A multi-condition satisfying metamaterial reverse design method and system

Abstract

This invention relates to the fields of artificial intelligence and metamaterials research technology, and in particular to a metamaterial inverse design method and system that satisfies multiple conditions. The proposed metamaterial inverse design method first generates metamaterial unit cell images using randomly generated initial variable combinations within a specified range. These images are then input into a trained prediction model to obtain dispersion maps and transmission loss data. Finally, the prediction results are substituted into a fitness function; if the requirements are met, the variables and prediction results are output; otherwise, a penalty is applied, and iterations are performed until the maximum number of iterations is reached. This invention enables rapid metamaterial design, and the designed metamaterials possess wide bandwidths, achieving ideal target bandwidths and transmission loss conditions. This invention utilizes a deep learning model to satisfy the required bandwidth and transmission loss conditions for metamaterial inverse design, achieving multi-objective performance requirements. This invention overcomes the problems of traditional metamaterial design methods in the prior art, which rely on experience-driven iterative optimization and are limited by computational efficiency, making it difficult to efficiently explore high-dimensional parameter spaces and meet complex multi-objective performance requirements.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of artificial intelligence and metamaterial research, and particularly relates to a multi-condition-satisfied metamaterial reverse design method and system. BACKGROUND

[0002] Metamaterials have a wide range of applications such as sound wave conduction, sound insulation and vibration reduction, negative refraction, and acoustic stealth. Traditional metamaterial design can only change its own characteristics by adjusting parameters when the shape is roughly determined, but the adjustable range of this method is not large and a large number of repeated trial and error are required. In recent years, the rise of machine learning has made it possible to predict and reverse design metamaterials. Some research uses the finite element method and a two-stage genetic algorithm to optimize the topology of metamaterials considering the influence of material contrast and predefined average density, expecting to obtain the maximum band gap width of metamaterials. Some research systematically constructs a deep learning-based metamaterial reverse design framework, which has three core contributions. First, the neural network model verifies the feasibility of band gap prediction, breaking through the efficiency bottleneck of traditional numerical methods. Then, it is expanded to a multi-element network architecture, which realizes the band gap prediction and configuration generation of one-dimensional layered, two-dimensional binary and ternary composite metamaterial systems, and reveals the generalization ability of the network model to different dimensions and material combinations. Finally, the band gap attenuation performance of the reverse-designed metamaterials is verified by finite element calculation, confirming the applicability of data-driven methods in metamaterial optimization.

[0003] Currently, few people use machine learning to study the transmission loss of metamaterials, and simultaneously optimize the structure of metamaterials using multiple indicators. Transmission loss is an important indicator reflecting the vibration reduction and isolation ability of metamaterials in reality. Optimizing transmission loss as the target in the reverse design process can make the designed metamaterials have the performance of attenuating waves that meet the needs of engineering practice. SUMMARY

[0004] In order to overcome the defects of the traditional metamaterial design method in the prior art that relies on experience-driven iterative optimization and is limited by calculation efficiency, and is difficult to efficiently explore high-dimensional parameter space and meet complex multi-objective performance requirements, the present application provides a multi-condition-satisfied metamaterial reverse design method, which can quickly design crystal shapes with multiple target performances.

[0005] The multi-condition-satisfied metamaterial reverse design method provided by the present application first obtains a prediction model for predicting dispersion diagrams and transmission losses based on crystal shape pictures, obtains crystal design targets, and selects a crystal design formula.

[0006] A plurality of crystal shapes are generated by the crystal design formula and input into the prediction model. Crystal shapes whose dispersion diagrams and transmission losses output by the prediction model satisfy the crystal design targets are selected as candidate crystal shapes.

[0007] iteratively updating the geometric parameters of the crystal design formula until the fitness of the candidate crystal shape is 0, fixing the geometric parameters of the crystal design formula, and generating a crystal shape satisfying the crystal design target.

[0008] Preferably, the penalty of the crystal shape is calculated according to the following formula:

[0009]

[0010] TLP = max(0, (TL-TTL))

[0011] Penalty = GP + TLP

[0012] wherein GP is the fitness function of the band gap; CGS(i) and CGE(i) are the start point and end point of the ith band gap in the dispersion diagram respectively; i is the number of the band gap; TGS is the target band gap start point, and TGE is the target band gap end point; TLP is the fitness function of the transmission loss, TTL is the target average value of the transmission loss, and TL is the average value of the transmission loss in the predicted band gap interval.

