Data-Driven Surrogate-Assisted Optimization of Metamaterial-Based Filtenna Using Deep Learning

Round 1

Reviewer 1 Report

Authors presented FSS based filtering antenna in this research. The topic is interesting and worth publishing after solving the following comments.

1. The introduction in the paper is very poor. Authors need to improve it with recent citations

2. The language of the paper needs to be improved.

3.  Can the authors show some variation at particular angles?   4.  Can the author provide more results comparisons?

Author Response

Dear Editor,

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the Reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), (b) an updated manuscript with red highlighting indicating changes (Supplementary Material for Review), and (c) a clean updated manuscript without highlights (Main Manuscript).

Authors would like to mention that we had done our best to be able to answer all comments of the Reviewers in the 7 days limit by the editorial board. However as you might now due to the recent earthquake disaster in Turkey we lost some of our laboratory equipment and a possibility of accessing to our designs in Hatay Iskenderun Technical University.

 

Best regards,

Assoc. Prof. Dr.

Peyman Mahouti

 

 

Reviewer 1

Authors presented FSS based filtering antenna in this research. The topic is interesting and worth publishing after solving the following comments. 1. The introduction in the paper is very poor. Authors need to improve it with recent citations

Authors are grateful for Reviewer’s kind comments that provided a chance to improve our work.  With respect to your comments the literature overview of the work have been improved with more recently published works. The total number of cited works form 2023 is increased to 16, the total number of cited works form 2023 is increased to 23. The following references have been added to the manuscript.

[2]-[10];[12]-[13]; [16]-[20];[22]-[25];[33]-[45].

 

2. The language of the paper needs to be improved.

The overall language of the work has been improved with a help from a native speaker.

 

3. Can the authors show some variation at particular angles?  

With respect to yours and other reviewers comment additional analyses have been added to the manuscript.

 

Fig. 5 has been revised with requested results.

 

Figure 5. Scattering parameters responses of the 3D unit element and proposed filtenna: (a) simulated |S₁₁|, (b) simulated |S₂₁|, (c) measured |S₁₁|, (d) gain, simulated (e) |S₁₁|, and (f) |S₂₁| for different oblique incidences.

 

4. Can the author provide more results comparisons?

With respect to your comment, Table 4 has been extended with additional examples.

 

Table 4. Comparison of gain enhancement of state-of-the-art filtennas operating in similar frequency bands

Work	Operating band [GHz]	Design size [mm]	Gain Alteration [dBi]/[GHz]
			4	5	6	7	8
This work	4-8	60 ´ 60	–7.2	1.9	2.3	2.1	–5.7
[104]	5-15	16 ´ 16	0	1	0.5	0	0.5
[105]	1-15	60 ´ 100	2	2.5	3	3	4
[106]	2-13	25 ´ 73.5	1	1.5	2	2.5	2.7
[107]	2-13	100 ´ 100	0	5	4.5	5	2
[108]	3-12	80 ´ 800	2	1	3	2	3
[109]	6-18	90x90	---	---	4	5	5.5
[110]	8-12	114x114	---	---	---	---	1.5
[111]	8-18	106x16	---	---	---	---	2
[112]	6-12	22x20	---	---	1	0	1.5

 

Reviewer 2 Report

 

This manuscript presents a data-driven optimization of metamaterial-based filtenna using deep learning. The results were acceptable with detailed design steps. Overall, the manuscript was organized well. Other comments:

1. The novelty of this manuscript can be emphasized with more details.

2. The filtenna has high back radiation, as can be seen from Fig. 5. How to overcome this issue?

Author Response

Dear Editor,

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the Reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), (b) an updated manuscript with red highlighting indicating changes (Supplementary Material for Review), and (c) a clean updated manuscript without highlights (Main Manuscript).

Authors would like to mention that we had done our best to be able to answer all comments of the Reviewers in the 7 days limit by the editorial board. However as you might now due to the recent earthquake disaster in Turkey we lost some of our laboratory equipment and a possibility of accessing to our designs in Hatay Iskenderun Technical University.

