Materials & Design 207 (2021) 109855

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Materials & Design

journal homepage: www.elsevier .com/locate /matdes

Accelerated topological design of metaporous materials of broadbandsound absorption performance by generative adversarial networks

https://doi.org/10.1016/j.matdes.2021.1098550264-1275/� 2021 Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding authors.E-mail addresses: h_zhang00@163.com (H. Zhang), wenjihong@vip.sina.com (J. Wen).

Hongjia Zhang a,⇑, Yang Wang a, Honggang Zhao a, Keyu Lu b, Dianlong Yu a, Jihong Wen a,⇑aVibration and Acoustics Research Group, Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligence Science and Technology, National Universityof Defense Technology, Changsha 410073, Chinab Institute of Unmanned Systems, College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

h i g h l i g h t s

� GANs newly used for topologicaldesign of metaporous materials forsound absorption.

� Huge acceleration (~0.04s/design) fordesign process enablinginstantaneous designing.

� Successful designs of broadbandsound absorption checked bysimulation and experiment.

� Creative configurations and rich localfeatures generated in GANs-designedpatterns.

� AI-guided designing/optimizing asnew possibility for AI-materialsinterdiscipline.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 10 March 2021Revised 23 May 2021Accepted 26 May 2021Available online 28 May 2021

Keywords:GANsTopological designMetaporous sound absorption materialsAI-materials interdiscipline

a b s t r a c t

The topological design and optimization of metaporous materials is one of the key challenges in the fieldof sound absorption. Limited by the expensive computational cost, it is particularly disadvantaged wheninstantaneous multiple designs are required. In recent years, an increasing number of research fields areharnessing machine learning approaches thanks to their experience-free manner and outstanding effi-ciency. Generative Adversarial Networks (GANs), as a type of machine learning algorithms, enjoy the spe-cial benefit of powerful generative capability, making them brilliantly suitable for designing purposes.Additionally, it can fully explore the data distribution space with enormous computational power andcreate brand new designs. In this work, GANs are newly employed for the topological design of meta-porous materials for sound absorption. Trained with numerically prepared data, they successfully pro-pose designs with high-standard broadband absorption performance, verified by simulation andexperiment. The designing process is dramatically accelerated by hundreds of times using GANs (100designs in 4.372 s). This allows GANs to easily provide more structures and configurations, and achieveinstantaneous multiple solutions, giving designers more choices to satisfy various constraints such asmass or porosity. In addition, GANs are demonstrated remarkably capable of generating creative config-urations and rich local features. This work proposes a new designing principle, illustrates the value ofmachine learning in guiding the designing and optimizing process in the mechanical world, and opensnew possibilities for the future of AI-materials interdisciplinary research.� 2021 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://

creativecommons.org/licenses/by-nc-nd/4.0/).

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

Fig. 1. Typical patterns in the training set.

1. Introduction

Materials for high-efficient airborne-sound absorption havebeen extensively pursued for decades. Classical porous materials,e.g., foam, glass fiber and mineral wool, are unsuitable for low fre-quency sound absorption as bulky and heavy materials arerequired in this case [1]. To overcome the shortcoming of the clas-sic porous materials, using metaporous materials, i.e., a porousmatrix embedded with inner scatterers, provides a promisingalternative. The last twenty years has seen a growing number ofworks devoted to the designing of metaporous materials [2–10].However, limited by intuition, the reported designs feature mostlyregular shapes, leaving the potential of the metaporous materialslargely unexploited. As an inverse design strategy, topology opti-mization was capable of producing more complex designs thatachieve far more enhanced absorption at multiple target frequen-cies owing to the possession of different resonance mechanismsin the same design [11]. Nevertheless, the existing topology opti-mization methods suffer inherent drawbacks in terms of computa-tional time and cost due to extensive variables and numerousiterations needed. Particularly, it becomes even more expensive ifa number of designs are required. Moreover, instantaneous design-ing is hardly possible. To this end, the emerging machine learningalgorithms are considered to possess great potential to substan-tially boost the efficiency of designing and exploring newtopologies.

