Mechanical metamaterial structure forward-reverse fusion design and performance prediction method

Abstract

The application belongs to the technical field of metamaterial structure design, and aims to solve the problem of metamaterial structure design depending on experience and manual adjustment. A mechanical metamaterial structure forward and reverse fusion design and performance prediction method is provided, N original metamaterial structures are designed, and combinations of N structure parameters and material parameters are extracted; modeling and simulation are performed to obtain N characteristic parameter groups; a double deep learning model including a front neural network and a rear neural network is constructed and trained based on the above data; given combinations of structure parameters and material parameters of a new metamaterial structure and required performance parameters such as low-frequency band gap value, Poisson's ratio, etc.; the combinations of new structure parameters and material parameters are input into the double deep learning model, and whether the required performance is reached is judged based on the characteristic parameters output by the front neural network; if reached, the rear neural network outputs the reconstructed optimal original material structure. The application can reduce the design complexity of metamaterials.

Description

Technical Field

[0001] This invention belongs to the field of metamaterial structure design technology, specifically relating to a method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures. Background Technology

[0002] Mechanical metamaterials are a class of materials that exhibit unconventional mechanical properties and structural characteristics through carefully designed geometries. They have attracted widespread attention in the field of mechanical research. By meticulously designing their microstructure and geometry, metamaterials can exhibit unique properties such as negative refractive index, negative Poisson's ratio, negative mass density, and negative elastic modulus. The design and fabrication of metamaterials have already demonstrated enormous potential in fields such as electromagnetic wave manipulation, acoustic wave control, and photonics.

[0003] With the development of technology, vibration reduction and noise reduction technologies have become increasingly important in engineering applications. Traditional methods, such as sound-absorbing materials and sound insulation structures, are inefficient or unsuitable in certain scenarios. Therefore, metamaterial structure design, as an emerging vibration reduction and noise reduction technology, has received widespread attention in recent years.

[0004] The existing technical solutions for metamaterial structure design have the following drawbacks:

[0005] 1. Reliance on experience and manual adjustments: Traditional metamaterial design often relies on the designer's experience and manual adjustments, which limits the accuracy and efficiency of the design. Designers need to spend a lot of time and effort trying different combinations of structures and parameters, and it is difficult to guarantee the optimality of the design.

[0006] 2. High Computational Costs: The design of metamaterials typically involves extensive and complex calculations and simulations. Changing even one parameter necessitates remodeling, especially for multi-scale, multi-physics coupled problems, where the computational costs are enormous. This results in lengthy design processes and high computational resource requirements. The design of metamaterials involves numerous dimensional and material parameters that influence the final performance of the structure. In recent years, forward design has been commonly employed in metamaterial structure design. This approach focuses first on structural design and then studies its performance characteristics through numerical simulations. When designing metamaterial structures, a few key parameters are adjusted to investigate their impact on performance. However, when facing specific engineering problems, multiple parameters need to be adjusted to optimize metamaterial performance. A comprehensive understanding of the impact of each parameter on performance requires extensive calculations and the determination of feasible methods.

[0007] 3. Limited to specific applications: Traditional metamaterial designs are often optimized for specific application scenarios, resulting in insufficient versatility. Once the application scenario or requirements change, the metamaterial structure needs to be redesigned. Summary of the Invention

[0008] In order to solve at least one of the above-mentioned technical problems in the prior art, the present invention provides a method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures.

[0009] This invention employs the following technical solution: a method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures, comprising the following steps:

[0010] S1: Design N original metamaterial structures, extract N combinations of structural and material parameters; perform modeling and simulation to obtain N characteristic parameter sets;

[0011] S2: Construct a dual deep learning model that includes a pre-neural network and a post-neural network;

[0012] S3: Use the combination of N structural parameters and material parameters as input layer data I, and the N feature parameter groups as output layer data I, to train and test the pre-neural network;

[0013] S4: Take the M feature parameter sets that meet the design requirements from the N feature parameter sets as input layer data II, and take the combination of M structural parameters and material parameters that match the M feature parameter sets in S1 as output layer data II, and perform training and testing of the post-neural network.

[0014] S5: Given a new metamaterial structure with a combination of structural and material parameters, and the required design parameters;

[0015] S6: Input a new combination of structural and material parameters into the dual deep learning model, and determine whether the required design indicators are met based on the feature parameter set output by the previous neural network.