 

Best regards,

Assoc. Prof. Dr.

Peyman Mahouti

 

 

Reviewer 2

This manuscript presents a data-driven optimization of metamaterial-based filtenna using deep learning. The results were acceptable with detailed design steps. Overall, the manuscript was organized well. Other comments:

1. The novelty of this manuscript can be emphasized with more details

Authors are grateful for the Reviewer’s kind comments that provided a chance to improve our work.  With respect to yours and other reviewers comment, the abstract and introduction sections have been revised to clearly present the novelty of the proposed work to the literature.

The following descriptions have been added to the manuscript to clearly present the novelty of the work.

2. Data-Driven Surrogate Model of Frequency Selective Surface Unit Element

 

 “…The model exhibits the error of less than 5% both according to cross-validation and the hold-out test, which suggest that it is not only well-trained but also it is not over-fit. Here, it is worth mentioning that there are other type of approaches for modeling of FSS unit elements such as the usage of equivalent circuit models [93] or physics-based models [94]. However, these methods have a major limitation. They are computationally intensive, which prevents their direct use for circuit design. In most cases, it is inevitable to introduce simplifying assumptions in order to make the model computationally tractable [94]. Consequently, in this work, to ensure computational efficiency, a Deep-Learning-based surrogate modeling approach is taken into consideration, which exhibits excellent generalization capability even when working with small amounts of data [61]. Consequently, the M2LP model will be employed for filtenna design as elaborated on in Section 3.”

 

4. Experimental Results

“…Consequently, the radiation characteristic of the antenna is enhanced by almost 2 dBi at the desired operating range but also a pre-filtering characteristic is obtained for the unwanted frequencies. Thus, with the proposed approach, the major obstacle of geometry parameter adjustment of the FSS unit cell to ensure proper electrical performance and to maintain the required size, have been achieved through a computationally-efficient design optimization procedure. It should be emphasized that accurate evaluation of the cell requires EM analysis, which is computationally heavy. In particular, direct EM-based optimization is usually impractical. With the typical simulation time of around 1 minute, and global optimization of the FSS cell requiring at least 5,000 analyzes, the overall design time exceeds 80 CPU hours. The approach adopted here employs a deep-learning-based model M2LP to create a fast surrogate. M2LP has been found superior to commonly used state-of-the-art techniques such as MLP, SVRM, Boosted Trees, Depp NN and Gaussian Process regression, in terms of predictive power. With the use of metamodel, the unit cell optimization cost becomes negligible (surrogate model evaluation takes less than a 1 ms). The obtained numerical and experimental data indicate that the proposed design approach is highly reliable and computationally efficient. The estimated speedup with respect to direct EM-driven optimization using population-based methods is almost 90%.”

 

5. Conclusions

 

“Herein, computationally-efficient design optimization of an FSS-based filtering antenna using data-driven surrogate models has been proposed. Our methodology employs a deep-learning-based model M2LP to create a fast surrogate, which is also found to be superior to benchmark models reported in the literature in terms of predictive power. In our case, the FSS has been optimized using the HBMO algorithm. The HBMO routine has been deployed to carry out design optimization of geometry parameters of printable FSS for a filtenna operating in 5-to-7 GHz range. Experimental validation…”

 

 

2. The filtenna has high back radiation, as can be seen from Fig. 5. How to overcome this issue?

In the laboratory the Filtenna is placed as the transmitting antenna. The side lobes visible in Fig. 5(d) at 8GHz are due to the rejection of the EM waves in the main directions. This, in turn, occurs due to the reflected EM waves in the rejection band.

Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript claims to present “Data-Driven Surrogate-Assisted Optimization of Metamaterial Based Filtenna Using Deep Learning”. I do not support its publication in the current form, and some improvements are required. Please address the below comments in the manuscript to improve its quality.

