Configuration generation method of tunable phononic crystals based on deep learning

Abstract

The present invention discloses a configuration generation method of an adjustable phononic crystal based on deep learning, a computing device, a computer program product and a storage medium. The configuration generation method of an adjustable phononic crystal based on deep learning is executed in a computing device. The method includes: inputting a first eigenfrequency vector indicating the dispersion relation of the phononic crystal configuration to be generated into a configuration generation model for processing to obtain at least one candidate configuration image; performing image preprocessing on each candidate configuration image to obtain multiple similar images; inputting each similar image into a dispersion relation prediction model for processing to obtain a second eigenfrequency vector representing the dispersion relation of each similar image; calculating the average absolute percentage error value of the first eigenfrequency vector and each second eigenfrequency vector respectively, and selecting the similar image indicated by the second eigenfrequency vector corresponding to the smallest average absolute percentage error value as the configuration image of the phononic crystal to be generated.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a configuration generation method for an adjustable phononic crystal based on deep learning, a computing device, a computer program product, and a storage medium. Background Art

[0002] With the acceleration of urbanization, noise pollution has become a significant source of environmental pollution in modern cities. Noise pollution refers to the presence of unwanted sounds or acoustic signals in the environment. It originates from a variety of sources, including traffic, industry, and social activities. Not only does noise have a wide range of sources, it can also negatively impact human health, including hearing loss, tinnitus, sleep disorders, and mental health issues. Noise pollution is particularly prevalent in residential areas, workplaces, and learning environments, reducing productivity and quality of life. It can also trigger social problems and cause economic losses. At the community level, noise can lead to neighborhood disputes and social unrest. For businesses and tourism, noise can negatively impact the business environment and tourist experience, leading to economic losses. Therefore, noise reduction technologies are needed to control noise transmission. Phononic crystals, due to their ability to attenuate sound transmission within a specific frequency range, have attracted extensive research for their sound absorption properties.

[0003] Phononic crystals are a new type of artificial composite structure composed of different material phases distributed periodically in space. If elastic waves cannot propagate within a certain characteristic frequency range within a phononic crystal, this property is called a band gap. This band gap property can be exploited to manipulate the propagation of acoustic or elastic waves, such as for acoustic damping, noise control, waveguide filters, acoustic focusing, and acoustic energy harvesting.

[0004] In recent years, phononic crystals with tunable band gaps have received widespread attention in multiple disciplines. Early research mainly focused on the tunable materials or geometric parameters of phononic crystals. However, most of the proposed structures are difficult to manufacture, which limits the application of phononic crystals.

[0005] Topology optimization, a method for calculating material distribution, has shown great potential in structural design, and numerous studies have applied it to designing the configurations of phononic crystals. However, the topological design of phononic crystals with tunable band gaps is difficult. Furthermore, many existing methods struggle to design phononic crystals with tunable band gaps given a given dispersion relation. Summary of the Invention

[0006] In view of the above problems, the present invention is proposed to provide a configuration generation method, computing device, computer program product and storage medium of an adjustable phononic crystal based on deep learning that overcomes the above problems or at least partially solves the above problems.

[0007] According to one aspect of the present invention, a configuration generation method for an adjustable phononic crystal based on deep learning is provided, which is executed in a computing device, and the method comprises: inputting a first eigenfrequency vector indicating the dispersion relation of the configuration of the phononic crystal to be generated into a configuration generation model for processing to obtain at least one candidate configuration image; performing image preprocessing on each candidate configuration image to obtain multiple similar images; inputting each similar image into a dispersion relation prediction model for processing to obtain a second eigenfrequency vector representing the dispersion relation of each similar image; calculating the average absolute percentage error value of the first eigenfrequency vector and each second eigenfrequency vector respectively, and selecting the similar image indicated by the second eigenfrequency vector corresponding to the smallest average absolute percentage error value as the configuration image of the phononic crystal to be generated.

[0008] Optionally, in the configuration generation method according to the present invention, for each candidate configuration image, image preprocessing is performed to obtain multiple similar images, including: performing image symmetry transformation processing on the candidate configuration image to obtain multiple initial similar images, the image symmetry transformation includes horizontal flipping, vertical flipping and diagonal transformation; using a median filter to filter the discrete pixels of each initial similar image; and binarizing the initial similar image with the discrete pixels filtered to obtain a similar image.

[0009] Optionally, the configuration generation method according to the present invention further includes: generating a second training sample set based on the constructed configuration image database, the second training sample set including configuration images of multiple phononic crystals and their corresponding dispersion relations, wherein the dispersion relations are represented by characteristic frequency vectors; based on the second training sample set, generating a dispersion relation prediction model by training using a regression loss function.

[0010] Optionally, in the configuration generation method according to the present invention, generating a second training sample set based on the constructed configuration image database includes:

[0011] The phononic crystal configuration images were generated by MATLAB, and the generated phononic crystal configuration images were used to build a configuration image database. The phononic crystal configuration images have various shapes and are single-material phononic crystal configurations. Equibiaxial stretching was used to perform stretching deformation to generate a band gap. COMSOL with The MATLAB interface is used to input the phononic crystal configuration image into COMSOL to establish a geometric model; the geometric model is simulated and solved according to the defined relevant parameters and boundary conditions to obtain the dispersion relation atlas corresponding to different phononic crystal configuration images. The relevant parameters include the hyperelastic material properties and shape control parameters of the geometric model, and the boundary conditions include specified displacement conditions and periodic conditions. The dispersion relation atlas includes the dispersion relation diagrams corresponding to the phononic crystal under different tensile strain states. The dispersion relation diagram consists of 11 curves, each of which consists of 31 characteristic frequency points. Among them, the band gap characteristics corresponding to different tensile strain states are different. Any dispersion relation diagram indicates the corresponding relationship between its wave vector and frequency under the target tensile strain state; for each dispersion relation diagram, its corresponding fourth eigenfrequency vector is extracted; and the second training sample set is constructed using the fourth eigenfrequency vector and its corresponding dispersion relation diagram.

[0012] Optionally, the configuration generation method according to the present invention also includes the step of training a configuration generation model: constructing a generative adversarial model based on the Wasserstein distance, the generative adversarial model including a generator and a discriminator; generating a first training sample set, wherein any training sample of the first training sample set includes a real image of the sample phononic crystal and a third eigenfrequency vector representing the dispersion relationship of the sample phononic crystal configuration; inputting each third eigenfrequency vector into the generator, and outputting a generated image after processing; inputting the generated image and the corresponding real image into the discriminator together, and outputting a metric value indicating whether the generated image is consistent with the corresponding real image after processing; based on the metric value, iteratively training the generator and the discriminator using a loss function with gradient penalty until the number of training rounds reaches a preset number of rounds and the training is completed, and the generator generated by the training is used as the configuration generation model.