[0016] If this is achieved, the subsequent neural network outputs the reconstructed optimal original material structure.

[0017] If the target is not met, the structural and / or material parameters are manually adjusted until the required design specifications are achieved. Then, the neural network outputs the reconstructed optimal original material structure.

[0018] Preferably, the characteristic parameter set is a characteristic frequency set related to the band gap width.

[0019] Preferably, the structural parameters of the metamaterial structure include the dimensional parameters of the metamaterial matrix structure and the dimensional parameters of the local resonant units, and the material parameters include the material density, Poisson's ratio, and Young's modulus;

[0020] A combination of structural and material parameters corresponds to a set of characteristic frequencies.

[0021] Preferably, the structural band diagram of the metamaterial structure is obtained through modeling and simulation using COMSOL software;

[0022] Each characteristic frequency group includes K characteristic frequencies, which are obtained from the structural band diagram; each characteristic frequency group includes a maximum value and a minimum value; each characteristic frequency group is used to characterize the performance of a metamaterial structure.

[0023] Preferably, a low-frequency characteristic index Z(n) is defined to evaluate the low-frequency characteristics of metamaterials:

[0024] Define the complete bandgap band range function F(n) and the position function L(n):

[0025] F(n) = min(fr) k (n+1))-max(fr k (n))(1.1)

[0026]

[0027] Where fr k Let n be the solution for the characteristic frequency of the wave vector k along the structural Brillouin zone, and n be the number of eigenvalue solutions calculated.

[0028]

[0029] The magnitude of Z(n) is specifically determined by the maximum and minimum values ​​in each set of characteristic frequency solutions.

[0030] Preferably, in step S4, satisfying the low-frequency bandgap index means that Z(n) > 0; the K characteristic frequencies of the characteristic frequency group of the input layer data II are extracted by Z(n) that satisfy the low-frequency bandgap index.

[0031] Preferably, the feature frequency search baseline value is 0Hz, each feature frequency group includes 20 feature frequencies, and the number of maximum and minimum values ​​of the corresponding feature frequencies is 40.

[0032] Preferably, in step S1, the combination of structural parameters and material parameters, the number of characteristic frequency groups N is greater than 1000, and the number of characteristic frequency groups M after screening in S4 is less than 1000.

[0033] Preferably, the characteristic parameter set includes, but is not limited to, a characteristic frequency set related to bandgap width, a characteristic sound absorption coefficient set related to transmission loss, a characteristic resolution set related to negative refractive index, and a characteristic energy absorption coefficient set related to negative Poisson's ratio.

[0034] Preferably, the front neural network has a built-in forward optimization module, and the back neural network has a built-in reverse prediction module. First, the metamaterial is designed for performance optimization based on the forward optimization module of the front neural network to explore the structural configuration with the best performance. Then, the structural parameters required for the target performance are determined based on the reverse prediction module of the back neural network.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] This invention reduces the design complexity of metamaterials. A pre-trained neural network can perform rapid optimization calculations on metamaterial structures, eliminating the need for complex and tedious modeling, simulation, and performance processing calculations. Inspirational metamaterial structural parameters (structural and material parameters) can be directly input into the neural network to obtain the structure's performance. If the structural performance is unsatisfactory, the input parameters can be directly modified, allowing for manual fine-tuning of the model parameters and rapid acquisition of the performance results. Through forward performance optimization and inverse structural optimization, the reconstructed optimal structure is obtained. This technology is expected to bring significant applications and drive industry development in the fields of precision instruments and rotating machinery. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a method framework diagram of the present invention;

[0039] Figure 2 This is a flowchart of the method of the present invention;

[0040] Figure 3 This is a schematic diagram of the front neural network of the dual deep learning model of the present invention;

[0041] Figure 4 This is a schematic diagram of the post-neural network of the dual deep learning model of the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described 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 implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should fall within the scope of the technical content disclosed in the present invention. It should be noted that in this specification, relational terms such as "first" and "second" are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0044] In this application, the characteristic parameter set includes, but is not limited to, the characteristic frequency set related to bandgap width, the characteristic sound absorption coefficient set related to transmission loss, the characteristic resolution set related to negative refractive index, and the characteristic energy absorption coefficient set related to negative Poisson's ratio.