1) Comparison Table 4 at page 9 is very short and few of the references are old, please provide recent state of the art, with same frequency as well as both flexible and rigid based materials designs.

2). Abstract is too long with irrelevant material. It should be short and it should contain kinds of novelty or contribution. 

3). In order to broadening the BW of FSS, please provide the parametric analysis varying design parameters, including tuning the period of array elements, or adjusting the structure elements, the effect of roughness of the copper tape. 

4). Recently, the design systems continuously demand diversity in polarization. It is desired to achieve good co-polarized FSS with a low cross-polarization level for broadband of frequencies and oblique incident angles. Please explain in details the manuscript.

5). For a better understanding of the operating principle, the equivalent circuit model of the proposed FFS design at normal incidence will be required.

6). The performance of the FFS surface under different oblique incidence up to 50° is required to be studied for both TE and TM polarizations.

7). In order to measure the cross-polarization performance with the variation at 0° and 30°, please provide the measured results of S21 that exhibit a good reduction of cross-polarization in the whole frequency band.

8). Conclusion is very lengthy and should reflect the abstract. Please provide a brief conclusion. However, the authors can do discussion in the above sections as well.

 

 

Author Response

Dear Editor,

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the Reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), (b) an updated manuscript with red highlighting indicating changes (Supplementary Material for Review), and (c) a clean updated manuscript without highlights (Main Manuscript).

Authors would like to mention that we had done our best to be able to answer all comments of the Reviewers in the 7 days limit by the editorial board. However as you might now due to the recent earthquake disaster in Turkey we lost some of our laboratory equipment and a possibility of accessing to our designs in Hatay Iskenderun Technical University.

 

Best regards,

Assoc. Prof. Dr.

Peyman Mahouti

 

Reviewer 3

This manuscript claims to present “Data-Driven Surrogate-Assisted Optimization of Metamaterial Based Filtenna Using Deep Learning”. I do not support its publication in the current form, and some improvements are required. Please address the below comments in the manuscript to improve its quality.

1) Comparison Table 4 at page 9 is very short and few of the references are old, please provide recent state of the art, with same frequency as well as both flexible and rigid based materials designs.

Authors are grateful for the Reviewer’s kind comments that provided a chance to improve our work.  With respect to your comments, the literature overview of the work has been extended by adding more recently published works.

Furthermore, Table 4 has been extended with additional examples.

 

Table 4. Comparison of gain enhancement of state-of-the-art filtennas operating in similar frequency bands

Work	Operating band [GHz]	Design size [mm]	Gain Alteration [dBi]/[GHz]
			4	5	6	7	8
This work	4-8	60 ´ 60	–7.2	1.9	2.3	2.1	–5.7
[104]	5-15	16 ´ 16	0	1	0.5	0	0.5
[105]	1-15	60 ´ 100	2	2.5	3	3	4
[106]	2-13	25 ´ 73.5	1	1.5	2	2.5	2.7
[107]	2-13	100 ´ 100	0	5	4.5	5	2
[108]	3-12	80 ´ 800	2	1	3	2	3
[109]	6-18	90x90	---	---	4	5	5.5
[110]	8-12	114x114	---	---	---	---	1.5
[111]	8-18	106x16	---	---	---	---	2
[112]	6-12	22x20	---	---	1	0	1.5

 

 

2). Abstract is too long with irrelevant material. It should be short and it should contain kinds of novelty or contribution. 

With respect to yours and other reviewers comment the abstract and introduction sections have been revised to clearly present the novelty of the proposed work to the literature.

 

3). In order to broadening the BW of FSS, please provide the parametric analysis varying design parameters, including tuning the period of array elements, or adjusting the structure elements, the effect of roughness of the copper tape. 

Authors are grateful for reviewer suggestion that provided us a chance to improve the overall quality of the work. With respect to your comments the mentioned analyses have been added to the manuscript. Following description are added to the manuscript.