[0013] Preferably, the prediction model is obtained in the following manner: first, determine the crystal design formula, and randomly initialize the geometric parameters of the crystal design formula; generate multiple crystal shapes using the crystal design formula corresponding to each set of geometric parameters, perform finite element simulation on each crystal shape, obtain the corresponding dispersion diagram and transmission loss, and construct a data set {crystal shape; dispersion diagram, transmission loss}; then train the prediction model on the data set using a machine learning algorithm.

[0014] Preferably, the crystal design formula corresponding to the crystal design target is the same as the crystal design formula used to construct the data set.

[0015] Preferably, if the fitness of the candidate crystal shape is not equal to 0, the genetic algorithm is used to update the geometric parameters of the crystal design formula.

[0016] Preferably, the prediction model is composed of a VAE model and an iTransformer model, the VAE model encodes the crystal shape picture, and the encoding vector is processed by the iTransformer model to obtain the dispersion diagram and the transmission loss.

[0017] Preferably, the crystal design target includes a target band gap and a target average value of the transmission loss.

[0018] Preferably, after determining the crystal design formula, the crystal design formula is used to generate a crystal shape as a candidate target, each candidate target is simulated by finite element calculation, and the target design scheme is selected.

[0019] The application provides a multi-condition satisfying metamaterial reverse design system, which comprises a memory and a processor, the memory stores a computer program, and the processor is connected with the memory and used for executing the computer program to realize the multi-condition satisfying metamaterial reverse design method.

[0020] The application provides a storage medium, which stores a computer program, and the computer program is used for realizing the multi-condition satisfying metamaterial reverse design method when executed.

[0021] The application has the advantages that:

[0022] (1) The application provides a multi-condition satisfying metamaterial reverse design method, which firstly generates a metamaterial unit cell picture by using an initial variable combination randomly generated in a range, then inputs the picture into a trained prediction model to obtain dispersion diagram and transmission loss data, finally substitutes the prediction result into a fitness function, and if the requirement is met, the variable and the prediction result are output, otherwise, a penalty is applied for iteration until the maximum iteration number is reached.

[0023] (2) The application uses the encoder dimension reduction of the VAE (variational autoencoder) model for the unit cell image (crystal shape), trains a prediction model by using dispersion and transmission loss data obtained by the FEM (finite element method), then inputs target band gap and target transmission loss conditions, and uses the genetic algorithm containing the VAE encoder and the iTransformer model to reversely design the geometric parameters of the metamaterial meeting the requirements.

[0024] (3) The VAE introduces the idea of probabilistic modeling and combines the variational inference technology, and can effectively solve the problem of insufficient continuity of the latent space of the traditional autoencoder.

[0025] (4) The core mechanism of iTransformer is to calculate the global dependency between elements in the input sequence based on self-attention. The self-attention mechanism allows the model to assign different attention weights according to different parts of the input sequence, enabling the model to consider all positions in the input sequence simultaneously. This greatly improves the performance of the model when facing long sequence MIMO problems. The variable division method can better capture the relationship between different modes and different boundary points in the Brillouin zone of metamaterials, as well as the relationship between different points on the transmission loss curve, to obtain more accurate prediction results of the metamaterial dispersion diagram and transmission loss curve. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 Flowchart of the proposed deep learning model training and metamaterial optimization;

[0027] Figure 2(a) is a picture of the shape of a metamaterial crystal (unit cell sample);

[0028] Figure 2(b) is a parameter design diagram of Figure 2(a);

[0029] Figure 2(c) is an irreducible Brillouin zone diagram;

[0030] Figure 3 Figure 2(d) is a schematic diagram of various bending arm metamaterial unit cell samples;

[0031] Figure 4 Figure 3(a) is a finite element model for calculating the transmission loss;

[0032] Figure 5(a) is an error distribution diagram of the dispersion diagram test set;

[0033] Figure 5(b) is an error distribution diagram of the transmission loss test set;

[0034] Figure 5(c) is a comparison of the finite element calculation frequency points and the predicted frequency points of the dispersion diagram test set;

[0035] Figure 5(d) is a comparison of the finite element calculation sample points and the predicted sample points of the transmission loss test set;

[0036] Figure 6(a) is a reverse design result in the embodiment;

[0037] Figure 6(b) is another reverse design result in the embodiment;

[0038] Figure 7(a) is a schematic diagram of an experimental device;

[0039] Figure 7(b) is a metamaterial formed by different arrangements of the unit cells shown in Figure 6(a);

[0040] Figure 7(c) is the output of the 3x3 metamaterial under the action of the 600hz excitation input within the band gap, which is the result of the experiment and the finite element simulation.