The last decade has witnessed the booming of machine learningtechnology. It has become not only popular in computer sciencerelated subjects but also other fields such as mechanics, biologyand material science [12–22]. It enjoys the advantage of being anexperience-free approach as well as allowing instantaneous multi-ple designs simultaneously with extremely high efficiency [23]. Inaddition, it has been favorable for its capability of discovering com-plex intrinsic pattern of large datasets with the prevailing big dataera [13].To the best of our knowledge, machine learning methodshave so far not been employed for the design of sound absorptionmaterials. However, we are seeing a rising trend of machine-learning-based designing of two-dimension (2D) architectures[24]. He et al. achieved inverse design of topological metaplatesfor flexural waves through finding the non-linear mappingbetween the key parameters and the topology via neural networks[23]. A framework integrating topology optimization and genera-tive models was proposed and validated on the case of 2D wheeldesign using Boundary Equilibrium Generative Adversarial Net-works (GANs) [25]. A convolutional neural network (CNN)-basedencoder and decoder network together with conditional GANswas employed as a two-stage refinement to realize near-optimaltopological design [26].

Most of the existing works on topological design or optimiza-tion adopt basic convolutional neural networks. Those algorithmsare usually effective at indirectly designing the structure by decid-ing its individual parameters (such as the length of an edge or theradius of a circle), but can hardly make a sophisticated designbased on complete patterns. As a contrast, our work can directlygenerate topological patterns using a generative network - GANs.GANs feature a generator and a discriminator that learn simultane-ously in competition with each other [27,28]. The generator cangenerate brand new data (e.g. the topological structure of meta-porous materials in this paper) based on the captured potentialdistribution of the training data. Since the generator is extraordi-narily powerful computationally, it can thoroughly explore thedata space and produce creative designs that potentially exceedthe limitation of the existing ones. Previous works have success-fully employed GANs to obtain over 400 complex two-

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dimensional architectures that approach the Hashin-Shtrikmanupper bounds [29]. Conditional GANs were used to designnanophotonic antennae with desired optical properties [30].

In this paper, GANs are employed to carry out topologicaldesign of metaporous materials for sound absorption in a signifi-cantly accelerated and efficient manner. Trained with numericallyprepared data, GANs are demonstrated capable of generatingdesigns with high-standard broadband absorption performance,verified by Finite Element Modeling (FEM) simulation and experi-ment. Meantime, brand new configurations and local features areseen in the designs by GANs, illustrating its ability of ‘creativity’and potential to further improve the existing materials forenhanced performance.

2. Dataset

The training set prepared with FEM simulation consists of 1832images of a � a = 64 � 64 pixels. Each image represents a patternfor metaporous material. Typical patterns are shown in Fig. 1where the solid black domain denotes the scatterer and the whitearea is filled with porous media. The patterns are stored as binaryimages composed of 0 and 1, corresponding to porous media andscatterer, respectively. The shapes of the scatterer in the trainingset are composed of three types of basic primitives, i.e., slottedcube, slotted elliptic cylinder and thin partitions. For the slottedcube, the lower (upper) bounds of the outer side lengths and slotwidth are 0.4a (0.8a) and 0.08a (0.48a), respectively. The minimum(maximum) lengths of outer semi-axis and slot are 0.2a (0.4a) and0.08a (0.48a) for the slotted elliptic cylinder. As for the thin parti-tion, the lower and the upper bounds of the length are respectively0.2a and 0.8a. The thickness for all three primitives is no largerthan 0.0625a. The generation procedure for all the patterns startsfrom a porous media (64 � 64 null matrix). The scatterer is subse-quently ‘embedded’ into the porous media at a random location,imitating the mutation process in the genetic algorithm [31], i.e.,some pixels of porous media (0) are changed to that of scatterer(1). To increase the diversity of the patterns, a perturbation opera-tor is applied to the pattern where the pixels inside the scattererare reversed with 20% probability. Finally, in order to improvethe geometric topology and eliminate checkerboard pattern, theabuttal filter is employed [32], i.e., some isolated porous elementsare changed to scatterer elements and vice versa.