4. Experimental Results

“…filtenna and horn antenna without FSS array have been shown in Figs. 5(c) and 5(d). As for a furthered analyses on the performance of the FSS design, the effect of oblique incident angles are also studied in Figs. 5 (e-f). As it can be seen from the measurement results…”

 

“…while the outer bands of the antenna are reduced by almost 7 dBi. The 3D printed filtenna then is metalized using copper tapes. It is worth mentioning that surface roughness is a parameter that might deteriorate the overall performance of a design [99-103]. However, as it can be seen form the simulated results and measurements, the surface roughness on the prototype FSS can be neglected. Consequently, the radiation characteristic…”

 

4 & 6 & 7).  (4) Recently, the design systems continuously demand diversity in polarization. It is desired to achieve good co-polarized FSS with a low cross-polarization level for broadband of frequencies and oblique incident angles. Please explain in details the manuscript. (6) The performance of the FFS surface under different oblique incidence up to 50° is required to be studied for both TE and TM polarizations. (7). In order to measure the cross-polarization performance with the variation at 0° and 30°, please provide the measured results of S21 that exhibit a good reduction of cross-polarization in the whole frequency band.

Authors are grateful for reviewer kind and constructive suggestions that provided us a chance to improve the quality of our work. Authors would like to mention that we had done our best to be able to answer all review comments within the seven-day limit set up by the Editorial Board. However, as you might know, due to the recent earthquake disaster in Turkey we lost some of our laboratory equipment and the possibility of accessing to our designs in Hatay Iskenderun Teknik University. Consequently, the authors kindly ask for reviewer’s understanding for not to be able to fully provide the requested measured results. Notwithstanding, the following revisions and descriptions have been added to the manuscript with respect to your comments.

 

Fig. 5 has been revised by adding the requested results.

 

Figure 5. Scattering parameters responses of the 3D unit element and proposed filtenna: (a) simulated |S₁₁|, (b) simulated |S₂₁|, (c) measured |S₁₁|, (d) gain, simulated (e) |S₁₁|, and (f) |S₂₁| for different oblique incidences.

1. Introduction

“As mentioned earlier, FSSs have gradually become the structures of choice for communication systems in applications that require high-quality co-polarization with a low cross-polarization level over broad ranges of frequencies [30-32], especially for radars and antennas in military platforms such as aircrafts, ships, and missiles, where it is imperative that they are not impacted by unnecessary external signals [33-45]. A powerful electromagnetic interference (EMI)…”

 

 

 

5). For a better understanding of the operating principle, the equivalent circuit model of the proposed FFS design at normal incidence will be required.

Equivalent circuit modeling is indeed one of the methods that enable better understanding of the operating principle of unit elements. However, in this work, instead of using an equivalent circuit model for optimization process of Filtenna, black-box modelling approach is taken into consideration for the design optimization of Filtenna design. In other words, our primary goal is not to elaborate on the operating principles of the unit cell, but rather handle its geometry parameters in a computationally-efficient manner so as to ensure appropriate performance of the Filtenna with respect to the assumed design specifications. Clearly, equivalent circuit model would not be of much use for a purpose like this. Consequently, the authors kindly ask for Reviewer’s understanding on not providing an equivalent circuit model. Still, a brief explanation about this matter is added to the manuscripts.

 

Following description has been added to the manuscript:

“…The model exhibits the error of less than 5% both according to cross-validation and the hold-out test, which suggest that it is not only well-trained but also it is not over-fit. Here, it is worth mentioning that there are other type of approaches for modeling of FSS unit elements such as the usage of equivalent circuit models [93] or physics-based models [94]. However, these methods have a major limitation. They are computationally intensive, which prevents their direct use for circuit design. In most cases, it is inevitable to introduce simplifying assumptions in order to make the model computationally tractable [94]. Consequently, in this work, to ensure computational efficiency, a Deep-Learning-based surrogate modeling approach is taken into consideration, which exhibits excellent generalization capability even when working with small amounts of data [61]. Consequently, the M2LP model will be employed for filtenna design as elaborated on in Section 3.”