[0041] Figure 7(d) shows the experimental and finite element simulation outputs of the 3×3 metamaterial under an excitation input of 200 Hz outside the band gap;

[0042] Figure 7(e) shows the experimental and finite element simulation outputs of the 5×5 metamaterial under a 600 Hz excitation input within the band gap;

[0043] Figure 7(f) shows the experimental and finite element simulation outputs of the 5×5 metamaterial under a 200Hz excitation input outside the band gap;

[0044] Figure 7(g) shows the experimental and finite element simulation outputs of the 7×7 metamaterial under a 600 Hz excitation input within the band gap;

[0045] Figure 7(h) shows the experimental and finite element simulation outputs of the 7×7 metamaterial under an excitation input of 200 Hz outside the band gap;

[0046] Figure 8 The flowchart of a metamaterial reverse design method that satisfies multiple conditions proposed in this invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0048] Reference Figure 1 , Figure 8 This embodiment proposes a metamaterial reverse design method that satisfies multiple conditions, including the following steps:

[0049] S1. Obtain the prediction model and predict the dispersion map and transmission loss based on the crystal shape image;

[0050] In practice, the prediction model consists of a VAE model and an iTransformer model. The VAE model encodes the crystal shape image, and the encoded vector is processed by the iTransformer model to obtain the dispersion map and transmission loss.

[0051] The prediction model is obtained by machine learning on the dataset {crystal shape; dispersion map, transmission loss}.

[0052] The dataset {crystal shape; dispersion map, transmission loss} is obtained as follows: First, the crystal design formula is determined, and the geometric parameters of the crystal design formula are randomly initialized; multiple crystal shapes are generated using the crystal design formula corresponding to each set of geometric parameters, and finite element simulation is performed on each crystal shape to obtain the corresponding dispersion map and transmission loss.

[0053] The crystal design formula can be selected according to the type of metamaterial. For example, in the subsequent embodiments, when designing a flexible-arm metamaterial, the crystal design formula can be specifically defined using a Bézier curve.

[0054] S2. Obtain the crystal design objectives, which include the target bandgap and the target mean transmission loss. The target bandgap can be specifically represented as the target bandgap start point and the target bandgap end point. The target mean transmission loss represents the average transmission loss over the target bandgap. Initialize the crystal design formula.

[0055] It is worth noting that the form of the crystal design formula in step S2 is the same as that of the crystal design formula for constructing the dataset in step S1, except that the geometric parameters of the crystal design formula are iterated.

[0056] S3. Generate multiple crystal shapes using crystal design formulas; input images of each crystal shape into the prediction model to obtain the dispersion map and transmission loss corresponding to each crystal shape, extract the bandgap interval from the dispersion map and record it as the predicted bandgap interval, and calculate the mean transmission loss in the predicted bandgap interval and record it as the mean predicted transmission loss.

[0057] S4. Obtain the crystal shape that has a predicted transmission loss mean less than or equal to the target transmission loss mean, and the lower end of the predicted bandgap interval is greater than or equal to the starting point of the target bandgap, and the upper end of the predicted bandgap interval is less than or equal to the ending point of the target bandgap (i.e., the predicted bandgap includes the target bandgap) as the candidate crystal shape.

[0058] S5. The suitability of the candidate crystal shape, Penalty, is calculated using the following formula;

[0059]

[0060] TLP = max(0, (TL - TTL))

[0061] Penalty = GP + TLP

[0062] Wherein, GP is the fitness function for the bandgap; CGS(i) is the starting point of the i-th bandgap in the dispersion map, i.e., the i-th curve (pattern) on the dispersion map; CGE(i) is the ending point of the i-th bandgap in the dispersion map, i.e., the (i+1)-th curve (pattern) on the dispersion map; i is the bandgap number. Obviously, in this embodiment, 10 curves on the dispersion map form 9 bandgap segments; TGS is the starting point of the target bandgap, and TGE is the ending point of the target bandgap; TLP is the fitness function for transmission loss, TTL is the target mean of transmission loss, and TL is the predicted mean of transmission loss, i.e., the average value of transmission loss within the target bandgap interval predicted by the model. Finally, Penalty is the sum of the two fitness functions, which is used to evaluate the individual fitness to impose a penalty.