[0045] like Figures 1 to 4 As shown, this embodiment takes acoustic materials as an example, and describes a method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures, including the following steps:

[0046] S1: Design N original metamaterial structures, extract N combinations of structural and material parameters; perform modeling and simulation to obtain N characteristic frequency groups;

[0047] S2: Construct a dual deep learning model that includes a pre-neural network and a post-neural network;

[0048] S3: Use the combination of N structural parameters and material parameters as input layer data I, and N feature frequency groups as output layer data I to train and test the pre-neural network;

[0049] S4: Take the M characteristic frequency groups that satisfy the low-frequency bandgap index from the N characteristic frequency groups as the input layer data II, and take the combination of the M structural parameters and material parameters that match the M characteristic frequency groups in S1 as the output layer data II, and perform training and testing of the post-neural network.

[0050] S5: Given a new metamaterial structure with a combination of structural and material parameters, and the desired low-frequency bandgap value;

[0051] S6: Input a new combination of structural and material parameters into the dual deep learning model, and determine whether the required low-frequency bandgap value is achieved based on the feature frequency group output by the previous neural network.

[0052] If this is achieved, the subsequent neural network outputs the reconstructed optimal original material structure.

[0053] If the desired low-frequency bandgap value is not achieved, the structural and / or material parameters are manually adjusted until the required low-frequency bandgap value is reached. Then, the neural network outputs the reconstructed optimal original material structure.

[0054] In this embodiment, the structural parameters of the metamaterial structure include the dimensional parameters of the metamaterial matrix structure and the dimensional parameters of the local resonant units. The material parameters include material density, Poisson's ratio, and Young's modulus. In this embodiment, a combination of structural and material parameters corresponds to a characteristic frequency group. Each characteristic frequency group includes K characteristic frequencies, which are obtained from the structural band diagram. Each characteristic frequency group includes a maximum value and a minimum value. Each characteristic frequency group is used to characterize the performance of a metamaterial structure. Each characteristic frequency group includes 20 characteristic frequencies, corresponding to 40 maximum and minimum values.

[0055] The specific steps are as follows: First, an initial metamaterial structure with initial inspiration is designed. Software is used to model the structure with specific parameters, and numerical analysis is performed to extract structural and material parameters and other characteristic data to determine its initial performance. Then, the performance is optimized and predicted using the pre-neural network in the dual deep learning model to obtain the improved performance; this process is the forward design process. Predicting the structure from known performance is the reverse design process. This process first determines the performance of the designed metamaterial, then uses the post-neural network in the dual deep learning model to establish a structural database, reconstruct the model, establish the optimal structure, and complete the design scheme.

[0056] The dual deep learning model initially uses COMSOL software for parametric scanning to generate the data required for neural network training. Then, the post-neural network within the dual deep learning model is used for structural optimization design. The deep learning model is continuously trained to extract metamaterial structural features. Combined with simulation analysis and experimental verification, the optimized metamaterial structure is finally determined. By combining forward and inverse design with the dual deep learning model, the metamaterial structural parameters, material parameters, and performance indicators are continuously integrated and optimized, thus providing a structural design and performance prediction scheme for metamaterial structures from initial to optimized structures.

[0057] Pre-neural networks are used for rapid optimization of metamaterial structure performance. The rapid optimization process involves modeling an initially inspired metamaterial structure, performing parametric scanning simulations of material and structural parameters using COMSOL software, and generating a database to train the neural network. The trained pre-neural network can then perform rapid optimization calculations on the metamaterial structure. Users can directly input the inspired metamaterial structure parameters (structural and material parameters) into the pre-neural network without performing complex and tedious modeling, simulation, and performance processing calculations, directly obtaining the structure's performance. If the structural performance is unsatisfactory, the input parameters can be directly changed, and the model parameters can be manually fine-tuned to quickly obtain the performance results of the model adjustments.

[0058] This technology has two objectives: first, to rapidly determine the full bandgap width (CBW) of the designed two-unit metamaterial monolithic structure. This means that within this width, no structural wave of any kind can propagate. Second, it enables reverse design: given the desired full bandgap width, designing the required metamaterial structure for a specific engineering problem.

[0059] First, define the full bandgap band range function F(n) and the position function L(n):

[0060] F(n) = min(fr) k (n+1))-max(fr k (n))(1.1)

[0061]

[0062] Where fr k Let be the solution for the characteristic frequencies calculated along the structural Brillouin zone for wave vector k; n is the number of eigenvalue solutions calculated.