Fig. 2. Schematic diagram of the full-wave simulation model

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

The patterns in the training data contain up to three primitives.Fig. 1(a)-(d) plots those with only one primitive. The employmentof perturbation operator during the generation process leads to thenon-smooth peripheries of the slotted scatterer as well as the dis-crete dotted black pixels inside. It is also the reason for the exis-tence of the closed cylinder shown in Fig. 1(c). The patternsconsisting two or three primitives are shown in Fig. 1(e)-(l). Forinstance, Fig. 1(e) and Fig. 1(g) show the patterns with two primi-tives of the same type. The examples for multiple primitives withdifferent types are given in Fig. 1(k) and (l). Particularly, we shallpay attention to the correlation between primitives in the samepattern. They can be simply apart as in Fig. 1(g), half intersectedin Fig. 1(f) or internally tangent in Fig. 1(h).

To obtain the absorption coefficients of each pattern, full-wavesimulation is performed via Pressure Acoustic and Frequencydomain module with the commercial finite element softwareCOMSOL�. As shown in Fig. 2, a plane wave is incident to the pat-tern with the amplitude of 1 Pa from the background pressurefield. Perfectly matched layer (PML) is applied at the left boundaryof the background pressure field to simulate anechoic terminationfor outgoing wave (i.e., reflective wave). The horizontal blackdashed lines denote the periodic boundary while the green black

Table 1Acoustical parameters of the melamine foam for FEM simulation.

U a1 K K0 r

0.95 1.42 180 lm 360 lm 8900N � s �m�4

Fig. 3. Schematic illustration of the design proce

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solid line at the right end is the hard acoustic boundary. The porousmedia in the metaporous material is melamine foam as in our pre-vious work [9]. The acoustic parameters of the melamine foam aredescribed using Johnson-Champoux-Allard (JCA) model [33] inPoroacoustics Domain, as listed in Table 1, whereU is the porosity,r the flow resistivity, a1 the tortuosity,K the viscous length andK0

the thermal characteristic length. The sample frequencies in thesimulation are from 300 Hz to 3000 Hz at the interval of 50 Hz.Since GANs generate new patterns based on what they are feedwith, we prepared 1832 patterns whose average absorption coeffi-cients are larger than 0.9 to form the training set, aiming to obtainpatterns with at least equally high absorption performance.

3. Methods

3.1. Generative adversarial networks

GANs feature a pair of networks, a generator G and a discrimi-nator D, competing with each other. As a two-player zero-sumgame, G aims to generator ‘fake’ data that are as ‘real’ as possibleto ‘fool’ G, while G learns to discriminate fake data generated byG from real ones as accurately as possible. This is essentially a min-max process where G and D can both respectively sharpen theirgenerative and discriminative skills [34]. Importantly, G does notdirectly access real images and it learns only through interactingwith D [28]. Consequently, G learns to generate usable data (pat-terns in our case) for the purpose of the specific model setup. Even-tually, a Nash equilibrium is reached, meaning each player cannotobtain a better result without changing the other players’ strategy,and two players stay equally good [35].

dures of metaporous materials with GANs.

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

3.2. Design procedures

Fig. 3 demonstrates the procedure to design and verify themetaporous materials. Three main steps are necessary for a com-plete and reliable design: 1) training data preparation; 2) generat-ing designs using trained GANs; 3) verify those designs with FEMsimulation and experiments.

The left part of Fig. 3 shows the design procedures of meta-porous materials with GANs in this work. The model is built withPytorch. Pytorch is a commonly used open-source deep learningframework, basically a library that provides building blocks fordesigning, training and validating deep neural networks via ahigh-level programing interface [36,37]. Being a python library,Pytorch enjoys the advantages of possessing both GPU-

Fig. 4. Designs proposed by GANs and their absorption performance simulated by FEM:Absorption coefficients of Design 5–8.

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accelerated tensor computation and performance at the same time.With packages from Pytorch, procedures in deep learning such asnetwork building and gradient descent can be programed with acouple of code lines, making it far more efficient.