[0013] Optionally, in the configuration generation method according to the present invention, the discriminator includes: a plurality of coupled convolution modules and an output module; the convolution module includes a convolution layer, an instance normalization layer, an activation function layer and a random inactivation layer coupled in sequence; the output module includes a fully connected module.

[0014] Optionally, in the configuration generation method according to the present invention, the dispersion relation prediction model includes: a basic network component, a multi-layer perception component and a prediction output component coupled in sequence; wherein, the basic network component includes multiple residual modules, and each residual module includes an attention mechanism module, and the attention mechanism module includes a channel attention submodule and a spatial attention submodule; the multi-layer perception component includes a coupled fully connected layer, an activation function layer and a random inactivation layer.

[0015] Optionally, in the configuration generation method according to the present invention, the regression loss function is:

[0016]

[0017] Where y represents the true value of each training sample in the second training sample set, f(x) represents the predicted value of the training sample, δ is the hyperparameter of the regression loss function, and δ = 1.

[0018] Optionally, in the configuration generation method according to the present invention, the geometric model is represented by the following formula:

[0019] x1=r(θ)cosθ,x2=r(θ)sinθ

[0020] Among them, r(θ)=r0[1+c1cos(n1θ)+c2cos(n2θ)+c3cos(n3θ)+c4cos(n4θ)]

[0021] (x1, x2) are the position coordinates of the intersection points of the scatterer and the matrix in the unit cell model, θ is the filling rate control parameter of the scatterer, c1~c4, n1~n4 and r0 are shape control parameters, the range of c1~c4 is [-0.35,0.35], the range of n1~n4 is [1,20], and the range of r0 is [0.65,2].

[0022] Optionally, in the configuration generation method according to the present invention, the specified displacement condition is to adopt an equibiaxial stretching method.

[0023] Optionally, in the configuration generation method according to the present invention, the first eigenfrequency vector indicating the dispersion relationship of the phononic crystal configuration to be generated is input into the configuration generation model for processing to obtain at least one candidate configuration image, including: performing dimensionality reduction processing on the first eigenfrequency vector; fusing the first eigenfrequency vector after dimensionality reduction with a random vector by dot product to obtain a fused vector; and inputting the fused vector into the configuration generation model for processing to obtain at least one candidate configuration image.

[0024] Optionally, in the configuration generation method according to the present invention, the first eigenfrequency vector is subjected to dimensionality reduction processing, including: sequentially inputting the first eigenfrequency vector into two groups of fully connected layers coupled to each other for processing, to obtain a first eigenfrequency vector having the same dimension as the random vector.

[0025] Optionally, in the configuration generation method according to the present invention, it also includes: the discriminator is iteratively trained 5 times per iteration, and the generator is iteratively trained 1 time.

[0026] Optionally, in the configuration generation method according to the present invention, the average absolute percentage error value of the first eigenfrequency vector and each second eigenfrequency vector is calculated respectively, including: scaling each eigenfrequency value contained in the first eigenfrequency vector and the second eigenfrequency vector; and calculating the average absolute percentage error value using each eigenfrequency value after scaling.

[0027] Optionally, in the configuration generation method according to the present invention, the characteristic frequency value is scaled using the following formula:

[0028] p t =a+k*(pa)

[0029] Among them, p t represents the characteristic frequency value after scaling, p represents the characteristic frequency value before scaling, a is a constant, and a=0.001, k is the scaling factor, and b=1,c max is the maximum value among the characteristic frequency values, c min is the minimum value of the characteristic frequency value.

[0030] Optionally, in the configuration generation method according to the present invention, the mean absolute percentage error value is calculated by the following formula:

[0031]

[0032] in, and p ij are the j-th predicted eigenfrequency value of the i-th second eigenfrequency vector and the j-th actual eigenfrequency value of the corresponding first eigenfrequency vector, M is the number of second eigenfrequency vectors, and N is the number of eigenfrequency values ​​contained in the second eigenfrequency vector.

[0033] According to another aspect of the present invention, a computing device is provided, comprising: at least one processor; and a memory storing program instructions, wherein the program instructions are configured to be suitable for execution by the at least one processor, and the program instructions include instructions for executing the above method.

[0034] According to another aspect of the present invention, a computer program product is provided, comprising a computer program / instruction, wherein the computer program / instruction implements the above method when executed by a processor.

[0035] According to another aspect of the present invention, a readable storage medium storing program instructions is provided. When the program instructions are read and executed by a computing device, the computing device executes the above method.

[0036] According to the solution of the present invention, a deep learning framework that combines a configuration generation model and a dispersion relation prediction model is proposed. By using this deep learning framework to generate adjustable phononic crystal configurations, near-optimal candidate configurations can be selected, thereby improving the accuracy of generating adjustable phononic crystal configurations. At the same time, it can greatly reduce the time cost of generating adjustable phononic crystals and increase the configuration generation speed of adjustable phononic crystals.

[0037] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are specifically listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0039] Figure 1 A block diagram of the physical components (i.e., hardware) of computing device 100 is shown;

[0040] Figure 2 A flowchart of a method 200 for generating a configuration of a tunable phononic crystal based on deep learning according to an embodiment of the present invention is shown;

[0041] Figure 3 A phononic crystal configuration diagram (3a) according to an embodiment of the present invention and a corresponding dispersion relation diagram (3b) when no stretching deformation occurs are shown;

[0042] Figure 4a A schematic diagram of a network structure of a generative adversarial model generator according to one embodiment of the present invention is shown;

[0043] Figure 4b A schematic diagram of a generative adversarial model discriminator network structure according to one embodiment of the present invention is shown;

[0044] Figure 5 A schematic diagram of an image preprocessing process according to an embodiment of the present invention is shown;

[0045] Figure 6 A schematic diagram showing candidate configuration images and corresponding similar images according to one embodiment of the present invention;

[0046] Figure 7 A schematic diagram of a ResNet18 network residual block according to an embodiment of the present invention is shown;

[0047] Figure 8 A schematic diagram of a multi-layer perception component according to an embodiment of the present invention is shown;

[0048] Figure 9 A schematic diagram of the process of constructing a second training sample set according to an embodiment of the present invention is shown;

[0049] Figure 10 A schematic structural diagram of a phononic crystal unit cell configuration according to an embodiment of the present invention is shown;

[0050] Figure 11 A schematic diagram of the boundary conditions of a phononic crystal unit cell configuration according to one embodiment of the present invention is shown;

[0051] Figure 12a and Figure 12b Schematic diagrams showing a phononic crystal configuration image and its corresponding dispersion relation diagram according to an embodiment of the present invention are respectively shown;

[0052] Figure 13 A schematic diagram showing a comparison between a first target dispersion relation and a corresponding first simulated dispersion relation;

[0053] Figure 14 A schematic diagram showing a comparison between a second target dispersion relation and a corresponding second simulated dispersion relation;

[0054] Figure 15 A schematic flow chart of a method for generating a configuration of an adjustable phononic crystal based on deep learning according to another embodiment of the present invention is shown. DETAILED DESCRIPTION

[0055] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0056] Due to their special properties, phononic crystals have received widespread attention in multiple disciplines, especially their band gap characteristics. The band gap characteristics of phononic crystals provide new solutions to practical engineering problems such as sound insulation and noise reduction. Tunable soft phononic crystals made of soft materials can perform real-time reversible control of the band gap, so band gap regulation technology has been further developed.