[0063]

[0064] In the calculation of the low-frequency bandgap index Z(n), it is determined by calculating the eigenvalues ​​of the wave vector k along the Brillouin zone. The steps to obtain the structural bandgap diagram include: establishing the Brillouin zone of the metamaterial structure; setting periodic boundary conditions using COMSOL software; introducing the Bloch wave vector k and taking values ​​along the Brillouin zone boundary; calculating the reciprocal lattice; selecting the Wigner-Seitz unit cell; and transforming the problem into solving the characteristic frequency problem of the structural unit; setting the characteristic frequency search benchmark value and the required number of characteristic frequencies; and drawing the structural bandgap diagram, which is used to view the bandgap range of the structural unit.

[0065] After multiple calculations, the frequency reached over 1 kHz when more than 15 sets of characteristic frequencies were calculated. To simplify the computation of different parameters during the initial training of the neural network data database, we set the number of characteristic frequency solutions to 20 to ensure that most results exceeded 500 Hz. If Z(n) is still found to be less than 0 after calculating 20 sets of solutions, then we temporarily assume that the metamaterial structure does not have low-frequency full bandgap characteristics within the considered parameter range.

[0066] The analysis index Z(n) shows that a bandgap range exists only when F(n) is greater than 0, and there is no bandgap range when F(n) is less than 0. Furthermore, the larger the bandgap range, the smaller the bandgap position. Therefore, Z(n) less than 0 is meaningless. A larger Z(n) indicates better low-frequency bandgap performance of the structure. The specific value of Z(n) is determined by the maximum and minimum values ​​in each set of solutions. During neural network training, selecting the 40 maximum and minimum values ​​from each set of 20 solutions as the output values ​​of the first neural network simplifies performance prediction. In this embodiment, the K sets of feature frequencies of the input layer data II are extracted by satisfying the low-frequency bandgap index Z(n).

[0067] In this application, the algorithm framework consists of four units: a data preprocessing unit, a pre-neural network forward optimization unit, a data postprocessing unit, and a post-neural network structure inverse prediction unit. This method can quickly calculate and analyze the performance of the designed two-unit metamaterial structure, and can also predict the corresponding metamaterial structure based on the required bandgap range and bandgap location.

[0068] The database structure consists of a set of data comprising a one-to-one input layer set (metamaterial structural parameters and material parameters) and a set of output layer data (20 characteristic frequency solutions representing the structure's band structure). During neural network training, we selected over 200,000 data points from COMSOL simulations, forming over 1000 sets of data for model training, with 10% used as the test set. Data was filtered based on the low-frequency bandgap index Z(n) being greater than 0, resulting in fewer than 1000 sets of data. However, each set still includes a one-to-one input layer set (metamaterial structural parameters and material parameters) and a set of output layer data (20 characteristic frequency solutions representing the structure's band structure).

[0069] Data preprocessing unit:

[0070] The data preprocessing unit primarily generates input layer data l and output layer data l. Through software modeling and analysis of the metamaterial model, it was found that 11 structural dimension parameters and 6 material property parameters are necessary. Simultaneously parametrically scanning all 17 input layer neuron variables would require an enormous amount of computation. Therefore, by controlling variables, only one set of input layer structural dimension parameters is parametrically scanned at a time, and the difference is used to create an input layer database.

[0071] Considering the subsequent optimization and adjustment of arbitrary material properties by neural networks, theoretically, specific densities, Young's modulus, and Poisson's ratios can be achieved by adjusting the proportions of various components and the structural design of composite materials. Composite materials are typically composed of two or more materials with different properties, and their properties can be controlled through appropriate combinations.

[0072] In COMSOL software, 0Hz is used as the baseline value for characteristic frequency search, and 20 sets of characteristic frequencies are calculated. Since the structure band diagram needs to be calculated, the 20 sets of characteristic frequencies are processed, and the maximum and minimum values ​​of each set of data are taken as the output layer database.

[0073] To improve the training speed and generalization ability of the neural network, the input layer data is controlled between 0 and 100. First, the range of each set of variable parameters is determined, and then each set of parameters is linearly processed, as shown in Formula 1.4 below:

[0074] x′=k n x0 (1.4)

[0075] x0 represents the original data, k n The linear coefficients of the current parameters, the specific parameter range, and k. n The values ​​are shown in Table 1 below:

[0076] Table 1 Initial structural parameters used in the calculation

[0077]

[0078] After linearizing the 11 structural dimension parameters and 6 material property parameters in the table to reduce the dimensionality difference, and normalizing the 40 (20 groups) feature frequencies of the output layer neurons (each group has a maximum and a minimum value) using the deviation standardization method, the data is normalized to the range [0, 1], as shown in Formula 1.5 below:

[0079]

[0080] Where x′ is the data after linear processing, min is the minimum value in the input layer, max is the maximum value, and x is the normalized data.

