Deep learning low-frequency sound absorption metamaterial step-by-step inverse design method considering sensitivity

Abstract

The invention belongs to the field of acoustic metamaterial reverse design, and discloses a sensitivity deep learning low-frequency sound absorption metamaterial step-by-step reverse design method which specifically comprises the following steps: step 1, performing sensitivity analysis on structural parameters to be designed; 2, establishing a data set of acoustic metamaterial structure parameters and corresponding sound absorption coefficients in a fixed frequency band of the acoustic metamaterial structure parameters; 3, training different prediction modules according to the parameters with different sensitivities, and performing cascade optimization on the different prediction modules; 4, all the prediction models after cascade optimization form a complete cascade step-by-step prediction model A; and 5, evaluating the generalization ability and performance of the cascade step-by-step prediction model A by using the test model. According to the method, the generalization ability of the model is enhanced through a step-by-step physical parameter method, and the prediction accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the field of inverse design of acoustic metamaterials, and specifically relates to a step-by-step inverse design method of low-frequency sound-absorbing metamaterials by deep learning considering sensitivity. Background Art

[0002] By adjusting the structure and shape of the material, metaacoustic materials can achieve precise control over the propagation and reflection of sound waves. This feature has opened up a new direction for research in the field of acoustics. In actual scenarios, people usually expect to quickly obtain the geometric parameters of acoustic metamaterials based on their sound absorption properties. How to design artificial structures such as high-performance metaacoustic materials. Making them play the expected acoustic performance is the core issue of metaacoustic material design. The traditional forward design method, that is, based on the initial structure, obtains the acoustic response data of the device through simulation or experiment, and then modifies the parameters of the initial structure according to the response data, and gradually designs the target device through trial and error. As the complexity of the device increases, the computational cost and time consumption of the design are also increasing. The traditional forward design method is not enough to handle the computational complexity of actual design problems.

[0003] Inverse design is to directly generate the corresponding working structure according to the required response target, thus avoiding lengthy parameter scanning or trial and error. Deep learning algorithms can establish nonlinear mapping relationships between high-dimensional input and output data, and have powerful feature extraction, generalization and complex data processing capabilities. These advantages make it a powerful tool for solving inverse design problems. For acoustic metamaterials, their sound absorption performance is closely related to structural parameters. These parameters include but are not limited to material thickness, pore size, pore spacing, arrangement, and cavity size. Changes in these parameters will directly affect the impedance characteristics of the device and the effect of regulating sound waves. The interaction between multiple parameters will make different geometric structures have the same sound absorption response curve. This multi-mapping situation will cause the trained network to not always converge, which is a typical problem in inverse mapping. Zhang et al. (Zhang, H., Liu, J., Ma, W. et al. Learning to inversely design acoustic metamaterials for enhanced performance. Acta Mech. Sin. 39, 722426 (2023)) proposed a tandem neural network architecture to train the model using the error between the target absorption spectrum and the predicted absorption spectrum in the inverse design of three-dimensional mixed-size cavity water-based acoustic metamaterials. However, the generator part of the tandem model does not introduce real structural data during training, which will affect the final prediction results. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes an inverse design method for acoustic metamaterials based on sensitivity to achieve physical mechanism enhancement. Compared with the traditional method, the generalization ability of the model is enhanced by the step-by-step physical parameter method, and the accuracy of the prediction is improved. In order to achieve the above purpose, the present invention is implemented by the following technical solutions:

[0005] The present invention is a step-by-step inverse design method for low-frequency sound-absorbing metamaterials by deep learning considering sensitivity, and the method specifically comprises the following steps:

[0006] Step 1: Conduct sensitivity analysis on the structural parameters to be designed;

[0007] Step 2, establishing a data set of acoustic metamaterial structural parameters and the sound absorption coefficient corresponding to the fixed frequency band;

[0008] Step 3: train different prediction modules according to parameters with different sensitivities, and optimize network parameters of different prediction modules;

[0009] Step 4: The prediction models after cascade optimization form a complete cascade step-by-step prediction model A;

[0010] Step 5: Use the test dataset to evaluate the generalization ability and performance of the cascaded step-by-step prediction model A.

[0011] A further improvement of the present invention is that the step 1 of performing sensitivity analysis on the structural parameters to be designed specifically comprises the following steps:

[0012] Step 1.1, determine the value range of the input parameters according to the specific design requirements, perform finite element simulation on the target structure, and randomly generate multiple groups of data points of each parameter value within the value range of the design parameters;

[0013] Step 1.2, for each set of data points generated in step 1.1, calculate its sensitivity;

[0014] Step 1.3: Calculate the average value of the sensitivity results of all data points to evaluate the overall sensitivity and uncertainty, customize the MATLAB script for sensitivity analysis, and create a graphical report to intuitively obtain the sensitivity relationship between geometric parameters and structural sound absorption coefficient, and sort the design parameters according to sensitivity.