[0057] Due to its powerful learning ability, deep learning has also been applied to the field of phononic crystal design, mainly focusing on two aspects: forward prediction of properties and reverse design of configurations. However, there is currently little research on the application of deep learning in the design of tunable phononic crystals.

[0058] To address the problems in the prior art, the present invention proposes a solution. This application proposes a deep learning framework that combines a configuration generation model with a dispersion relation prediction model. This deep learning framework is used to generate tunable phononic crystal configurations. Nearly optimal candidate configurations can be selected, improving the accuracy of generating tunable phononic crystal configurations. This significantly reduces the time cost of generating tunable phononic crystals and increases the speed of tunable phononic crystal configuration generation.

[0059] The deep learning-based configuration generation method for tunable phononic crystals can be executed in a computing device 100. The computing device 100 can be implemented as a server, such as an application server, a web server, etc.; it can also be implemented as a desktop computer, a laptop computer, a processor chip, a tablet computer, etc., but is not limited thereto. Figure 1 1 shows a block diagram of the physical components (i.e., hardware) of a computing device 100. In a basic configuration, the computing device 100 includes at least one processing unit 102 and system memory 104. According to one aspect, the system memory 104 includes, but is not limited to, volatile storage (e.g., random access memory), non-volatile storage (e.g., read-only memory), flash memory, or any combination of such memories, depending on the configuration and type of the computing device.

[0060] According to one aspect, system memory 104 includes operating system 105. System memory 104 also includes program modules 150. According to one aspect, operating system 105, for example, is suitable for controlling the operation of computing device 100. Furthermore, examples may be practiced in conjunction with graphics libraries, other operating systems, or any other application programs, and are not limited to any particular application or system. Figure 1 This basic configuration is illustrated in FIG by those components within dashed line 108. According to one aspect, computing device 100 has additional features or functionality. For example, according to one aspect, computing device 100 includes additional data storage devices (removable and / or non-removable), such as magnetic disks, optical disks, or tapes. Such additional storage Figure 1 1 is illustrated by a removable storage device 109 and a non-removable storage device 110.

[0061] As stated above, according to one aspect, a program module 150 is stored in the system memory 104. According to one aspect, the program module 150 can be implemented as one or more computer program products. The present application does not limit the type of computer program products. For example, the computer program products may include: email, word processing applications, spreadsheet applications, database applications, slide presentation applications, drawing or computer-aided applications, web browsers, etc. In some embodiments according to the present application, computer programs / instructions related to the configuration generation method 200 of a tunable phononic crystal based on deep learning are packaged into a computer program product. When these computer programs / instructions are executed by the processor (i.e., the processing unit 102), the configuration generation method 200 of a tunable phononic crystal based on deep learning according to the present application is implemented.

[0062] According to one aspect, examples may be practiced on a circuit comprising discrete electronic components, a packaged or integrated electronic chip containing logic gates, a circuit utilizing a microprocessor, or a single chip containing electronic components or a microprocessor. Figure 1 Each or many components shown in can be integrated into a system on a chip (SOC) on a single integrated circuit to practice examples. According to one aspect, such an SOC device may include one or more processing units, a graphics unit, a communication unit, a system virtualization unit, and various application functions, all of which are integrated (or "burned") onto a chip substrate as a single integrated circuit. When operated via SOC, the functions described in this article can be operated via dedicated logic integrated with other components of the computing device 100 on a single integrated circuit (chip). Embodiments of the present invention can also be practiced using other technologies capable of performing logical operations (such as AND, OR, and NOT), including but not limited to mechanical, optical, fluid, and quantum technologies. In addition, embodiments of the present invention can be practiced in a general-purpose computer or in any other circuit or system.

[0063] According to one aspect, the computing device 100 may also have one or more input devices 112, such as a keyboard, a mouse, a pen, a voice input device, a touch input device, and the like. It may also include an output device 114, such as a display, a speaker, a printer, and the like. The aforementioned devices are examples, and other devices may also be used. The computing device 100 may include one or more communication connections 116 that allow communication with other computing devices 118, such as printing devices, such as printers. Examples of suitable communication connections 116 include, but are not limited to, RF transmitter, receiver, and / or transceiver circuitry; Universal Serial Bus (USB), parallel, and / or serial ports.

[0064] As used herein, the term computer-readable medium includes computer storage media. Computer storage media can include volatile and non-volatile, removable and non-removable media implemented with any method or technology for storing information (e.g., computer-readable instructions, data structures, or program modules). System memory 104, removable storage device 109, and non-removable storage device 110 are all examples of computer storage media (i.e., memory storage). Computer storage media can include random access memory (RAM), read-only memory (ROM), electrically erasable read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical storage, cassette tape, magnetic tape, disk storage or other magnetic storage device, or any other product that can be used to store information and can be accessed by computer device 100. According to one aspect, any such computer storage medium can be a part of computing device 100. Computer storage media does not include carrier waves or other propagated data signals.

[0065] According to one aspect, communication media is implemented by computer-readable instructions, data structures, program modules, or other data in a modulated data signal (e.g., a carrier wave or other transport mechanism), and includes any information delivery media. According to one aspect, the term "modulated data signal" describes a signal that has one or more characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, radio frequency (RF), infrared, and other wireless media.

[0066] In an embodiment of the present invention, the computing device 100 is configured to execute the configuration generation method 200 of an adjustable phononic crystal based on deep learning according to the present invention. The computing device 100 includes one or more processors and one or more readable storage media storing program instructions. When the program instructions are configured to be executed by the one or more processors, the computing device executes the configuration generation method 200 of an adjustable phononic crystal based on deep learning according to the embodiment of the present invention.