In general, the architectures of G and D are described as follows.The input of G is a greyscale image with 64 � 64 size. G containsten convolutional layers. Each convolutional layer is followed bya batch normalization layer and a ReLU layer. The output of G isstill a grey image with the same size as the input one. D takesthe grey image generated by G as the input. D consists of five con-volutional layers and a softmax layer. Each convolutional layer isalso followed by a ReLU layer. The output of D is a binary classifi-cation label which indicates if the generated image is legitimate ornot.

(a) I: designs 1–4; (b) II: designs 5–8; (c) Absorption coefficients of Design 1–4; (d)

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

Specifically, with a random noise (64 � 64 size) as input, G out-puts a ‘fake’ pattern (64 � 64 size) which is subsequently inputinto D together with the ‘real’ patterns – the training data. D judgeswhether the generated pattern is legitimate by comparing it withtraining data. With the advancement of the minmax process, Gfinally learns to generate designs that are comparable with thetraining data. Delightfully, patterns generated this way possessnew features since G is computationally extremely powerful toexplore the full distribution of the data space (i.e., fullpossibilities).

Note that the criterion of D’s judgement on whether a pattern islegitimate or not is actually learned via training, instead of adopt-ing a handcrafted criterion. The criterion is essentially representedby the weights in the convolutional kernels that are constantlyapplied to the input images to extract features at each convolu-tional layer in the neural networks. Starting with a random D witha cross-entropy loss that calculates the difference between the out-put pattern of the G with the input pattern, D’s aim is to maximize

Fig. 5. Pressure distribution inside Design 3 at the characteristic frequencies

Table 2Average absorption coefficient for designs.

Design 1 Design2 Design3 Design4

0.925 0.929 0.930 0.926

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the loss while G’s aim is to minimize it, which forms a minmax‘competition’. D’s capability of judging whether the generated pat-tern is legitimate is basically equal to its capability to maximize theloss, which relies on the choice of weights. The same logic goes toG’s capability of generating legitimate patterns. During training,the ‘competition’ advances, where D and G continuously adjuststheir own weights based on the loss until a balance is reached(i.e. the Nash equilibrium). Eventually, a capable D is obtained witha set of learned weights to represent the criterion that is good at‘judging’.

4. Results

4.1. GANs-designed patterns and numerical verification

GANs bring extreme acceleration of the designing process,enhancing the efficiency by hundreds of times compared with

of: (a) f1 = 950 Hz; (b) f2 = 1300 Hz; (c) f3 = 1960 Hz; (d) f4 = 2600 Hz.

Design5 Design6 Design7 Design8

0.925 0.931 0.927 0.927

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

the existing approaches such as density-based approach andgenetic algorithm [38]. The generation of 100 patterns takesapproximately only 4.372 s (with commonly used NvidiaRTX3090) once the model is well trained. More details regardingthe time needed for data preparation and model training aredescribed in Appendix A.

More than a hundred designs of metaporous materials are pro-posed by GANs out of which eight typical ones are presented inFig. 4. The height and the width of a pattern are both 64 mm(and 64 pixels). So, one pixel inside the pattern has the size of1 mm � 1 mm. Overall, all the designs can be classified into twocategories: I - multiple slotted cavities with different orientationsand creative variation on the periphery (Design 1–4 in Fig. 4(a));II - a single slotted cavity with large opening and rich local featuresinside (Design 5–8 in Fig. 4(b)). Note that ‘annulus’ here is a gen-eral term describing the circle-like or rectangle-like outlines inthe pattern. Additionally, to differentiate GAN-generated patternsfrom the training data, patterns below are highlighted in blue(scatterer) and pink (foam).

The FEM-calculated absorption coefficient curves of the eightdesigns are illustrated in Fig. 4(c) and (d). Overall, all the eightdesigns show broadband absorption capability. The averageabsorption coefficients (between 300 Hz and 3000 Hz with theinterval of 50 Hz) are listed in Table 2. It is shown that the averageabsorption coefficients of all designs are larger than 0.925, which isa rather high standard.