[0015] A further improvement of the present invention is that the step 1.2 of calculating the sensitivity specifically includes the following steps:

[0016] Step 1.2.1, for each set of data points (x1, x2, ..., x i ,x i+1 ,...,x n), calculate the sound absorption coefficient spectrum α(x1,x2,...,x i ,x i+1 ,...,x n ) as the benchmark solution;

[0017] Step 1.2.2: Let the structural parameter x i There is a small perturbation Δx, and the difference format is used to calculate the effect of α on the design variable parameter x i The approximate derivative of Wherein, i=1,2,...n, and α represents the sound absorption coefficient spectrum.

[0018] A further improvement of the present invention is that in step 1.2.1, the fixed frequency range is fixed between 0-700 Hz, with a step length of 0.5.

[0019] A further improvement of the present invention is that the method for generating a data set in step 2 includes a formula analysis method based on acoustic-electric analogy and a COMSOL numerical calculation batch generation method. Among them, acoustic-electric analogy is a method of analogizing acoustic problems with electromagnetic problems. This method studies the phenomenon of acoustic vibration by using circuit theory and circuit diagram analysis methods, but the formula analysis method based on acoustic-electric analogy is not suitable for all sound-absorbing structures, especially for some sound-absorbing structures with irregular shapes of sound-absorbing units. For some irregular sound-absorbing structures, COMSOL Multiphysics with MATLAB joint simulation is used: a script written in MATLAB is used to load the COMSOL model and perform batch scanning. The function of this script includes looping through the parameter values, running the COMSOL model solver at each parameter value, generating the required data, integrating and exporting the data set.

[0020] A further improvement of the present invention is that in step 3, different prediction modules are trained for parameters with different sensitivities, specifically including the following steps:

[0021] Step 3.1: Determine the prediction task of each prediction module based on the results of the sensitivity analysis in step 1. For the parameter with the lowest sensitivity, the corresponding prediction module is set as the most basic prediction unit. This prediction module only accepts known features as input, and no additional auxiliary prediction parameters are required. As the sensitivity of the parameter increases, the auxiliary prediction parameter, i.e., the output result of the previous prediction module, is added to the input of the prediction module to improve the prediction accuracy.

[0022] Step 3.2: Define the convolutional neural network structure and adjust the network layer parameters according to the design tasks of each prediction module;

[0023] Step 3.3: Use the same training set to train each prediction module, and adjust the hyperparameters for different modules to obtain the network module with the lowest validation error for each parameter.

[0024] A further improvement of the present invention is that: in the step 4, the cascaded step-by-step prediction model A is composed of prediction modules M1, M2, M3...Mn of each parameter, and the acquisition process of the cascaded step-by-step prediction model A is: writing a MATLAB script to realize the cascade of each prediction module, a group of features predicts the parameter with the lowest sensitivity through the first-level prediction module M1; the next-level module adds the output parameter of the previous-level module as the input data of this module on the basis of the input data of the previous-level module, and completes the cascade of all modules in turn.

[0025] A further improvement of the present invention is that: the step 5 of evaluating the generalization ability and performance of the cascaded step-by-step prediction model A refers to selecting the mean absolute error (MAE) as an indicator to measure the difference between the prediction results of the step-by-step prediction model A and the actual parameters, specifically: the sound absorption response spectrum of the test data is input into the overall model for prediction, and the mean absolute error (MAE) is used as a measure of the difference between the model prediction results and the actual parameters, and multiple groups of prediction parameters are randomly selected to compare the sound absorption coefficient curve of the predicted structure with the target sound absorption coefficient curve to verify the actual prediction of model A.

[0026]

[0027] where x i is the actual parameter, x i ' is the prediction parameter.

[0028] The beneficial effect of the present invention is that the present invention proposes a method for assisting convolutional neural networks to complete the step-by-step inverse design of acoustic metamaterials by analyzing the sensitivity of design parameters. Sensitivity analysis evaluates the sensitivity of different parameters to the acoustic response of the model, providing the prediction network with prior knowledge about acoustic metamaterials; on this basis, the use of step-by-step superposition of auxiliary parameter input avoids the non-uniqueness of the prediction and significantly improves the accuracy of the inverse design. Especially in practical applications, it can more clearly guide designers in the design of structural parameters under specific requirements, realize on-demand design applications, and greatly improve the flexibility of design. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A flow chart of the step-by-step acoustic metamaterial inverse design method based on convolutional neural network provided by the present invention.