[0067] Figure 2 A flowchart of a method 200 for generating a configuration of a tunable phononic crystal based on deep learning according to an embodiment of the present invention is shown. The method 200 is suitable for execution in a computing device (such as the aforementioned computing device 100).

[0068] like Figure 2As shown, the purpose of method 200 is to realize a method for generating an adjustable phononic crystal configuration by using a deep learning framework that combines a configuration generation model and a dispersion relation prediction model, which can select a candidate configuration close to the optimal one, thereby improving the accuracy of generating the adjustable phononic crystal configuration, and at the same time greatly reducing the time cost of generating the adjustable phononic crystal, thereby improving the configuration generation speed of the adjustable phononic crystal.

[0069] The method 200 begins at step 202 , where a first eigenfrequency vector indicating a dispersion relation of a to-be-generated phononic crystal configuration is input into a configuration generation model for processing to obtain at least one candidate configuration image.

[0070] The dispersion relation of the phononic crystal configuration describes the relationship between the frequency and wave vector of the phonon, that is, the energy-momentum (Ek) relationship of the phonon. The band gap characteristic in the dispersion relation is a key property of the phononic crystal. By utilizing the band gap characteristic, the propagation of sound waves or elastic waves can be artificially controlled, such as acoustic damping, noise control, waveguide filters, acoustic focusing and acoustic energy collection.

[0071] The dispersion relation of phononic crystal configuration is generally characterized by a dispersion relation diagram, such as Figure 3 As shown, Figure 3 A phononic crystal configuration diagram (3a) according to an embodiment of the present invention and its corresponding dispersion relationship diagram (3b) when no tensile deformation occurs are shown. According to some embodiments of the present application, each phononic crystal configuration diagram corresponds to three dispersion relationship diagrams under different tensile deformations, for example, a first dispersion relationship diagram with a tensile displacement of 0 mm, a second dispersion relationship diagram with a tensile displacement of 0.5 mm, and a third dispersion relationship diagram with a tensile displacement of 1 mm. The three dispersion relationship diagrams are each composed of 11 curves, and each curve is composed of 31 characteristic frequency points, that is, each phononic crystal configuration corresponds to 3*11*31=1023 characteristic frequency points, and the characteristic frequency values ​​of these 1023 characteristic frequency points constitute the characteristic frequency vector indicating the dispersion relationship.

[0072] It is worth noting that in order to avoid insufficient fusion of the first eigenfrequency vector and the noise information (random vector) in this embodiment, the configuration generation model is difficult to capture the label features corresponding to the phononic crystal configuration, resulting in a decrease in the diversity of the generated image. To this end, it is necessary to reduce the dimension of the first eigenfrequency vector before inputting it into the network. Specifically, the first eigenfrequency vector is subjected to dimensionality reduction. The first eigenfrequency vector after dimensionality reduction is fused with the random vector by dot product to obtain a fusion vector. The fusion vector is used as the input vector of the configuration generation model.

[0073] In some embodiments, the first eigenfrequency vector is subjected to dimensionality reduction processing, including: sequentially inputting the first eigenfrequency vector into two groups of fully connected layers coupled to each other for processing, to obtain a first eigenfrequency vector having the same dimension as the random vector.

[0074] In some embodiments, the step of training a configuration generation model is further included:

[0075] First, a generative adversarial model (WGAN) based on Wasserstein distance is constructed. The generative adversarial model includes a generator and a discriminator.

[0076] Referring to FIG4 , FIG4 shows a schematic diagram of a network structure of a generative adversarial model generator according to an embodiment of the present invention ( Figure 4a ) and the discriminator network structure diagram ( Figure 4b ), wherein the generator includes: an input module, a fully connected module, a batch normalization processing module, multiple groups of convolution modules, and an output module coupled in sequence. The discriminator includes: multiple coupled convolution modules and an output module, the convolution module includes a convolution layer, an instance normalization layer, an activation function layer, and a random dropout layer coupled in sequence, and the output module includes a fully connected module.

[0077] Then, a first training sample set is generated, where any training sample in the first training sample set includes a real image of the sample phononic crystal and a third eigenfrequency vector representing the dispersion relation of the sample phononic crystal configuration.

[0078] Afterwards, each third eigenfrequency vector is input into the generator, and the generated image is output after processing.

[0079] Subsequently, the generated image and the corresponding real image are input into the discriminator together, and after processing, a metric value indicating whether the generated image is consistent with the corresponding real image is output.

[0080] Finally, based on the metric value, the generator and discriminator are iteratively trained using a loss function with gradient penalty until the number of training rounds reaches a preset number of rounds. The training is completed, and the generator generated by the training is used as the configuration generation model.

[0081] The WGAN model is prone to problems such as gradient explosion or gradient vanishing. To solve these problems, this embodiment introduces a gradient penalty technique to limit the gradient norm of the WGAN. In fact, the gradient penalty (GP) is used to constrain the gradient norm of the WGAN network discriminator. Compared with the weight clipping technique, the gradient penalty can better satisfy the Lipschitz constraint and can also make the weight distribution of the WGAN network discriminator more uniform. Generally speaking, adding a gradient penalty term to the discriminator loss function can make the training process of the network model more stable and can better solve problems such as mode collapse. The WGAN with the addition of the gradient penalty term is called WGAN-GP, and its objective function is shown in the following formula.

[0082]

[0083] Among them, the hyperparameter γ is the gradient penalty coefficient, Satisfying Equation 4.11, the range of ε is [0,1].

[0084]

[0085] Preferably, the preset number of rounds can be set to 500. Furthermore, it is worth noting that the discriminator, which is used to distinguish true and false configurations, requires a longer training time. The generator, on the other hand, only needs to generate images and requires less training time. Therefore, to ensure the effectiveness of the training, this embodiment trains the generator once after training the discriminator five times. That is, for every five training iterations of the discriminator, the generator is trained once.

[0086] After the candidate configuration images are obtained, the process proceeds to step 204 , where each candidate configuration image is subjected to image preprocessing to obtain a plurality of similar images.

[0087] In some embodiments, as Figure 5 As shown, the candidate configuration image is preprocessed, including:

[0088] First, the candidate configuration images are subjected to image symmetry transformation to obtain multiple initial similar images. The image symmetry transformation includes horizontal flipping, vertical flipping and diagonal transformation.

[0089] Then, the discrete pixels of each initial similar image are filtered using a median filter.

[0090] Finally, the initial similarity image after filtering out discrete pixels is binarized to obtain a similarity image. For example, Figure 6 As shown, Figure 6 Schematic diagram showing two candidate configuration images and corresponding similar images after image preprocessing. It is worth noting that Figure 6Only five similar images of each candidate configuration image are shown, and not all corresponding similar images are shown. This application does not limit the specific number of similar images.