[0081] Forward optimization unit of the previous neural network:

[0082] A Back Propagation Neural Network (BPNN) is used to construct the pre-neighborhood. A typical BPNN consists of three parts: an input layer, hidden layers, and an output layer. Since there are 17 input parameters, the input layer has 17 nodes. These 40 feature frequencies are used to perform subsequent bandgap calculations on the structure, resulting in an output layer with 40 nodes.

[0083] The number of hidden nodes in a BP neural network has a certain impact on the overall network performance. The following empirical formula 1.6 is used for selection:

[0084]

[0085] Where b1 is the number of hidden layers, m1 is the number of input layers, n1 is the number of output layers, a1 ranges from 1 to 10 (in this model, a1 is 10, m1 is 17, and n1 is 40), and b1 is rounded down to calculate the number of hidden layers as 18. Based on these parameter selections, a 17-18-40 backpropagation (BP) neural network is constructed for the metamaterial structure design. The neural network is trained using input layer data I and output layer data I.

[0086] Data post-processing unit:

[0087] The output layer neural network contains the size parameters and material property parameters of the structure. During the initial training of the neural network, the maximum and minimum frequencies of the output layer data I that satisfy the low-frequency bandgap index are searched. The output layer data I of the previous neural network are matched to establish a temporary database, which includes the structural parameters and size parameters of the metamaterial structure.

[0088] The maximum and minimum values ​​of the characteristic frequencies of each structure are calculated using a neural network. The range function F(n) and position function L(n) are calculated according to formulas 1.1 and 1.2. The low-frequency bandgap index Z(n) is calculated using formula 1.3. The index Z(n) is then associated with the corresponding structure to construct a new database: Output Layer Data II, used for generating the neural network output layer data. In step S1, the combination of structural and material parameters and the number of characteristic frequency groups N are greater than 1000, while the number of characteristic frequency groups M after filtering in S4 is less than 1000.

[0089] After the predicted structural and material property parameters are normalized, an inverse normalization operation is required to calculate the original dimensional data x'. According to Formula 1.7, in Table 1, the predicted data x' is divided by the linear coefficient k of the current parameter. n This is to achieve the denormalization process.

[0090]

[0091] Post-neural network structure inverse prediction unit:

[0092] The dataset used in this unit comes from the previous neural network forward optimization unit. First, the output layer data of the previous neural network is filtered, retaining data with low-frequency bandgap, i.e., index Z(n) > 0. As shown in Equation 1.3, Z(n) is determined by F(n) and L(n). Therefore, when predicting a metamaterial structure with a specific bandgap, F(n) and L(n) are used as input parameters for the designer. F(n) and L(n) are determined by 20 sets of feature frequencies. The algorithm flowchart searches the output layer data I of the previous neural network to create 20 sets of feature frequencies. In the later structure prediction stage, the 20 sets of feature frequency parameters that meet the conditions are calculated.

[0093] The method was validated using a designed metamaterial structure, with 17 neurons in the output layer. Using Equation 1.6, with a1 set to 10, the number of neurons in the hidden layer of the neural network was calculated to be 18. A 40-18-17 neural network was then constructed.

[0094] To describe the propagation characteristics of the structure, a frequency transmission loss function Tr is defined as shown in Equation 1.8, where Pout is the displacement of the output measurement point and Pin is the displacement of the excitation measurement point.

[0095]

[0096] Advantages of this invention:

[0097] A forward and inverse design approach is proposed for the optimization of mechanical metamaterial structures. By combining the forward optimization module of a pre-neural network with the inverse prediction module of a post-neural network, the pre-neural network is first used to optimize the metamaterial's performance, rapidly exploring structural configurations with optimal performance. Subsequently, the inverse prediction module of the post-neural network accurately determines the structural parameters required for the target performance. This forward and inverse fusion method not only accelerates the design and optimization process of metamaterials but also improves the accuracy of predicting structural properties, achieving efficient transformation from design to application.