[0063] S6. Determine if the fitness Penalty is 0;

[0064] Yes, then the geometric parameters of the fixed crystal design formula are used to generate a crystal shape that meets the crystal design target by combining the crystal design formula with the geometric parameters;

[0065] If not, a genetic algorithm is used to iterate the geometric parameters of the crystal design formula. After the number of iterations reaches the set number of 100, the iterated geometric parameters are substituted into the crystal design formula, and then the process returns to step S3.

[0066] The following specific embodiments illustrate and verify the above-mentioned reverse design method for flexible metamaterials based on the iTransformer model.

[0067] In this embodiment, Bézier curves are used as the crystal design formula to define the bend arm and adjust its shape and curvature.

[0068] In this embodiment, firstly, values ​​are randomly selected within the range of geometric parameters of the Bézier curve. This allows the Bézier curve to be combined with different geometric parameters to construct 10,000 unit cell samples, and corresponding crystal shape images are plotted to form a dataset. Some metamaterial unit cell shapes, i.e., crystal shape images, are shown below. Figure 3 As shown in the figure. In this embodiment, considering factors such as bandgap frequency, accuracy, and computational resource consumption, a transmission loss curve consisting of frequency points from 0-2000Hz with 5Hz intervals was selected for annotation. Specifically, the dispersion plots and transmission loss curves corresponding to each crystal shape image in the dataset were obtained through finite element simulation.

[0069] The unit cell sample defined by the Bézier curve consists of four symmetrically rotated 90° arms and a mass block with a radius of 3 mm located at the center. The material of the arms in the unit cell is TPU (thermoplastic polyurethane), and the mass block is made of steel. Their material properties are shown in Table 1 below.

[0070] Table 1: Material parameters of single-cell samples

[0071]

[0072]

[0073] The parametric modeling process of a metamaterial unit cell is shown in Figures 2(a), 2(b), and 2(c); where P1, P2, P3, and P4 are control points, r0 is the radius of the mass block, and r1 is the radius of P1 from the center of the circle.

[0074] In this embodiment, the first control point P1 of two Bézier curves defined on the same curve has an angle difference of 90° in polar coordinates, the second control point P2 has an angle difference of 2z², the third control point P3 has an angle difference of 2z³, and the fourth control point P4 is symmetrical about y = x. The remaining three bending arms are constructed using the same method. The coordinate constraint formulas for P1-P4 are expressed as follows:

[0075]

[0076] In the polar coordinate system, r1 is the distance between control points P1 of the two curves on the same curved arm, r2 is the distance between control points P2 of the two curves on the same curved arm, r3 is the distance between control points P3 of the two curves on the same curved arm, and r4 represents the axis coordinate of P4 in the rectangular coordinate system; o1 is the angle of P1, o2 is the angle between P2 and the midpoint of the line connecting the two P2s, and o3 is the angle between P3 and the midpoint of the line connecting the two P3s; z2 is the angle between the midpoint of the line connecting two different P2s on the same curved arm, and z3 is the angle between the midpoint of the line connecting two different P3s on the same curved arm; w1, w2, w3, and w4 are the weighting coefficients of P1, P2, P3, and P4, respectively.

[0077] r1, r2, r3, r4, o1, o2, o3, z2, z3, z4, w3, w4, P1, P2, P3, P4 constitute the geometric parameters of the Bézier curve. By determining each geometric parameter within a specified range, a crystal shape that meets the constraints can be randomly generated using the Bézier curve, i.e., the shape of a unit cell sample.