[0091] Then, in step 206, each similar image is input into a dispersion relation prediction model for processing to obtain a second characteristic frequency vector representing the dispersion relation of each similar image.

[0092] The dispersion relation prediction model includes: a base network component, a multi-layer perception component, and a prediction output component coupled in sequence. In this embodiment, ResNet18 is selected as the base network component, which can further improve the accuracy of dispersion relation prediction.

[0093] In this embodiment, if Figure 7 As shown in the figure, in order to further reduce the error, the CBAM attention mechanism module is added to all residual blocks of the ResNet18 network, that is, the basic network component includes multiple residual modules, and each residual module contains an attention mechanism module, and the attention mechanism module includes a channel attention submodule and a spatial attention submodule.

[0094] In a specific example, ResNet18 with the CBAM attention mechanism module added is compared with the original ResNet18. The experimental results are shown in Table 1. As can be seen from the table, after adding the CBAM attention mechanism, the error of ResNet18 has decreased from 2.26% to 1.29%.

[0095] Table 1 Comparison of models with and without CBAM

[0096]

[0097]

[0098] like Figure 8 As shown, the multi-layer perception component (MLP component) includes a coupled fully connected layer, an activation function layer, and a random dropout layer.

[0099] Fully connected layers are one of the foundational layers in deep learning models. In a fully connected layer, the outputs of all input neurons are connected to all output neurons, forming a fully connected network structure. These layers are typically added at the end of a neural network to transform the feature maps extracted by previous layers into the final output. Fully connected layers can be used for tasks such as classification and regression, effectively representing and predicting input data by learning complex relationships between them. However, it's important to note that fully connected layers have a large number of parameters and are prone to overfitting. To prevent overfitting, regularization methods such as dropout and L1 / L2 regularization can be used.

[0100] ReLU (Rectified Linear Unit) is a commonly used activation function, widely used in deep learning. Its mathematical expression is f(x) = max(0, x), which means that when the input is greater than 0, the output is x, otherwise the output is 0. The ReLU activation function has simple calculation and derivative calculation methods, and can alleviate the vanishing gradient problem and accelerate network convergence. Compared with traditional activation functions (such as Sigmoid and Tanh), ReLU generally provides better performance and faster training speed when training deep neural networks.

[0101] Dropout is a widely used regularization technique designed to reduce the risk of overfitting in deep neural networks. During training, Dropout randomly sets the output of some neurons to zero with a specified probability, temporarily shutting down these neurons. This reduces the dependencies between neurons and prevents the model from over-relying on specific neurons, making the network more robust and improving generalization capabilities. During testing, Dropout has no effect. Instead, the output of neurons that were shut down during training is scaled to maintain the desired output. Dropout layers are typically added between fully connected layers, but can also be used within convolutional layers. Appropriate Dropout probabilities can help improve model performance and generalization capabilities and are commonly used in deep neural network training.

[0102] In some embodiments, the MLP component is set at the end of ResNet18, and the number is set to 1.

[0103] In some embodiments, the method 200 further includes the step of training and generating a dispersion relation prediction model:

[0104] Based on the constructed configuration image database, a second training sample set is generated, wherein the second training sample set includes a plurality of phononic crystal configuration images and their corresponding dispersion relations, wherein the dispersion relations are represented by characteristic frequency vectors. And

[0105] Based on the second training sample set, a dispersion relation prediction model is generated by training using a regression loss function.

[0106] Among them, such as Figure 9 As shown, based on the constructed configuration image database, generating the second training sample set specifically includes:

[0107] First, MATLAB is used to generate a phononic crystal configuration image, and the generated phononic crystal configuration image is used to construct the configuration image database, wherein the phononic crystal configuration image has a variety of shapes and is a single-material phononic crystal configuration, and is stretched and deformed using an equibiaxial stretching method to generate a band gap.

[0108] Then, through the COMSOL with MATLAB interface, the phononic crystal configuration image is input into COMSOL to establish a geometric model.

[0109] Then, according to the defined relevant parameters and boundary conditions, the geometric model is simulated and solved to obtain a dispersion relation atlas corresponding to different phononic crystal configuration images. The relevant parameters include the hyperelastic material properties and shape control parameters of the geometric model, and the boundary conditions include specified displacement conditions and periodic conditions. The dispersion relation atlas includes the dispersion relation diagrams corresponding to the phononic crystal under different tensile strain states. The dispersion relation diagram consists of 11 curves, each of which consists of 31 characteristic frequency points. Among them, the band gap characteristics corresponding to different tensile strain states are different. Any dispersion relation diagram indicates the corresponding relationship between its wave vector and frequency under the target tensile strain state.

[0110] Then, for each dispersion relation diagram, the corresponding fourth eigenfrequency vector is extracted.

[0111] Finally, the second training sample set is constructed using the fourth eigenfrequency vector and its corresponding dispersion relation diagram.

[0112] In some embodiments, the regression loss function is:

[0113]

[0114] Where y represents the true value of each training sample in the second training sample set, f(x) represents the predicted value of the training sample, δ is the hyperparameter of the regression loss function, and δ = 1.

[0115] In a specific example, the choice of loss function is crucial for achieving better model convergence. Commonly used loss functions for regression problems include MAE (mean absolute error), MSE (mean squared error), and Huber Loss (regression loss function). The MAE curve is V-shaped and continuous, but not differentiable at yf(x) = 0. Its gradient is constant elsewhere. This means that even for small loss values, its gradient is relatively large. This property of MAE results in poor function convergence and poor model learning. Because MAE calculates absolute error, without the squared term, the penalty is uniform, making it insensitive to outliers. The MSE curve is characterized by smoothness, continuity, and differentiability. When the difference between y and f(x) is greater than 1, the MSE imposes a large penalty on the model, while a small penalty is imposed when the difference is less than 1. Therefore, it is sensitive to outliers. However, as the error decreases, the gradient also decreases, which actually promotes convergence. Even with a fixed learning rate, the function can converge to the minimum relatively quickly. The Huber loss function combines the advantages of both MSE and MAE. Compared to MAE, it is universally differentiable and converges faster. It is also less sensitive to outliers and abnormal values ​​than MSE. The formulas for the MAE, MSE, and Huber loss functions are as follows.

[0116]

[0117] In the above formula, y i and y represent the true value of the training sample, f(x i ) and f(x) represent the predicted values ​​of the training samples. δ is the hyperparameter of Huber Loss. The size of δ determines the emphasis of Huber Loss on MSE and MAE. The default value is 1.

