applying the proposed method, from the user side?
• The relevance of the proposed method for the contemporary industrial problems must be clearly presented.
• The practical implications must be also clearly elaborated in a broader sense, e.g. who/why/when should use the proposed approach.
• The limitations are adequately presented for BO. But, authors are requested to clearly present the limitation of the proposed overall approach, as well as the directions for future research.
• The cited papers are mainly outdated. The literature review must be significantly increased; this is particular refers to papers published on the related topics in the last 5 years.

 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

No more comments

Author Response

We appreciate the reviewer’s positive assessment and are glad that the revised manuscript was found suitable for publication. No additional modifications were required.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Some important comments i.e. requests from the previous review are re-iterated, since they are not satisfactorily addressed by the revised paper, as follows.

1. It is still unclear why „intelligent manufacturing“ is selected as one of the key words. In
   the current form, the proposed research has only vague relevance to intelligent
   manufacturing. The authors must clearly elaborate how the proposed research directly
   addresses the intelligent manufacturing, or delete „intelligent manufacturing“ fro the list
   of key words.
2. The authors presented the application of the proposed method on one use case.
   However, this is not sufficient to judge the effectiveness of the proposed method. The
   authors are requested to compare their results to the results of the methods typically
   used to address the considered problem/use case. In the revised version the authors claim that they have identified a lack of literature combining machine learning with
   dimensionless numbers towards targeted outcomes. However, this was not convincingly demonstrated in the revised papers. Therefore, this request is reiterated, as well as the request regarding the literature review.
3. The literature review should be improved; this is particular refers to papers published on the related topics in the last 5-6 years. 

Author Response

We thank the reviewer for their continued feedback.

1. It is still unclear why „intelligent manufacturing“ is selected as one of the key words. In
   the current form, the proposed research has only vague relevance to intelligent
   manufacturing. The authors must clearly elaborate how the proposed research directly
   addresses the intelligent manufacturing, or delete „intelligent manufacturing“ from the list of key words.
• The keyword “intelligent manufacturing” has been removed from the list of keywords in the revised manuscript.
2. The authors presented the application of the proposed method on one use case. However, this is not sufficient to judge the effectiveness of the proposed method. The authors are requested to compare their results to the results of the methods typically used to address the considered problem/use case. In the revised version the authors claim that they have identified a lack of literature combining machine learning with dimensionless numbers towards targeted outcomes. However, this was not convincingly demonstrated in the revised papers. Therefore, this request is reiterated, as well as the request regarding the literature review.
• We believe that direct benchmarking is not applicable in this case. The proposed framework does not aim to improve an existing optimisation algorithm but to integrate two complementary strategies—Bayesian Optimisation and dimensionless analysis—into a single, unified process that achieves both efficient optimisation and fundamental system understanding. This conceptual novelty has been clarified in the revised manuscript.
3. The literature review should be improved; this is particular refers to papers published on the related topics in the last 5-6 years.

• Finally, the literature review has been updated and refined. Several new, recent references (2018–2025) have been added to strengthen the context, and some of our previous self-citations have been removed to improve balance and focus.

Round 3

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The paper was improved, adequately addressing the reviewer recommendations.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I agreed to review this manuscript because I am presently working on two projects that optimize using dimensionless variables.   My optimization is not experimental, but the motivation is similar: Reduce the number of independent and dependent variables.  This can be especially important when performing expensive factorial experiments that might be treated as a black box as described in this manuscript.  That nondimensionalization by design experiments is not used is especially frustrating since that design emphasizes doing as few experiments as possible. This manuscript's motivation should be on designed experiments and not optimization.  

I have done very expensive designed experiments using dimensional variables and have realized a few years later how stupid I was.  Nondimensionalization is typical in relatively few disciplines (like my thermal-fluid field). To my knowledge, it is never emphasized in experimental designs. Hence the statement, "To the best of our 51 knowledge, they are not actively used to guide the optimisation of processes towards target outcomes" could and maybe should be changed to "To the best of our knowledge, they are not actively used to guide the design of factorial experiments." Dimensionless numbers are used regularly in optimization  For instance, one of the most studied problems in physics is the experiment and analysis of
            Nu_max=f(Ra, Pr,A),
where left to right the groups are the Nusselt number, The Rayleigh number, The Prandtl number, and the aspect ratio. 

This manuscript needs work.  It was poorly proofread -- starting at the very beginning when author affiliations were messed up by changing from number to letter subscripts.  It carries over to the first line of the abstract with "Dimensionless groups (numbers) describe the balance between the main forces...". "Forces" needs to be replaced by variables or factors. And balance should be replaced by ratio.     Since the manuscript is trying to reach those not converted to nondimensionalization, it might have to state these remedial concepts, but it still could be tightened up!

Other selected errors/typos:

several "Error! Reference source not found"
dangling "Suggested First batch:" in the first unlabelled table
     what does A-G mean for speed?  Can it be determined in units??
     It seems like it is being nondimensionalized?!