[0078] In this embodiment, the wave propagation analysis model consists of a 1×5 unit cell array, two periodic plates made of the same material as the unit cell matrix, and perfectly matched layers on both sides. After applying displacement excitation to the left side of the periodic plates, the wave passes uniformly through the metamaterial after passing through the periodic plates, and is picked up after passing through the periodic plates again. The model effectively suppresses edge scattering noise caused by finite size by adding perfectly matched layers (PML) on both sides of the excitation propagation direction (X direction) to absorb boundary reflections and combining them with homogeneous periodic plates to achieve an equivalent medium transition. Furthermore, by applying periodic boundary conditions on both sides of the model in the direction perpendicular to wave propagation (Y direction), the model realizes an infinite number of periodic arrays, such as...Figure 4 As shown.

[0079] In this embodiment, the crystal shape images in the dataset are preprocessed to obtain 64×64×3 single-cell color images. In the prediction model provided in this embodiment, the VAE model reduces the dimensionality of the crystal shape images to 192-dimensional vectors, significantly reducing the input data size while preserving as much original image information as possible, thus saving computational resources. The 64×64 resolution effectively balances computational complexity and feature preservation requirements: its pixel scale is sufficient to capture lattice details at subwavelength scales, while avoiding the curse of dimensionality introduced by high-resolution images. The RGB three channels can encode multi-physics information, significantly improving the expressive power of the feature space compared to grayscale images. The 192-dimensional vector is sufficient to preserve the details and features of the original image.

[0080] In this embodiment, the dataset is divided into a training set, a validation set, and a test set in a ratio of 8:1:1. The prediction model performs machine learning on the training set and calculates the average MRE loss on the validation set. After the prediction model is trained to convergence, its performance is tested on the test set.

[0081] In this embodiment, the performance of the prediction model on the training set, validation set, and test set is shown in Figures 5(a), 5(b), 5(c), 5(d), and Table 2.

[0082] Table 2: Performance of Prediction Models

[0083]

[0084] Figures 5(a), 5(b), 5(c), and 5(d) show the quantitative evaluation of the prediction model using scatter plots of the mean relative error (MRE) distribution and the coefficient of determination (R²). As can be seen from the figures, the prediction model exhibits excellent accuracy in dispersive map prediction, with its MRE distribution significantly concentrated below 0.8%, and R²... 2 The value reached 0.989, indicating a high linear correlation between the predicted and actual values; the prediction model had a slightly wider error range in predicting the transmission loss curve, with MRE mainly distributed within 4%, and R... 2 The value is 0.955, maintaining good predictive consistency. Comparative analysis shows that, on both the training and test sets, the dispersion map and transmission loss curve output by the predictive model are highly consistent with the dispersion map and transmission loss curve obtained from finite element simulation (i.e., dataset labels), achieving engineering-acceptable prediction accuracy. Among them, the dispersion map prediction has advantages in error control and goodness of fit, mainly due to the smoother dispersion curve, while the numerous abrupt changes in the transmission loss curve increase the difficulty of model learning.

[0085] After the prediction model is trained, this embodiment further verifies the above-mentioned reverse design method for flexible metamaterials based on the iTransformer model; the verification steps are as follows:

[0086] Step 1: Set the crystal design objectives, which include the target bandgap start point, target bandgap end point, and target mean transmission loss; initialize the geometric parameters of the Saibel curve;

[0087] For ease of description, the target band gap range will be defined as the interval between the target band gap start point and the target band gap end point.

[0088] St2. Generate multiple crystal shapes using crystal design formulas; input images of each crystal shape into the prediction model to obtain the dispersion map and transmission loss corresponding to each crystal shape, extract the bandgap interval from the dispersion map and record it as the predicted bandgap interval, and calculate the mean transmission loss in the predicted bandgap interval and record it as the mean predicted transmission loss.

[0089] St3. Obtain the crystal shape that has a predicted transmission loss mean less than or equal to the target transmission loss mean, and has a predicted bandgap interval lower end value greater than or equal to the target bandgap start point, and a predicted bandgap interval upper end value less than or equal to the target bandgap end point as the candidate crystal shape.

[0090] St4, calculate the fitness of the candidate crystal shapes (Penalty);

[0091] St5, use a genetic algorithm to iterate the geometric parameters of the crystal design formula;

[0092] Step 6: Repeat the above steps until the fitness of the candidate crystal shape is 0. Then stop the geometric parameter iteration and fix the geometric parameters of the crystal design formula.