 

8). Conclusion is very lengthy and should reflect the abstract. Please provide a brief conclusion. However, the authors can do discussion in the above sections as well.

 

With respect to your comments and additional analyses after revision process, the Abstract, Experimental Results, and Conclusion sections of the work are revised for clearly present the contributions of the work.

 

Following descriptions have been added to the manuscript:

4. Experimental Results

“…Consequently, the radiation characteristic of the antenna is enhanced by almost 2 dBi at the desired operating range but also a pre-filtering characteristic is obtained for the unwanted frequencies. Thus, with the proposed approach, the major obstacle of geometry parameter adjustment of the FSS unit cell to ensure proper electrical performance and to maintain the required size, have been achieved through a computationally-efficient design optimization procedure. It should be emphasized that accurate evaluation of the cell requires EM analysis, which is computationally heavy. In particular, direct EM-based optimization is usually impractical. With the typical simulation time of around 1 minute, and global optimization of the FSS cell requiring at least 5,000 analyzes, the overall design time exceeds 80 CPU hours. The approach adopted here employs a deep-learning-based model M2LP to create a fast surrogate. M2LP has been found superior to commonly used state-of-the-art techniques such as MLP, SVRM, Boosted Trees, Depp NN and Gaussian Process regression, in terms of predictive power. With the use of metamodel, the unit cell optimization cost becomes negligible (surrogate model evaluation takes less than a 1 ms). The obtained numerical and experimental data indicate that the proposed design approach is highly reliable and computationally efficient. The estimated speedup with respect to direct EM-driven optimization using population-based methods is almost 90%.”

 

5. Conclusions

 

“Herein, computationally-efficient design optimization of an FSS-based filtering antenna using data-driven surrogate models has been proposed. Our methodology employs a deep-learning-based model M2LP to create a fast surrogate, which is also found to be superior to benchmark models reported in the literature in terms of predictive power. In our case, the FSS has been optimized using the HBMO algorithm. The HBMO routine has been deployed to carry out design optimization of geometry parameters of printable FSS for a filtenna operating in 5-to-7 GHz range. Experimental validation…”

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors need to revisit their manuscript and reduce the number of references used in this manuscript which is 112. These many references cannot be accepted in the article paper of MDPI. So authors are suggested to reduce this number to a great extent. The reduction in the number is going to affect the manuscript content so authors are given major revisions to accommodate these changes in a reasonable time.

Author Response

Authors are grateful for the Reviewer’s kind comments both in the previous and this round of revisions that provided us chances to improve our work. With respect to your and the second Reviewer’s remark, the literature overview of the work has been shortened and the relevant sections have been revised. Although some additional citations have been added to the work in this round due to other review comments, the total number of cited works has been reduced to 84.

Reviewer 3 Report

Point-1. Previous comment is not properly addressed such as equivalent circuit model if included that would be much better.

Point-2. Metamaterials are artificial materials that have the robust ability to manipulate the intrinsic properties of EM waves, with frequency, polarization, and wavefront etc. In authors case, they have discussed the FSS, and optimized using the HBMO algorithm, it’s a swarm-based approach to optimization. How about a convolutional neural network (CNN) or fuzzy inverse or a fully connected regression model (FCRM) design method and so on. Provide a comparison between different approaches and compare why the authors have chosen this one in the designing process.

Point-3. In a deep neural network approach, an inverse design procedure of a metasurface within an ultra-wide working frequency band has been recently addressed [1]. As a result, an output unit cell can be directly computed for a particular design target, as well as the determination of the metasurface directly, without time-consuming optimization processes. Therefore, an ultra-wide working frequency and high average accuracy equip a motivating approach without the need for a complex structure. Please explain in detail with respect to the authors optimized technique, and if possible, the authors should try the same.

 

 [1] Ghorbani, F., Beyraghi, S., Shabanpour, J. et al. Deep neural network-based automatic metasurface design with a wide frequency range. Sci Rep 11, 7102 (2021).

