A method for designing disordered hyperuniform acoustic metamaterials based on reversible neural networks

Abstract

The application discloses a disordered hyperuniform acoustic metamaterial design method based on an invertible neural network, which not only overcomes the one-to-many mapping problem from the spectral response to the structure factor in the traditional disordered hyperuniform acoustic metamaterial design process, but also can directly obtain the inverse process to predict the solution during the training forward process, thereby significantly reducing the overall calculation time and improving the design efficiency. The design method comprises the following steps: firstly, a data set comprising the structure parameters, the structure factor and the corresponding spectral response of the disordered hyperuniform acoustic metamaterial is constructed; then, an INN model is constructed in a reversible block cascading manner comprising multiple inner full connection layers, and the data set is preprocessed and trained; then, the target spectrum is input into the trained INN model, the latent variable z distribution predicted by the INN model is probabilistically sampled, and the structure factor is directly generated through the inverse process of the model; finally, the structure factor is subjected to inverse Fourier transform to obtain the structure parameters meeting the conditions.

Description

Technical Field

[0001] This invention relates to a method for designing disordered, ultra-uniform acoustic metamaterials based on reversible neural networks, belonging to the field of acoustics. Background Technology

[0002] In the field of acoustics, designing disordered, ultrahomogeneous acoustic metamaterials to achieve acoustic transparency is a fundamental problem. Designing such structures is typically only applicable to weak scattering conditions, which are often not met in real-world scenarios, thus limiting its application. To achieve acoustic transparency under arbitrary scattering conditions (including strong scattering), researchers have conducted extensive studies on the synergistic mechanisms of ultrahomogeneity and strong scattering, such as multi-scattering interference, local resonance, and long-range correlation coupling, but these have not effectively achieved acoustic transparency under strong scattering conditions. On the other hand, deep learning-based inverse design has received widespread attention in acoustic metamaterial research. However, in strong scattering environments, local resonance disrupts the deterministic injective and surjective correlation between the spectral response and structural factors of disordered, ultrahomogeneous acoustic metamaterials, leading to a one-to-many mapping problem. Traditional artificial neural networks struggle to solve this type of multi-valued mapping problem. Existing research has proposed several solutions for multi-valued problems, with a representative approach being an acoustic metamaterial design method based on the PGN model. However, this method still has significant technical limitations: on the one hand, it is difficult to adapt to complex sound field control conditions that include strong scattering and strong local resonance features; on the other hand, due to its complex overall architecture, the model consumes a lot of computing power for training, has low overall design efficiency, and has not yet built an efficient optimal solution selection mechanism. Summary of the Invention

[0003] Objective: To address the shortcomings of existing technologies, this invention proposes a design method for disordered ultrauniform acoustic metamaterials based on reversible neural networks. This method overcomes the technical bottleneck of achieving acoustic transparency under strong scattering conditions. Furthermore, it offers advantages such as high efficiency, high precision, and low cost, solving the one-to-many mapping problem between spectral response and structure factor in the design of disordered ultrauniform acoustic metamaterials in strong scattering environments.

[0004] Technical Solution: To solve the above-mentioned technical problems, the present invention provides a method for designing disordered ultra-uniform acoustic metamaterials based on reversible neural networks, comprising the following steps:

[0005] (1) Construct a dataset including the structural parameters, structural factors and corresponding spectral responses of disordered ultrahomogeneous acoustic metamaterials;

[0006] (2) Construct an INN model by cascading multiple reversible blocks containing multiple fully connected layers, and then preprocess the dataset and train it.

[0007] (3) Input the target spectrum into the trained INN model, perform probability sampling on the distribution of the latent variable z predicted by the INN model, and directly generate the structure factor through the inverse process of the INN model; perform inverse Fourier transform on the structure factor to obtain the structure parameter that meets the conditions.

[0008] As a preferred option, the basic architecture of each reversible block is an affine coupling layer:

[0009]

[0010]

[0011] The reverse process is as follows:

[0012]

[0013]

[0014] in, and The input is split into two parts. and The output is split into two parts. , , and is an affine function, representing an independent neural network.

[0015] Preferably, each reversible block contains four independent neural network blocks, which include an input layer, a hidden layer, and an output layer. The layers are connected by a fully connected method and use the ReLU activation function and the Adam optimizer.

[0016] As a preferred approach, during the forward training of the INN model, an auxiliary latent variable z is introduced to store the features of all structural factors that cannot be encoded by the spectral response. During training, z is constrained to follow a standard multivariate Gaussian distribution and is correlated with... The square of the maximum mean difference (MMD) is used independently as the distribution constraint loss.