[0098] Disadvantages of the alternative:

[0099] 1. Traditional Optimization Methods: Traditional optimization algorithms, such as genetic algorithms and particle swarm optimization, are used to optimize metamaterial structures. However, these methods may require more computational resources and time, and may not accurately predict the performance of the structure.

[0100] 2. Other Machine Learning Models: Using machine learning models other than neural networks, such as support vector machines and random forests, to predict the performance of metamaterial structures. However, these models may require more data and feature engineering, and their accuracy may not be as good as this neural network.

[0101] 3. Manual Design Method: This method involves attempting to design metamaterial structures suitable for specific applications through experience and manual design. This method may be limited by the designer's experience and knowledge and is not very efficient.

[0102] Although these alternatives exist, the neural network algorithms and neural network structures of this technology are a better choice because they can optimize the structure more quickly and predict performance more accurately.

[0103] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures, characterized in that, Includes the following steps: S1: Design N original metamaterial structures and extract N combinations of structural and material parameters. The structural parameters of the metamaterial structure include the size parameters of the metamaterial matrix structure and the size parameters of the local resonant units. The material parameters include material density, Poisson's ratio, and Young's modulus. Perform modeling and simulation to obtain N characteristic parameter sets. The characteristic parameter sets include characteristic frequency sets related to bandgap width, characteristic sound absorption coefficient sets related to transmission loss, characteristic resolution sets related to negative refractive index, and characteristic energy absorption coefficient sets related to negative Poisson's ratio. Each characteristic frequency set includes K characteristic frequencies, and each characteristic frequency set includes a maximum value and a minimum value of a characteristic frequency. Define the low-frequency characteristic index of the structure Evaluating the low-frequency properties of metamaterials: Define the complete bandgap band range function and position function : (1.2) in wave vector The solution of characteristic frequencies calculated along the structural Brillouin zone, The number of eigenvalue solutions calculated; (1.3) The specific size is determined by the maximum and minimum values ​​in each set of characteristic frequency solutions; S2: Construct a dual deep learning model that includes a pre-neural network and a post-neural network; S3: Use the combination of N structural parameters and material parameters as input layer data I, and N feature frequency groups as output layer data I to train and test the pre-neural network; S4: M characteristic frequency groups from N characteristic frequency groups that meet the design requirements are used as input layer data II. The combination of M structural and material parameters from S1 that match the M characteristic frequency groups is used as output layer data II for training and testing the post-neural network. The K characteristic frequencies of the input layer data II are selected based on meeting the low-frequency bandgap index. The extraction process, which satisfies the low-frequency bandgap index, refers to: ; S5: Given a new metamaterial structure with a combination of structural and material parameters, and the desired low-frequency bandgap value; S6: Input a new combination of structural and material parameters into the dual deep learning model, and determine whether the required low-frequency bandgap value is achieved based on the feature frequency group output by the previous neural network. If this is achieved, the subsequent neural network outputs the reconstructed optimal original material structure. If the desired low-frequency bandgap value is not achieved, the structural and / or material parameters are manually adjusted until the required low-frequency bandgap value is reached. Then, the neural network outputs the reconstructed optimal original material structure.

2. The method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures according to claim 1, characterized in that: A combination of structural and material parameters corresponds to a set of characteristic frequencies.

3. The method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures according to claim 1, characterized in that: Through modeling and simulation, the structural band diagram of the metamaterial structure is obtained to characterize its functional parameters; each characteristic frequency group is used to characterize the performance of a metamaterial structure, and K groups of characteristic frequencies are obtained from the structural band diagram.

4. The method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures according to claim 1, characterized in that: The baseline value for the feature frequency search is 0Hz. Each feature frequency group includes 20 feature frequencies, and the number of maximum and minimum values ​​of the corresponding feature frequencies is 40.

5. The method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures according to claim 1, characterized in that: In step S1, the combination of structural parameters and material parameters and the number of characteristic frequency groups N are greater than 1000, while the number of characteristic frequency groups M after screening in S4 is less than 1000.

6. The method for forward and reverse fusion design and performance prediction of mechanical metamaterial structures according to claim 1, characterized in that: The front neural network has a built-in forward optimization module, and the back neural network has a built-in backward prediction module. First, the metamaterial is designed to optimize its performance based on the forward optimization module of the front neural network, and the structural configuration with the best performance is explored. Then, the structural parameters required for the target performance are determined based on the backward prediction module of the back neural network.

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