[0118] In a specific example, Figure 10 FIG. 1 is a schematic diagram showing a structure of a phononic crystal unit cell configuration according to an embodiment of the present invention. Figure 10 As shown, a0 is the lattice constant, which is 10 mm, and the image pixel size is 128 × 128. In this embodiment, the unit cell model is composed of only one material, namely the black part (matrix) in the figure, and the white part is air (scatterer), which is a two-dimensional solid-fluid type tunable phononic crystal.

[0119] 1. Related parameters

[0120] (1) Material parameters.

[0121] This embodiment uses the neo-Hookean hyperelastic model to describe the material properties, and the corresponding strain energy density function is shown in the following equation: where I1 is the first strain deviator invariant, and J is the local volume change in the theoretical model.

[0122]

[0123] Since it is necessary to simulate the tensile deformation of the phononic crystal, this embodiment considers the use of a hyperelastic material, which is assumed to be silicone rubber. Its parameters are shown in Table 2, where ρ0 represents the initial density, K is the initial bulk modulus, and C 10 is a parameter in the strain energy density function. In this case, the initial Poisson's ratio is about 0.49, indicating that the material is almost incompressible and only stretchable.

[0124] Table 1

[0125]

[0126] (2) Shape control parameters

[0127] Figure 11 The white part in the figure is air, and its outline shape is represented by the (x1, x2) coordinates of the equation, which is shown below. Among them, r0 is a parameter that controls the length of r(θ).

[0128] x1=r(θ)cosθ,x2=r(θ)sinθ

[0129]

[0130] The area of ​​the white part and the area of ​​the entire phononic crystal configuration image are:

[0131]

[0132] Therefore, the fill rate of the white part can be expressed as:

[0133]

[0134] In this embodiment, a phononic crystal unit cell model is generated by using a fourth-order equation, as shown in the following equation.

[0135] x1=r(θ)cosθ,x2=r(θ)sinθ

[0136] r(θ)=r0[1+c1cos(n1θ)+c2cos(n2θ)+c3cos(n3θ)+c4cos(n4θ)]

[0137] The above equation has nine shape-controlling parameters: c1–c4, n1–n4, and r0. In this paper, c1–c4 are set to the range [-0.35, 0.35], n1–n4 to the range [1, 20], and r0 to the range [0.65, 2]. These nine control parameters can generate a wide variety of complex phononic crystal samples, most of which are uniaxially symmetrical. To facilitate subsequent analysis, we considered reducing the sample space appropriately.

[0138] This embodiment applies symmetry conditions to ensure that the generated image is symmetrical vertically, horizontally, and diagonally. Furthermore, increasing the fill factor helps enrich the initial band gap of the undeformed phononic crystal configuration. To maximize the evolution of the band gap opening or closing, the fill factor should be appropriately increased, preferably within the range of [0.5, 0.75].

[0139] 2. Boundary conditions

[0140] In this embodiment, the specified displacement condition determines that the deformation analysis is performed in the form of equibiaxial stretching, and fixed constraints and specified displacements are set at the same time, such as Figure 11 As shown, two edges on the coordinate axis are fixed, and the other two edges are set to displacement, which are Δl x and Δl y (Δl x =Δl y ), and then add periodic conditions to the geometry in both directions.

[0141] Figure 12a and Figure 12b Schematic diagrams of the phononic crystal configuration image and its corresponding dispersion relation diagram according to an embodiment of the present invention are shown respectively. During the simulation calculation, this embodiment scans 31 wave vectors along the path GXMG to calculate the first 11 eigenfrequencies, and the stretching displacement is set to 0mm, 0.5mm and 1mm respectively. Therefore, one phononic crystal configuration image can obtain three dispersion relation diagrams. Figure 14 As shown, two phononic crystal configuration images are shown ( Figure 12a and Figure 12b ) and its corresponding three dispersion relation graphs. In the figure, the three dispersion relation graphs corresponding to the same phononic crystal configuration image respectively represent the dispersion relation conditions when the stretching displacement is 0 mm, 0.5 mm, and 1 mm.

[0142] from Figure 12a It can be seen from the figure that the phononic crystal configuration has rich band gap characteristics. As the stretching displacement increases, the width of the band gap between the fifth and sixth energy bands gradually narrows until it closes. At the same time, the band gap between the ninth and tenth energy bands opens and its width gradually widens.

[0143] from Figure 12b As can be seen in the figure, this phononic crystal configuration also has rich band gap characteristics. As the stretching displacement increases, the width of the band gap between the fifth and sixth energy bands gradually narrows until it closes; at the same time, the band gap between the third and fourth energy bands opens. This further demonstrates that the change in configuration geometry caused by external mechanical tensile loads can effectively change the band gap and regulate its on / off switching.

[0144] Finally, in step 208, the mean absolute percentage error (MAPE) of the first eigenfrequency vector and each second eigenfrequency vector is calculated respectively, and the similar image indicated by the second eigenfrequency vector corresponding to the smallest mean absolute percentage error is selected as the configuration image of the phononic crystal to be generated.

[0145] Calculating the mean absolute percentage error of the first eigenfrequency vector and each second eigenfrequency vector includes: first scaling each eigenfrequency value included in the first eigenfrequency vector and the second eigenfrequency vector, and then calculating the mean absolute percentage error using each scaled eigenfrequency value.

[0146] In some embodiments, the characteristic frequency value is scaled using the following formula:

[0147] p t =a+k*(pa)

[0148] Among them, p t represents the characteristic frequency value after scaling, p represents the characteristic frequency value before scaling, a is a constant, and a=0.001, k is the scaling factor, and b=1,c max is the maximum value of the characteristic frequency value (since the characteristic frequency value is a decimal, it can be rounded to 7005 in this embodiment), c min is the minimum value of the characteristic frequency value (0).

[0149] In some embodiments, the mean absolute percentage error value can be calculated by the following formula:

[0150]

[0151] in, and p ij are the j-th predicted eigenfrequency value of the i-th second eigenfrequency vector and the j-th actual eigenfrequency value of the corresponding first eigenfrequency vector, M is the number of second eigenfrequency vectors, and N is the number of eigenfrequency values ​​contained in the second eigenfrequency vector.

[0152] In addition, in order to verify the accuracy of the phononic crystal configuration generated by the above method 200, in some embodiments, the method 200 further includes verifying the configuration image of the selected phononic crystal to be generated using a finite element simulation method.

[0153] Specifically, a target configuration image and a target dispersion relation diagram of the phononic crystal generated by method 200 are obtained, and the target configuration image is used as the actual configuration, and the target dispersion relation is used as the actual dispersion relation. The actual configuration is input into a COMSOL finite element simulation to obtain a generated configuration and a simulated dispersion relation diagram. The actual dispersion relation diagram and the simulated dispersion relation diagram are compared to verify the accuracy of the generated phononic crystal configuration.