[0017] As a preferred approach, during the forward training of the INN model, the structure factor and spectrum are first preprocessed by normalization, and then the structure factor is used as the basis for the training. As input, the spectral response As output, a positive mapping from structural factors to spectral response is established; the forward training of the INN model uses the error between the predicted spectral response and the true spectral response as the loss function, and MSE as the metric; training stops when the superimposed loss function converges, and the INN model is saved.

[0018] As a preferred option, the distribution-constrained loss function for the latent variable z is:

[0019]

[0020] in, To be from the distribution Sampling One sample, To be from the distribution Sampling One sample, Representing kernel functions, using inverse quadratic multikernels. .

[0021] As a preferred choice, the loss function of the INN model is:

[0022]

[0023] in The dimension representing the spectral response. This represents the predicted spectral response sample. This represents the actual spectral response sample.

[0024] As a preferred method, the process of probability sampling the distribution predicted by the INN model is as follows: from the Gaussian distribution... one sample The generated z is represented by the following formula:

[0025]

[0026] in The mean, The standard deviation is denoted as .

[0027] As a preferred option, the sample set The sampling method is as follows: batch samples are output through a feedforward network. Sample set The sampling method is as follows: 1. Randomly sample from the training set. 2. Regarding Perform independent sampling; 3. Stitching .

[0028] As a preferred approach, the target spectral response is input, and the latent variables predicted by the INN model are sampled multiple times to generate structural factors that meet the conditions. Then, the structural factors are subjected to inverse Fourier transform to obtain structural parameters that meet the conditions.

[0029] Beneficial effects: The design method of disordered ultra-uniform acoustic metamaterials based on reversible neural networks of the present invention designs disordered ultra-uniform acoustic metamaterials based on the INN model. It not only overcomes the problem of one-to-many mapping of spectral response to structural factors in the design process of disordered ultra-uniform acoustic metamaterials under strong scattering, but also significantly reduces the overall calculation time and improves design efficiency by obtaining the inverse process for free. For any target acoustic transparency spectrum, the structural parameters that meet the conditions can be optimized by the reversible neural network. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention;

[0031] Figure 2 This is a schematic diagram of a disordered, ultra-uniform, acoustically transparent metamaterial structure.

[0032] Figure 3 It is an INN model-optimized architecture for disordered, ultra-uniform, acoustically transparent metamaterials;

[0033] Figure 4 It is a design result based on the INN model. Detailed Implementation

[0034] The invention will now be further described with reference to the accompanying drawings.

[0035] This embodiment takes a straight tube waveguide-type acoustically transparent metamaterial with 25 randomly distributed ultrauniform scattering rings as the research object. The basic structural parameters of the waveguide are fixed: the inner diameter of the waveguide is d=2.5cm, the total length is L=1m, and the thickness of a single scattering ring is g=2mm. The outer diameter of the scattering ring can be selected in two specifications: 2.1cm and 1.7cm. The 25 scattering rings are randomly arranged to form a disordered ultrauniform discrete point configuration.

[0036] like Figure 1 As shown, the design method for disordered ultrahomogeneous acoustic metamaterials includes the following steps:

[0037] Step 1: Construct a dataset using disordered hyperuniform theory and finite element numerical simulation.

[0038] (1) Random sampling of scattering ring positions

[0039] In the effective axial range X of the waveguide Discrete position random sampling is performed within the system. Each sampling generates 25 non-overlapping axial coordinates, forming a single set of structural parameter vectors X=[x1,x2,...,x...]. 25 During the sampling process, two different scattering ring outer diameters d1, 2.1 cm or 1.7 cm, are alternately configured to enrich the differences in the scattering cross sections of the samples and improve the generalization ability of the dataset.

[0040] (2) Solving the structure factor using disordered hyperuniform theory

[0041] Based on the principle of discrete-point configuration superposition interference, the structure factor corresponding to each scattering configuration is calculated using the discrete summation formula.

[0042] Where W represents the number of scattering rings. It is the reciprocal lattice vector. This is the position vector of the w-th scattering ring. The spectral response is then calculated through finite element numerical simulation, thus establishing a dataset consisting of 50,000 training data points and 500 validation data points. The structural parameters corresponding to each set of samples are... The arrangement of the 25 scattering rings .