Author Response

1) Previous comment is not properly addressed such as equivalent circuit model if included that would be much better.

 

The authors are grateful for the Reviewer’s kind comments both in the previous and this round of revisions that provided us chances to improve our work.  As mentioned by the Reviewer, the authors did not add any equivalent circuit design approach of the studied problem. The authors would like to ask the Reviewer for understanding that, given the following circumstances:

• Utilization of the equivalent circuit is not relevant given the topic of the work, where our primary goal is not to elaborate on the operating principles of the unit cell, but rather handle its geometry parameters in a computationally-efficient manner so as to ensure appropriate performance of the Filtenna with respect to the assumed design specifications. In other words, the scope of the paper is computational modelling and optimization, but not design intricacies of a particular unit cell used as an example.
• The overall length of the work is evaluated as too long by the Editorial Team and Reviewer 1. Thus, the authors were forced to reduce the overall length the work including citations, while adding new information with respect to second round of review comments.

 

 

 

2) Metamaterials are artificial materials that have the robust ability to manipulate the intrinsic properties of EM waves, with frequency, polarization, and wavefront etc. In author’s case, they have discussed the FSS, and optimized using the HBMO algorithm, it’s a swarm-based approach to optimization. How about a convolutional neural network (CNN) or fuzzy inverse or a fully connected regression model (FCRM) design method and so on. Provide a comparison between different approaches and compare why the authors have chosen this one in the designing process.

 

The authors are grateful for this comment. The methods mentioned therein have been added to the manuscript. The performance of models is also included with the overall training time to clearly present the advantages and disadvantages of the considered models.

 

The following description has been added in Section 2:

“…The hyper-parameters of the models are determined using Bayesian Optimization with maximum objective evaluations epoch set to 30. Based on data in Table 2, although the best performance is achieved by the FCRM surrogate model (4.1% hold-out error), the required training time for the model and its optimization is more than twice of the time for M2LP surrogate model, which achieves a hold-out error of 4.7%. Both models exhibit a similar error rate of less than 5%, both according to cross-validation and the hold-out test, which suggest that they are not only well-trained but also not over-fit. Thus, in overall performance comparison, the M2LP model is evaluated as a better solution from the perspective of overall computational efficiency. Here, it is worth mentioning that there are other types of approaches for modelling of FSS unit elements such as the usage of equivalent circuit models [68] or physics-based models [69]…”

 

Table 2 has been revised.

Table 2. Performance comparison of data-driven surrogate models

Model	Hyper-Parameters	K-fold/Holdout	Total Training Time [Minutes]
MLP	Hidden Layer size-2; Hidden Layer Neurons sizes 15-20; Activation function sigmoid	6.0 % /7.5 %	~17.5
SVRM	Kernel-function: Radial, Type: Epsilon, Epsilon: 0.1.	6.4% / 8.1 %	~14.0
Gradient Boosted Tree	Learning-rate = 0.045; Depth: 5; N. estimators: 4800	7.6% / 8.4%	~8.5
Keras Deep Residual NN Regressor	N. Layers:2; N. Neurons: 512-512	4.6% / 5.4%	~27.0
Gaussian Process Regression	Kernel-function: ard-matern3/2; Prediction-method: Block-coordinate-descent; block-size: 750	5.4% / 6.2%	~27.0
M2LP	Depth: 3, initial Neuron N.: 64	3.9% / 4.7 %	~21.0
Convolutional Neural Networks	N. Layers:3; N. Neurons: 64-128-256	4.3% / 5.2 %	~29.0
FCRM [64]	Block size= 3; Sublock = Fully Connect + Leak ReLU Sublock neurons Number={256, 1024 ,1024})	3.2% / 4.1 %	~42.5

 

 

3) In a deep neural network approach, an inverse design procedure of a metasurface within an ultra-wide working frequency band has been recently addressed [1]. As a result, an output unit cell can be directly computed for a particular design target, as well as the determination of the metasurface directly, without time-consuming optimization processes. Therefore, an ultra-wide working frequency and high average accuracy equip a motivating approach without the need for a complex structure. Please explain in detail with respect to the author’s optimized technique, and if possible, the authors should try the same.