[0154] In some embodiments, as Figure 13 and 14 As shown, Figure 13 A schematic diagram showing a comparison between the first target dispersion relation and the corresponding first simulated dispersion relation is shown. Figure 14 A schematic diagram showing the comparison between the second target dispersion relation and the corresponding second simulated dispersion relation is shown.

[0155] Figure 13 The MAPE between the first target dispersion relation (corresponding to the true configuration on the upper left) and the first simulated dispersion relation (corresponding to the generated configuration on the lower left) is 2.95%. Figure 14 The MAPE between the second target dispersion relation and the second simulated dispersion relation is shown to be 1.91%.

[0156] As can be seen from the figure, the energy bands in the low-frequency range can be matched relatively accurately, while the accuracy in the higher-frequency range decreases. However, overall, the simulated dispersion relation of the generated configuration is quite consistent with the true dispersion relation in terms of characteristic frequency values ​​and overall trends, indicating that the phononic crystal configuration generated by method 200 is highly accurate.

[0157] In a specific example, combining Figure 15 The configuration generation method of the present application is further explained.

[0158] like Figure 15 As shown in FIG, given a dispersion relation (target dispersion relation), the characteristic frequency indicating the target dispersion relation is used as input data, and random noise is added to the input data before inputting it into the ACWGAN-GP generator (configuration generation model).

[0159] After being processed by the ACWGAN-GP generator, candidate configuration images are generated, and the candidate configuration images are post-processed (pre-processed) to obtain multiple similar images.

[0160] Each similar image is input into ResNet18 (dispersion relation prediction model) for processing to obtain the predicted dispersion relation corresponding to each similar image.

[0161] The mean absolute percentage error (MAPE) between the characteristic frequency of the target dispersion relation and the characteristic frequency of the predicted dispersion relation of each similar image is calculated respectively.

[0162] The similarity image with the smallest MAPE value is taken as the final configuration image of the target dispersion relation.

[0163] The final configuration image is simulated using finite element simulation (COMSOL) to obtain a simulated dispersion relation. The error between the simulated dispersion relation and the target dispersion relation is used to detect the accuracy of the generated configuration.

[0164] The method provided by the present invention proposes a deep learning framework that combines a configuration generation model and a dispersion relation prediction model. By using this deep learning framework to generate tunable phononic crystal configurations, near-optimal candidate configurations can be selected, thereby improving the accuracy of generating tunable phononic crystal configurations. At the same time, it can greatly reduce the time cost of generating tunable phononic crystals and increase the configuration generation speed of tunable phononic crystals.

[0165] A8. The method according to A3, wherein the regression loss function is: Where y represents the true value of each training sample in the second training sample set, f(x) represents the predicted value of the training sample, δ is a hyperparameter of the regression loss function, and δ = 1. A9. The method as described in A7, wherein the geometric model is represented by the following formula: x1 = r(θ)cosθ, x2 = r(θ)sinθ, wherein r(θ) = r0[1+c1cos(n1θ)+c2cos(n2θ)+c3cos(n3θ)+c4cos(n4θ)] (x1, x2) are the position coordinates of each intersection point of the scatterer and the matrix in the unit cell model, θ is the filling rate control parameter of the scatterer, c1~c4, n1~n4 and r0 are shape control parameters, the range of c1~c4 is [-0.35, 0.35], the range of n1~n4 is [1, 20], and the range of r0 is [0.65, 2]. A10. The method as described in A7, wherein the specified displacement condition is to adopt an equibiaxial stretching method. A11. The method as described in A1, wherein the first eigenfrequency vector indicating the dispersion relation of the phononic crystal configuration to be generated is input into the configuration generation model for processing to obtain at least one candidate configuration image, including: performing dimensionality reduction processing on the first eigenfrequency vector; fusing the first eigenfrequency vector after dimensionality reduction with a random vector by dot product to obtain a fused vector; and inputting the fused vector into the configuration generation model for processing to obtain at least one candidate configuration image. A12. The method as described in A11, wherein the first eigenfrequency vector is subjected to dimensionality reduction processing, including: inputting the first eigenfrequency vector into two groups of fully connected layers coupled to each other for processing in sequence to obtain a first eigenfrequency vector having the same dimension as the random vector. A13. The method as described in 5, wherein it also includes: the discriminator is trained 5 times per iteration, and the generator is trained once per iteration. A14. The method as described in A1, wherein the calculation of the mean absolute percentage error value of the first eigenfrequency vector and each second eigenfrequency vector comprises: scaling each eigenfrequency value contained in the first eigenfrequency vector and the second eigenfrequency vector; and calculating the mean absolute percentage error value using each scaled eigenfrequency value. A15. The method as described in A14, wherein the eigenfrequency value is scaled using the following formula: p t =a+k*(pa) where p t represents the characteristic frequency value after scaling, p represents the characteristic frequency value before scaling, a is a constant, and a=0.001, k is the scaling factor, and b=1,c max is the maximum value among the characteristic frequency values, c min A16. The method as described in A14 or A15, wherein the mean absolute percentage error value is calculated by the following formula: in, and p ij are the j-th predicted eigenfrequency value of the i-th second eigenfrequency vector and the j-th actual eigenfrequency value of the corresponding first eigenfrequency vector, M is the number of second eigenfrequency vectors, and N is the number of eigenfrequency values ​​contained in the second eigenfrequency vector.

[0166] Although the present invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of the foregoing description, will appreciate that other embodiments are contemplated within the scope of the invention thus described. Furthermore, it should be noted that the language used in this specification has been selected primarily for readability and didactic purposes, and not for the purpose of explaining or limiting the subject matter of the present invention. Consequently, numerous modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims.