[0043] (3) Solving the transmission spectrum using acoustic finite element simulation

[0044] The scattering ring arrangement parameters obtained from each group of samples were imported into the acoustic finite element model, and frequency domain simulation was carried out based on the acoustic propagation wave equation. The simulation frequency range covered 2000–6000 Hz, and 52 frequency sampling points were uniformly discretized to output a one-dimensional transmission spectrum vector T=[y1,y2,…,y]. 52 The transmission coefficient y ranges from [0,1], with values ​​closer to 1 indicating better acoustic transparency. The simulation model strictly matches the physical structure parameters: waveguide diameter 2.5cm, tube length 1m, scatterer thickness 2mm, and air medium acoustic impedance and scattering ring solid material parameters remain constant.

[0045] (4) Dataset partitioning and sample storage

[0046] Repeat the above sampling-structure factor calculation-finite element simulation process to generate 50,500 sets of valid paired samples. These are then divided at a 99:1 ratio: 50,000 sets are used as the training dataset for iterative updates of the INN model parameters; the remaining 500 sets serve as an independent validation dataset, used to monitor model generalization error in real time during training to prevent overfitting. Each set of samples uniformly stores triplet information: 25-dimensional scattering ring position parameters X, high-dimensional structure factor S, and 52-dimensional discrete transmission spectrum T.

[0047] Step 2: Construct a bidirectional reversible mapping INN reversible neural network model

[0048] like Figure 3 The mapping from structural factors to spectral responses is forward prediction, and the mapping from spectral responses to structural factors is backward retrieval. The INN model consists of multiple cascaded reversible blocks, each containing four independent neural network blocks, including an input layer, hidden layers, and an output layer. The layers are fully connected, and the ReLU activation function and Adam optimizer are used.

[0049] The basic architecture of each reversible block is an affine coupling layer:

[0050]

[0051]

[0052] The reverse process is as follows:

[0053]

[0054]

[0055] in, and The input is split into two parts. and The output is split into two parts. , , and is an affine function, representing an independent neural network.

[0056] Step 3: Introduce latent variables to solve the multi-valued mapping problem and design a distribution-constrained loss.

[0057] To address the multi-valued problem between the spectral response and the structural factor, latent variables are introduced. It stores the features of all structural factors that cannot be encoded by the spectral response. The network output concatenates the 52-dimensional transmission spectrum y with the latent variable z to form a joint output vector. The latent variable z specifically stores the scattering configuration differences that the spectrum cannot encode;

[0058] Network input: Zeros are padded to the end of the original 25-dimensional scattering position parameter x. The zero-padding vector o has the same dimension as the latent variable z. The vectors are concatenated to obtain the network input [x, o], which ensures that the input and output dimensions match and satisfies the invariant block dimension constraint.

[0059] The INN is trained using a dataset to establish a positive mapping from structural factors to spectral responses. The dataset is normalized before being input into the INN. During training, z is constrained to follow a standard multivariate Gaussian distribution and be independent of y. The square of the maximum mean difference (MMD) is used as the distribution constraint loss function.

[0060] The distribution-constrained loss function for the latent variable z is:

[0061]

[0062] in, To be from the distribution Sampling One sample, To be from the distribution Sampling One sample. Representing kernel functions, using inverse quadratic multikernels. .

[0063] Sample set The sampling method is as follows: batch output from INN forward propagation. , representing the actual output distribution of the model samples;

[0064] Sample set The sampling method is as follows: ① Randomly sample the real transmission spectrum y from the training set; ② Independently sample the latent variable z from the standard Gaussian distribution; ③ Concatenate the samples to obtain bi=[y,z].

[0065] Step 4: Forward training of the INN model uses the error between the predicted spectral response and the true spectral response as the loss function, and MSE as the metric; training stops when the superimposed loss function converges, and the INN model is saved.

[0066] The loss function for the INN model is:

[0067]

[0068] in , This represents the predicted spectral response sample. Predicting the transmission coefficient for the INN model. This represents the actual spectral response sample. The values ​​represent the true transmission coefficients obtained from finite element simulation. The normalized training set is input into the forward path of the INN in batches. In each iteration, the total loss for Ly and Lz is calculated simultaneously. The weights of the fully connected network within all reversible blocks are updated via backpropagation using the Adam optimizer. For each fixed number of training iterations, the validation loss is calculated using a validation set of 500 sets to monitor for overfitting.

[0069] Set a loss convergence threshold and a constraint on the number of consecutive iterations: when the total training loss and validation loss do not decrease significantly for several consecutive iterations, and the MSE spectral loss is lower than the preset accuracy threshold, the model is considered to have converged and training is stopped; save the complete INN network weights, network structure, normalized parameters, and the mean μ and standard deviation σ of the latent variable distribution for subsequent inverse structure retrieval.