Fig. 6. Pressure distribution inside Design 8 at the characteristic frequency

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It is illustrated that GANs are skilled at generating and alternat-ing local features. Being greatly capable at manipulating inputinformation, it can comprehensively assemble different shapes/primitives in creative configurations. For instance, the model haslearned from Fig. 1(h) that one primitive can be inside anotherone. Meanwhile, it has captured several different primitives outof the training data including slotted cylinders and thin rigid par-titions. Design 5 in Fig. 4(b) is a result of putting thin partitionsinside a slotted cylinder as well as making some modificationand variation on the cylinder’s periphery. Hence, we reckon thatGANs are capable of capturing different shapes in the training data,treating them as separate features and generating brand new com-binations and create rich variation on the features themselves.

Particularly noteworthy is the position of the opening on thecavity. The training data only contain patterns with opening posi-tioned towards the incident end of the sound wave, i.e., the top ofthe pattern. However, GANs have created new opening positionstowards the backing (the bottom of the pattern) as shown inDesign 3 and 4 in Fig. 4(a). This operation is of great importancefor sound absorption and is often highlighted in the existing non-machine-learning-based designing methods [39].

4.2. Broadband absorption mechanism

To explore the mechanism behind the broadband absorptionperformance, we choose Design 3 and Design 8 as representatives

of (a) f1 = 930 Hz; (b) f2 = 1280 Hz; (c) f3 = 1820 Hz; (d) f4 = 2400 Hz.

Fig. 7. Sample preparation process.

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

of the two categories of designs for deeper examination. Fig. 5(a)-Fig. 6(d) plot the pressure distribution of Design 3 at four charac-teristic frequencies. It is noted that the two slotted cylinders aresole ‘active’ at the frequencies of f1 and f3, i.e., maximum pressureis located at the two slotted cylinders and resonance state existsnear the two frequencies. At the frequency of f2, the pressure istrapped between the two slotted cylinders and the backing, whileboth two slotted cylinders are simultaneously ‘active’. However,

Fig. 8. Experimental setup: (a) sch

Fig. 9. Experimental results compared with FEM

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Design 3 shows a different coupled mode at the frequency of f4.Notable acoustic scattering is observed between the two slottedcylinders near the incident end and partial acoustic energy alsoenters the left slotted cylinder. It could be concluded that the col-laboration of resonance, acoustic trapping and scattering effectcontributes to the overall broadband absorption of Design 3.

Fig. 6(a)-(d) further illustrates the pressure distributions ofDesign 8 at four representative frequencies. At low frequency f1,

ematic illustration; (b) photo.

simulation for (a) Design 3 and (b) Design 8.

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

the main acoustic energy enters the full big cavity while partiallytrapped between the cavity and the backing. At frequencies f2and f4, it is interesting to note that two different local resonancemodes are triggered by the thin partitions inside the cavity. Thetwo local resonance modes together with the scattering outsidethe cavity also contribute to the sound absorption of Design 8 atfrequency of f3. Different form Design 3, Design 8 possesses morecomplex local modes inside the cavity, thanks to the rich local fea-tures of thin partition generated by GANs.

4.3. Experimental verification

Fig. 7 illustrates the process of sample preparation. Overall, themetaporous material is composed of three components, i.e., a coverlayer, an inner scatterer and melamine foam. The inner scattererand the cover layer are 3D printed with polylactic acid (PLA) withthe parameters of density q = 1250 kg/m3, Young’s modulusE = 1.2GPa and Poisson’s ratio v = 0.35. The thickness of the coverlayer is 1 mm. Compared with the size of the cubic sample 60 mm,the influence of the cover layer is neglectable. To facilitate theembedding of the scatterer, a pattern with the shape of the scat-terer is etched into the melamine foam. The metaporous materialis an assembly of all the components. Note that the sound waveis incident into the top face along the -y direction shown in Fig. 7.

The experiment is carried out in a home-made impedance tubeusing the two-microphone method [40]. As shown in Fig. 8(a), theimpedance tube features a square cross-section with the sidelength of d = 60 mm. The sample is attached to a rigid backing.The distances between the sample and the two microphones areL1 = 200 mm and L2 = 150 mm, respectively.