[0093] St7. Using the fixed crystal design formula, generate multiple crystal shapes; input the images of each crystal shape into the prediction model to obtain the dispersion map and transmission loss corresponding to each crystal shape; select the crystal shape whose predicted transmission loss mean is less than or equal to the target transmission loss mean, and whose lower end value of the predicted bandgap interval is greater than or equal to the starting point of the target bandgap, and whose upper end value of the predicted bandgap interval is less than or equal to the ending point of the target bandgap as the target crystal.

[0094] St8. Obtain the dispersion pattern and transmission loss of the target crystal through finite element simulation, and then compare them with the dispersion pattern and transmission loss of the target crystal predicted by the prediction model.

[0095] In this embodiment, for a certain crystal design target (target bandgap range of 400-800Hz, as shown in the gray bands of Figure 6(a) and Figure 6(b); the target mean transmission loss is -80dB), the geometric parameters of the crystal design formula are fixed by performing the above steps St1-St6, and then two crystal shapes (i.e., unit cell samples) are generated by the fixed crystal design formula as shown in Figure 6(a) and Figure 6(b). In this embodiment, finite element simulation is performed on the two unit cell samples, and the dispersion map and transmission loss of the finite element simulation are compared with the dispersion map and transmission loss predicted by the prediction model.

[0096] As can be seen from Figures 6(a) and 6(b), the relative bandgap widths predicted by the model and calculated by the finite element method (FEM) in the reverse design results are very close, with a maximum difference of no more than 6% and an average difference of only 2.76%. Furthermore, both the predicted and calculated bandgap ranges encompass the target bandgap. The maximum error in the average transmission loss within the target bandgap is 15.16 dB, and the average error is 10.21 dB. In the two cases shown in Figures 6(a) and 6(b), the average transmission losses within the target bandgap of the reverse design results are -81.08 dB and -84.14 dB, respectively, both meeting the target mean transmission loss of -80 dB.

[0097] In the reverse design results, the relative bandgap widths were 68.85% and 66.67%, respectively, which are close to the 74.18% and 67.55% of the finite element design, further proving the reference value of the reverse design results.

[0098] To further verify the vibration reduction performance of the reverse-designed metamaterial, this embodiment also employs sinusoidal excitation to perform time-history analysis and experimental verification on the metamaterial shown in Figure 6(a). In this embodiment, COMSOL analysis software was used to construct a time-history analysis finite element model based on the unit cell shape shown in Figure 6(a). The two-dimensional model was extended by 10 mm along the normal to construct a three-dimensional solid model, which was then arrayed into 3×3, 5×5, and 7×7 metamaterial structures, as shown in Figure 7(b). The material parameters were kept consistent with the two-dimensional model, and a specified acceleration was applied at the excitation point, while the corresponding output vibration was captured at the pickup point. To simulate the dynamic response under excitation using the time-history analysis method, this embodiment applied excitation to the target bandgap frequency band (600Hz) and its neighborhood (200Hz), and analyzed the bandgap attenuation effect through acceleration response analysis.

[0099] To verify the vibration reduction performance of the reverse-engineered metamaterial structure, a 3D model was 3D printed and the experiment was conducted using the apparatus shown in Figure 7(a). An excitation signal was output through a signal generator 1, amplified by a power amplifier 2, and then applied to the 3D printed crystal model (i.e., a 3×3, 5×5, or 7×7 metamaterial structure) through a vibrator 3. Two accelerometers 4 were placed on both sides of the 3D printed crystal model to collect the input and output vibrations. The input and output vibrations were then received and analyzed by a dynamic signal testing and analysis system 5, which was implemented using a computer.

[0100] In the three-dimensional finite element model, the boundaries are free boundaries. In the experiment, the 3D printed crystal model is suspended on the support 6 by a thin rope to achieve an approximate effect.

[0101] Metamaterials with different arrangements exhibit significantly different attenuation characteristics when subjected to excitations inside and outside the bandgap. As shown in Figure 7(c), the 3×3 arrangement of the metamaterial has a certain blocking effect on vibration; when the excitation frequency falls within 600 Hz (inside the bandgap), the peak displacement attenuation rate is only 64.28%. Meanwhile, as shown in Figures 7(e) and 7(g), the 5×5 and 7×7 arrangements of the metamaterial also demonstrate excellent vibration attenuation capabilities, resulting in the absorption of most of the energy by the metamaterial, with peak displacement attenuation rates reaching 78.04% and 96.09%, respectively. In contrast, when the dominant excitation frequency is outside the bandgap, the attenuation rates of the peak displacement at the output end of the 3×3, 5×5, and 7×7 arrangements are only 13.65%, 21.54%, and 54.43%, as shown in Figures 7(d), 7(f), and 7(h). Attenuation rate is a characterization index of transmission loss.