[1] Ghorbani, F., Beyraghi, S., Shabanpour, J. et al. Deep neural network-based automatic metasurface design with a wide frequency range. Sci Rep 11, 7102 (2021).

 

To begin with, it should be emphasized that inverse modelling is entirely out of the scope of the paper. In other words, our focus is on forward modelling and its application to unit-cell design. Notwithstanding, following the Reviewer comment, a discussion of inverse modelling, as well as its advantages and disadvantages, has been included in the revised paper. Furthermore, the reference mentioned by the Reviewer has been included into the reference list of the paper.

As mentioned by the Reviewer, there are techniques employed for modelling of high performance microwave circuits than the proposed direct modelling approach. While inverse modelling might be an efficient design method, it also exhibits a series of drawbacks, such as limited Design of Freedom (DOF) for variables of the problem, where same targeted performance might have more than one (or even dozens of) possible solution, effectively leading to non-uniqueness issues. In particular, the model may fail to render a unique response due to the failure in adjusting the model weighting coefficients for same input and different outputs. Consequently, the designer has to cancel out or take constant values of some of design variables that would reduce the DOF and performance of the obtainable optimal FSS design.

Another advantage of using data-driven surrogate model is that this approach eliminates the drawback of time-consuming optimization processes. Since each function evaluation using a data driven surrogate model is less than 1 millisecond, even an optimization process with 5,000 of function evaluation would be shorter than 1 minute, the time corresponding to EM simulation of a single unit cell.

With respect to your comment, the mentioned work and the difference of the proposed approach, and how the proposed approach allows the users to improve the efficiency of optimization processes is explained in details.

 

The following description has been added in Section 4.

 

“…The approach adopted here employs a deep-learning-based model M2LP to create a fast surrogate. M2LP has been found superior to commonly used state-of-the-art techniques such as MLP, SVRM, Boosted Trees, Depp NN and Gaussian Process regression, in terms of the predictive power. Here, it is worth mentioning that, there other data-driven surrogate approaches such as inverse modeling [75] can be used to yield high performance designs. However, these methods also exhibit drawbacks, such as limited Design of Freedom (DOF) for variables of the problem, where same targeted performance might have more than one (or even dozens of) possible solution, effectively leading to non-uniqueness issues. In particular, the model may fail to render a unique response due to the failure in adjusting the model weighting coefficients for same input and different outputs. Consequently, the designer has to cancel out or take constant values of some of design variables that would reduce the DOF and performance of the obtainable optimal FSS design. The direct (or forward) modeling approach is not affected by the aforementioned uniqueness issues. On the other hand, disadvantage of forward-modelling-based methods is the necessity of often time-consuming model optimization to determine the optimal solution for the target performance response. Yet, if the forward model is computationally cheap, as is the case in this work, the said drawback has been effectively eliminated: the unit cell optimization cost becomes negligible. As each (model-predicted) function evaluation takes less than one millisecond, even an optimization process involving 10,000 objective function calls would be shorter than one minute, the time corresponding to a single EM analysis of the unit cell. The obtained numerical and experimental data indicate that the proposed design approach is highly reliable and computationally efficient. The estimated speedup with respect to direct EM-driven optimization using population-based methods is almost 90%. Also in Table 4, the performance of the optimally design Filtenna is compared with state-of-the-art designs reported in the literature.”

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The authors have revised the paper according to the comments but the revised version is having so many references. Authors are advised to reduce the references which are not necessary.

Author Response

Authors are grateful for the Reviewer’s kind comments both in the previous and this round of revisions that provided us chances to improve our work. With respect to your and the second Reviewer’s remark, the literature overview of the work has been shortened and the relevant sections have been revised. The total number of cited works has been reduced to 55.