The physical problem seems interesting but not adequately described. Figure 7 does not look like experimental data, Figure 8 is just bizarre. Fix up and indicate how many fewer experiments were used as a result of nondimensionaization.

 

Author Response

We thank the reviewer for the insightful comments and useful suggestions. We wish to highlight that the main contributions of this manuscript are:

• The use of dimensionless numbers for experimental optimisation
• The use of combined BO, dimensionless numbers and regression trees as a way to elicit scientific information about largely non-characterised systems.

 

The majority of concerns of Reviewer 1 were addressed, adopting the suggested changes for description of dimensionless parameters.

 

Specific concerns are addressed below:

 

“what does A-G mean for speed?  Can it be determined in units??”

 

They are the settings of the shear mixer, this is explained in the text. We have added the wattage range, but it is not precise, since it depends a lot on viscosity and other factors. (Page 4 top)

 

“Figure 7 does not look like experimental data , Figure 8 is just bizarre. “

 

Fixed in the new version.

Reviewer 2 Report

Comments and Suggestions for Authors

In this article entitled "Harnessing the power of dimensional analysis to accelerate experimental optimisation" the eight authors from Australia present a methodology for applying dimensional analysis to Bayesian optimization. In order to demonstrate the results, they apply it to a real experiment on a mixture of wax and oil.

The paper in its current form needs significant changes to be considered for publication.

The method used to derive the dimensionless numbers are not described at all.

Throughout the text, in the current version of the document, there are several times (at least nine) where it can be read "Error! Reference source not found". The authors should check and correct this.

Although not explained in depth, a brief description of how the appropriate number of dimensionless parameters is obtained by means of Buckingham's theorem would allow the reader to better understand the information obtained.

The paper presented is a continuation of an earlier paper in which the researchers employed a Gaussian process model, but although they claim that time is saved by applying dimensional analysis it is not clear that this objective is achieved, so it is not clear what the benefit of the paper is to the scientific community.

In the conclusions it is mentioned as a peculiarity of BO systems that researchers can continue to dialogue with them. What exactly this means is not clear.

What does line 133 " Suggested First batch:" mean?

In line 145 the use of a GP model is mentioned for the first time. It is necessary to describe what it consists of in that paragraph, not further on.

In figure 2 there are variables marked with colours. Please, explain their meaning.

The format of the three equations, besides not being homogeneous, should be improved.

In table 1, the title is on a different page than the body of the table and should be corrected, as in table 3. Also space the text following the table. Do this for the rest.

In line 302 there is an inappropriate space.

Author Response

We thank the reviewer for the insightful comments and the suggested changes. Edits were performed in the manuscript to clarify its contribution and also to fix the formatting issues. Specific concerns from Reviewer 2 are addressed below:

 

“The method used to derive the dimensionless numbers are not described at all.”

 

It is done through the application of the Buckingham Pi theorem.

 

“The paper presented is a continuation of an earlier paper in which the researchers employed a Gaussian process model, but although they claim that time is saved by applying dimensional analysis it is not clear that this objective is achieved, so it is not clear what the benefit of the paper is to the scientific community.”

 

This manuscript describes how machine learning algorithms can take advantage of dimensionless groups to accelerate experimental optimization and help the experimenter derive key information from physical systems, even in non-thermodynamically stable states and in largely-unknown or unpredictable systems. We believe it is a new knowledge that can influence experimental scientist towards rge mix of dimensionless number and the machine learning based techniques. We have also edited the abstract to reflect the aim of the manuscript

 

“In the conclusions it is mentioned as a peculiarity of BO systems that researchers can continue to dialogue with them. What exactly this means is not clear.”

 

Clarified in the new version as a way to interactively provide human intuituion into the BO process.

 

“What does line 133 " Suggested First batch:" mean?”

 

Deleted and fixed the sentence.

 

“In line 145 the use of a GP model is mentioned for the first time. It is necessary to describe what it consists of in that paragraph, not further on.”

 

Fixed.

 

“In figure 2 there are variables marked with colours. Please, explain their meaning .”

 

The last column of the table clearly shows that white is constant values and beige are variables.

 

“The format of the three equations, besides not being homogeneous, should be improved.”

 

Fixed

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I will let my comments on the pdf file speak for themselves.  It looked better in the beginning, but I think the description is so incomplete that it will be hard for the reader to see how the study and analysis were carried out.  The emphasis on non-dimensionalization was lost in later figures. 

Comments for author File: Comments.pdf

Author Response

Thank you very much for taking the time to review this manuscript, your input demonstrated great attention to detail and a critical mind. Please find the detailed responses in the attached copy of your addressed comments, and the corresponding revisions/corrections commented in the re-submitted files. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

All comments have been addressed by the authors.

Author Response

Thank you very much for taking the time to review this manuscript, the authors appreciate your support and acknowledge your input into this article.