Design 3 and Design 8 are chosen for experimental verification.Fig. 9(a) and (b) compare results obtained by the experiment andFEM simulation. Overall, a good agreement is reached. However,some discrepancies still exist, especially for Design 8. We considerthat the mismatch is a result of two reasons: (1) the uncertainty offabrication for both 3D-printed frame and the etched melaminefoam; (2) the inaccuracies occurred during the assemblingprocess.

5. Conclusions

In this work, GANs are used to design metaporous materials forsound absorption. The training set is prepared with FEM simula-tion, containing 1832 binary images of 64 � 64 pixels. WithPytorch framework, trained GANs can generate 100 patterns inroughly 4.372 s, bringing tremendous acceleration of the designingprocess, boosting the efficiency by hundreds of times comparedwith the existing approaches. Eight typical designs proposed byGANs are chosen to be verified by FEM simulation, out of whichtwo are printed out with a 3D printer for experimental evaluation.The advantage in the computation time enables this approach toprovide more structures and configurations, and achieve instanta-neous multiple solutions with high absorption performance, com-pared to a unique solution as the case with the existing methods.

The results illustrate that GANs are capable of generating meta-porous material designs with satisfying broadband absorption per-formance. The FEM simulation of the eight designs demonstratedthat their average absorption coefficients are all larger than0.925. The experiments again confirm the quality of the two 3D-printed designs. Additionally, the numerical and experimentalresults show satisfying agreement.

As to the generative capability, GANs are demonstrated skilledat capturing input information and generating brand new configu-rations and rich local features comprehensively. Two typical cre-ations of GANs’ are observed. One is to learn a new assembling

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approach and alternating primitives (as well as adding local fea-tures) for the assembly to form a new design. The other is thatGANs have created new opening positions for the design, whichis of crucial significance in practice.

Overall, this work has for the first time utilized GANs to designmetaporous materials for sound absorption. The accelerateddesigning process and the satisfying results demonstrate that AI-materials interdisciplinary approach is of excellent potential andimportance in guiding the designing and optimizing process inthe mechanical world.

Declaration of Competing Interest

The authors declare that they have no known competing finan-cial interests or personal relationships that could have appearedto influence the work reported in this paper.

Acknowledgement

This work was supported by the National Natural Science Foun-dation of China (Grant No. 52001325, 51775549, 11991032 and11991030).

Appendix A. Computation time

The 1832 patterns with >0.9 average absorption coefficients areselected from a larger database with 7636 patterns in total viaexamining all their average absorption coefficients. That meanswe use COMSOL (full-wave simulation) to calculate the averageabsorption coefficient of all the 7636 patterns. Each calculationtakes about 3 s, making it 22,908 s (that’s roughly 382 min or6.36 h) in total. Note that the 7636 patterns are generated follow-ing the generation procedure described in ‘section 2 Dataset’,which is rather fast. The generation of 7636 patterns takes around234.7 s (roughly 3.9 min) in total. So, the preparation of the train-ing dataset of 1832 patterns takes approximately 386 min(~6.43 h), including 2 parts: the generation of 7636 patterns(3.9 min) and the COMSOL FEM calculation of 7636 patterns(382 min).

Model training time is related to the GPU computation power.With NVIDIA RTX3090, the whole training takes about 8 h. Thetraining process can easily speed up via training in parallel on mul-tiple GPUs.

In total, the pre-designing stage (including training set prepara-tion and model training) need <15 h.

On the other hand, based on our experience of the existingtopology optimization methods, one generation averagely takesabout 3 s and it needs around 200 generations for the algorithmto converge to give out a design, i.e. 600 s for one pattern. There-fore, to design 100 well-performed patterns with genetic algo-rithms takes about 1000 min (~16.7 h), which is already longerthan the GANs-based approach. The above comparison is only fordesigning 100 patterns. When more patterns are needed, theadvantage of GANs-based approach becomes a lot more obviousas it only needs multiple seconds (for generation) while the exist-ing methods need hours.

Therefore, the GANs-based approach has dramatically acceler-ated the designing procedure especially when instantaneous mul-tiple solutions are needed.

Data availability

The raw/processed data required to reproduce these findingscannot be shared at this time as the data also forms part of anongoing study.

H. Zhang, Y. Wang, H. Zhao et al. Materials & Design 207 (2021) 109855

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