[0102] The attenuation rates calculated from the input and output vibrations in the above experiments show that the metamaterial has a negligible effect on attenuating vibrations outside the bandgap. Therefore, the finitely arranged curved metamaterial exhibits significant attenuation capabilities within the bandgap, a fact verified by the high agreement between the finite element model time-domain analysis results and the experiments. The effective attenuation of the metamaterial demonstrates the feasibility and accuracy of deep learning in predicting dispersion relations and transmission losses when the excitation falls within the bandgap.

[0103] This embodiment presents a bendable-arm metamaterial defined by the Beizer curve, which has been shown to possess a wide and complete bandgap, with an average transmission loss exceeding 80 dB within each bandgap and an attenuation capability of up to 96.09% for excitations within the bandgap. This indicates that the bendable-arm metamaterial has a large potential bandgap range in the low-frequency range, meeting the requirements for good vibration damping and isolation in practical engineering applications over a relatively wide low-frequency range.

[0104] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0105] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0106] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A metamaterial reverse design method that satisfies multiple conditions, characterized in that: First, obtain a prediction model based on the crystal shape image to predict the dispersion map and transmission loss, obtain the crystal design target, and select the crystal design formula; Multiple crystal shapes are generated using crystal design formulas and input into the prediction model; crystal shapes whose dispersion patterns and transmission losses output by the prediction model meet the crystal design objectives are selected as candidate crystal shapes. The geometric parameters of the crystal design formula are iterated until the fitness of the candidate crystal shape is 0. Then the geometric parameters of the crystal design formula are fixed to generate a crystal shape that meets the crystal design target. The formula for calculating the Penalty fitness of crystal shape is as follows: Where GP is the fitness function of the bandgap; CGS( i ) and CGE ( i ) are the start and end points of the i-th band gap in the dispersion diagram, respectively; i is the bandgap number; TGS is the target bandgap start point, TGE is the target bandgap end point; TLP is the fitness function of transmission loss, TTL is the target mean of transmission loss, and TL is the average value of transmission loss within the predicted bandgap interval; The prediction model is obtained as follows: First, the crystal design formula is determined, and the geometric parameters of the crystal design formula are randomly initialized; multiple crystal shapes are generated using the crystal design formula corresponding to each set of geometric parameters, and finite element simulation is performed on each crystal shape to obtain the corresponding dispersion map and transmission loss, thus constructing a dataset {crystal shape; dispersion map, transmission loss}; then, machine learning algorithms are used to train the prediction model on the dataset.

2. The metamaterial reverse design method satisfying multiple conditions as described in claim 1, characterized in that, The crystal design formula corresponding to the crystal design goal is the same as the crystal design formula used to construct the dataset.

3. The metamaterial reverse design method satisfying multiple conditions as described in claim 1, characterized in that, If the fitness of the candidate crystal shape is not equal to 0, then a genetic algorithm is used to update the geometric parameters of the crystal design formula.

4. The metamaterial reverse design method satisfying multiple conditions as described in claim 1, characterized in that, The prediction model consists of a VAE model and an iTransformer model. The VAE model encodes the crystal shape image, and the encoded vector is processed by the iTransformer model to obtain the dispersion map and transmission loss.

5. The metamaterial reverse design method satisfying multiple conditions as described in claim 1, characterized in that, Crystal design objectives include the target bandgap and the target mean of transmission loss.

6. The metamaterial reverse design method satisfying multiple conditions as described in any one of claims 1-5, characterized in that, After determining the crystal design formula, the crystal shape generated by the crystal design formula is used as a candidate target. The candidate targets are simulated through finite element calculation, and the optimal target design scheme is selected.

7. A metamaterial reverse design system that satisfies multiple conditions, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, the processor is connected to the memory, and the processor is used to execute the computer program to implement the metamaterial reverse design method that satisfies multiple conditions as described in any one of claims 1-5.

8. A storage medium, characterized in that, The device contains a computer program that, when executed, is used to implement the multi-condition metamaterial reverse design method as described in any one of claims 1-5.

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