[0070] Step 5: Input the target acoustic transparent spectrum into the INN model trained in Step 4, perform multiple probability samplings on the distribution of the latent variable z predicted by the INN model to generate a structure factor that meets the conditions, and then perform an inverse Fourier transform on the structure factor to obtain the structure parameters that meet the conditions.

[0071] The probability sampling process starts from a Gaussian distribution. one sample The generated z is represented by the following expression:

[0072]

[0073] in The mean, The standard deviation is given. Multiple sets of different z correspond to multiple scattering configurations that satisfy the same target spectrum, enabling parallel design of multiple schemes. Each set of [y,z] is input into INN and decoded by inverse branch to obtain the corresponding structure factor. An inverse Fourier transform is performed on the structure factor to restore the axial arrangement position parameters X of 25 scattering rings, outputting multiple sets of physically feasible disordered ultrauniform configurations.

[0074] like Figure 4 As shown, to verify the performance of the INN model, the target acoustic transparency frequency band was set within the range of 3000–5000 Hz (gray area). The target acoustic transparency spectrum was input into the trained INN model to generate the corresponding structural parameters. We used these structural parameters to conduct numerical simulations and experimental tests, and the results are plotted by the dashed and solid lines in the figure, respectively. This disordered ultrahomogeneous acoustic metamaterial exhibits high acoustic transparency characteristics within the range of 3050–5356 Hz under strong scattering conditions. The spectrum of the material was consistent with the results of numerical simulation and experiments. The high-precision prediction results demonstrate the effectiveness of the proposed design method for disordered ultrahomogeneous acoustic metamaterials based on reversible neural networks.

[0075] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A design method for disordered ultrauniform acoustic metamaterials based on reversible neural networks, characterized in that: Includes the following steps: (1) Construct a dataset including the structural parameters, structural factors and corresponding spectral responses of disordered ultrahomogeneous acoustic metamaterials; (2) Construct an INN model by cascading multiple reversible blocks containing multiple fully connected layers, and then preprocess the dataset and train it. (3) Input the target spectrum into the trained INN model, perform probability sampling on the distribution of the latent variable z predicted by the INN model, and directly generate the structure factor through the inverse process of the INN model; perform inverse Fourier transform on the structure factor to obtain the structure parameter that meets the conditions.

2. The design method according to claim 1, characterized in that: The basic architecture of each reversible block is an affine coupling layer: The reverse process is as follows: in, and The input is split into two parts. and The output is split into two parts. , , and is an affine function, representing an independent neural network.

3. The design method according to claim 2, characterized in that: Each reversible block contains four independent neural network blocks, which include an input layer, a hidden layer, and an output layer. The layers are connected by a fully connected method and use the ReLU activation function and the Adam optimizer.

4. The design method according to claim 1, characterized in that: During the forward training of the INN model, an auxiliary latent variable z is introduced to store the features of all structural factors that cannot be encoded by the spectral response. During training, z is constrained to follow a standard multivariate Gaussian distribution and is associated with... The square of the maximum mean difference (MMD) is used independently as the distribution constraint loss.

5. The design method according to claim 1, characterized in that: During the forward training of the INN model, the structure factor and spectrum are first normalized and preprocessed, and then the structure factor is used as the basis for the training. As input, the spectral response As output, a positive mapping from structural factors to spectral response is established; the forward training of the INN model uses the error between the predicted spectral response and the true spectral response as the loss function, and MSE as the metric; training stops when the superimposed loss function converges, and the INN model is saved.

6. The design method according to claim 4, characterized in that: The distribution-constrained loss function for the latent variable z is: in, To be from the distribution Sampling One sample, To be from the distribution Sampling One sample, Representing kernel functions, using inverse quadratic multikernels. .

7. The design method according to claim 5, characterized in that: The loss function for the INN model is: in The dimension representing the spectral response. This represents the predicted spectral response sample. This represents the actual spectral response sample.

8. The design method according to claim 1, characterized in that: The process of probability sampling from the distribution predicted by the INN model is as follows: from the Gaussian distribution Sampling one The generated z is represented by the following formula: in The mean, The standard deviation is denoted as .

9. The design method according to claim 6, characterized in that: Sample set The sampling method is as follows: batch samples are output through a feedforward network. Sample set The sampling method is as follows: Random sampling from the training set ; ,right Perform independent sampling; splicing .

10. The design method according to claim 1, characterized in that: The target spectral response is input, and the latent variables predicted by the INN model are sampled multiple times to generate structural factors that meet the conditions. Then, the structural factors are subjected to inverse Fourier transform to obtain structural parameters that meet the conditions.

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