Claims

1. A method for generating a tunable phononic crystal configuration based on deep learning, executed in a computing device, comprising: Inputting a first eigenfrequency vector indicating the dispersion relation of the phononic crystal configuration to be generated into a configuration generation model for processing to obtain at least one candidate configuration image; For each candidate configuration image, perform image preprocessing to obtain multiple similar images; Inputting each similar image into a dispersion relation prediction model for processing to obtain a second characteristic frequency vector representing the dispersion relation of each similar image, the dispersion relation prediction model comprising: a basic network component, a multi-layer perception component, and a prediction output component coupled in sequence, wherein the basic network component comprises a plurality of residual modules, and each residual module comprises an attention mechanism module, the attention mechanism module comprises a channel attention submodule and a spatial attention submodule, and the multi-layer perception component comprises a coupled fully connected layer, an activation function layer, and a random dropout layer; Calculating the average absolute percentage error values ​​of the first eigenfrequency vector and each second eigenfrequency vector respectively, and selecting the similar image indicated by the second eigenfrequency vector corresponding to the smallest average absolute percentage error value as the configuration image of the phononic crystal to be generated; The method for generating the dispersion relation prediction model includes generating a second training sample set based on a constructed configuration image database, wherein the second training sample set includes configuration images of multiple phononic crystals and their corresponding dispersion relations, wherein the dispersion relation is represented by a characteristic frequency vector, and generating a dispersion relation prediction model based on the second training sample set using a regression loss function for training; The generating of a second training sample set based on the constructed configuration image database comprises: Generating phononic crystal configuration images using MATLAB, and constructing the configuration image database using the generated phononic crystal configuration images, wherein the phononic crystal configuration images have various shapes and are single-material phononic crystal configurations, and are stretched and deformed using an equibiaxial stretching method to generate a band gap; Through the COMSOL with MATLAB interface, the phononic crystal configuration image is input into COMSOL to establish a geometric model; According to the defined relevant parameters and boundary conditions, the geometric model is simulated and solved to obtain a dispersion relation atlas corresponding to different phononic crystal configuration images, wherein the relevant parameters include the hyperelastic material properties and shape control parameters of the geometric model, and the boundary conditions include specified displacement conditions and periodic conditions. The dispersion relation atlas includes dispersion relation diagrams corresponding to the phononic crystal under different tensile strain states. The dispersion relation diagram consists of 11 curves, each of which consists of 31 characteristic frequency points. The band gap characteristics corresponding to different tensile strain states are different, and any dispersion relation diagram indicates the corresponding relationship between its wave vector and frequency under the target tensile strain state; For each dispersion relation diagram, extract the corresponding fourth eigenfrequency vector; constructing the second training sample set using the fourth eigenfrequency vector and its corresponding dispersion relation diagram; The geometric model is represented by the following formula: x1=r(θ)cosθ,x2=r(θ)sinθ Where r(θ)=r0[1+c1cos(n1θ)+c2cos(n2θ)+c3cos(n3θ)+c4cos(n4θ)], (x1,x2) are the position coordinates of the intersection points of the scatterer and the matrix in the unit cell model, θ is the filling rate control parameter of the scatterer, c1~c4, n1~n4 and r0 are shape control parameters, the range of c1~c4 is [-0.35,0.35], the range of n1~n4 is [1,20], and the range of r0 is [0.65,2].

2. The method according to claim 1, wherein For each candidate configuration image, image preprocessing is performed to obtain multiple similar images, including: Performing image symmetry transformation on the candidate configuration image to obtain multiple initial similar images, wherein the image symmetry transformation includes horizontal flipping, vertical flipping, and diagonal transformation; Filter the discrete pixels of each initial similar image using a median filter; The initial similar image from which the discrete pixels are filtered is binarized to obtain the similar image.

3. The method according to claim 1, wherein It also includes the steps of training the configuration generation model: Constructing a generative adversarial model based on Wasserstein distance, wherein the generative adversarial model includes a generator and a discriminator; generating a first training sample set, wherein any training sample of the first training sample set includes a real image of a sample phononic crystal and a third eigenfrequency vector representing a dispersion relation of a configuration of the sample phononic crystal; Inputting each third eigenfrequency vector into the generator, and outputting a generated image after processing; The generated image and the corresponding real image are input to the discriminator, which outputs a metric indicating whether the generated image is consistent with the corresponding real image after processing; Based on the metric value, the generator and the discriminator are iteratively trained using a loss function with a gradient penalty until the number of training rounds reaches a preset number of rounds. The training is completed, and the generator generated by the training is used as the configuration generation model.

4. The method according to claim 3, wherein: The discriminator comprises: a plurality of coupled convolution modules and output modules; The convolution module includes a convolution layer, an instance normalization layer, an activation function layer and a random dropout layer coupled in sequence; The output module includes a fully connected module.

5. The method according to claim 1, wherein The regression loss function is: Where y represents the true value of each training sample in the second training sample set, f(x) represents the predicted value of the training sample, δ is the hyperparameter of the regression loss function, and δ = 1.

6. The method of claim 1, wherein: Inputting a first eigenfrequency vector indicating the dispersion relation of the to-be-generated phononic crystal configuration into a configuration generation model for processing, and obtaining at least one candidate configuration image, including: Performing dimensionality reduction processing on the first eigenfrequency vector; The first eigenfrequency vector after dimensionality reduction is fused with the random vector by dot product to obtain a fused vector; The fusion vector is input into a configuration generation model for processing to obtain at least one candidate configuration image.

7. The method according to claim 6, wherein: Performing dimensionality reduction processing on the first characteristic frequency vector includes: The first characteristic frequency vector is sequentially input into two groups of fully connected layers coupled to each other for processing, so as to obtain a first characteristic frequency vector having the same dimension as the random vector.

8. The method of claim 3, wherein: Also includes: The discriminator is trained 5 times per iteration, and the generator is trained once per iteration.

9. The method of claim 1, wherein: Calculating the mean absolute percentage error of the first eigenfrequency vector and each second eigenfrequency vector respectively includes: Scaling each eigenfrequency value included in the first eigenfrequency vector and the second eigenfrequency vector; The mean absolute percentage error value is calculated using each characteristic frequency value after scaling.

10. The method of claim 9, wherein: The characteristic frequency value is scaled using the following formula: p t =a+k*(p-a) Among them, p t represents the characteristic frequency value after scaling, p represents the characteristic frequency value before scaling, a is a constant, and a=0.001, k is the scaling factor, and b=1,c max is the maximum value among the characteristic frequency values, c min is the minimum value of the characteristic frequency value.

11. The method according to claim 9 or 10, wherein: The mean absolute percentage error value is calculated by the following formula: in, and p ij are the j-th predicted eigenfrequency value of the i-th second eigenfrequency vector and the j-th actual eigenfrequency value of the corresponding first eigenfrequency vector, M is the number of second eigenfrequency vectors, and N is the number of eigenfrequency values ​​contained in the second eigenfrequency vector.

12. A computing device comprising: at least one processor; and A memory storing program instructions, wherein the program instructions are configured to be executed by the at least one processor, and the program instructions include instructions for executing the method according to any one of claims 1 to 11.

13. A computer program product comprising a computer program / instructions, wherein: When the computer program / instructions are executed by a processor, the method according to any one of claims 1 to 11 is implemented.

14. A readable storage medium storing program instructions, wherein when the program instructions are read and executed by a computing device, the computing device is caused to execute the method according to any one of claims 1 to 11.

Images