[0030] Figure 2 1 is an example model of a sound absorbing device in an embodiment of the present invention; wherein (a) is a physical model diagram of the embodiment, and (b) is a schematic diagram of structural parameters that need to be reversely designed in the embodiment.

[0031] Figure 3 It is an acoustic-electric analogy diagram of the sound absorbing device in an embodiment of the present invention.

[0032] Figure 4 This is a diagram of the sound absorption coefficient simulated by COMSOL and calculated by the formula in an embodiment of the present invention.

[0033] Figure 5 4 is a sensitivity analysis diagram of each parameter in the embodiment of the present invention.

[0034] Figure 6 This is a structural diagram of a convolutional neural network model in an embodiment of the present invention.

[0035] Figure 7 Schematic diagram of the structure of the inverse design cascade step-by-step prediction model A in an embodiment of the present invention.

[0036] Figure 8 It is a MAE comparison chart of different prediction models in the embodiment of the present invention under the same task; wherein, (a) is a MAE comparison chart of the cascaded step-by-step prediction model A and the overall prediction model B on the same task in the embodiment, and (b) is a MAE comparison chart of the cascaded step-by-step prediction model A and the cascaded step-by-step prediction model C on the same task in the embodiment.

[0037] Fig. 9 1 is a comparison diagram of the target sound absorption curve and the model predicted sound absorption curve in the embodiment of the present invention; (a) is a comparison diagram of the predicted sound absorption curve of the cascaded step-by-step prediction model A and the overall prediction model B in the embodiment, and (b) is a comparison diagram of the predicted sound absorption curve of the cascaded step-by-step prediction model A and the cascaded step-by-step prediction model C in the embodiment. DETAILED DESCRIPTION

[0038] The following will disclose the embodiments of the present invention with drawings. For the purpose of clear description, many practical details will be described together in the following description. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

[0039] like Figure 1 As shown, the present invention is a step-by-step inverse design method of a low-frequency sound-absorbing metamaterial using deep learning considering sensitivity, and the method specifically comprises the following steps:

[0040] Step 1: Conduct sensitivity analysis on the structural parameters to be designed;

[0041] Step 2, establishing a data set of acoustic metamaterial structural parameters and the sound absorption coefficient corresponding to the fixed frequency band;

[0042] Step 3: train different prediction modules according to parameters with different sensitivities, and perform cascade optimization on different prediction modules;

[0043] Step 4: The prediction models after cascade optimization form a complete cascade step-by-step prediction model A, wherein the cascade step-by-step prediction model A includes a prediction module M1, a prediction module M2, and a prediction module M3;

[0044] Step 5: Use the test dataset to evaluate the generalization ability and performance of the cascaded step-by-step prediction model A.

[0045] The proposed design method is specifically described in this embodiment by taking the inverse design of a low-frequency sound-absorbing metamaterial unit structure as an example. Figure 2 As shown, the design parameter is the neck length l n , cavity length l c , cavity radius r c 、Neck radius r n ; Wherein the unit structure device height L = l n +l c are known geometric parameters;

[0046] The step-by-step inverse design method of the sound absorbing structure based on deep learning in this embodiment specifically includes the following steps:

[0047] Step 1: Treat the design parameter l n , l c 、r c 、r n Perform sensitivity analysis; the specific sensitivity analysis process in this embodiment is as follows:

[0050] Step 1.1: Perform finite element simulation on the target structure through COMSOL to determine the design parameters. n , l c 、r c 、r n Range, randomly generate 100 sets of data points in the space of input parameters.

[0051] The value ranges of the geometric parameters are shown in Table 1:

[0052]

[0053] Set Δx to 0.01 mm, and for each set of data points (l n ,l c ,r c ,r n ), using COMSOL Multiphysics with MATLAB joint simulation to batch obtain the sound absorption coefficient curve α(l within 0-700Hz n ,l c ,rc ,r n ), α(l n +Δx,l c ,r c ,r n ), α(l n ,l c +Δx,r c ,r n ), α(l n ,l c ,r c +Δx,r n ), α(l n ,l c ,r c ,r n +Δx).

[0054] Step 1.3, customize MATLAB script to perform sensitivity analysis; specifically calculate the sensitivity coefficients of the four parameters in each set of data points; then statistically calculate the average value of 100 sets of sensitivity results for each parameter, and create a graphical report; the sensitivity analysis of this embodiment is as follows Figure 5 As shown, the sensitivity from low to high is l c , l n 、r c 、r n .

[0055] Step 2: Construct a data set for the training process: establish a data set of acoustic metamaterial structural parameters and their corresponding sound absorption coefficients within a fixed frequency band.

[0056] First, the acoustic-electric analogy formula analysis method is used for design calculation; the acoustic-electric analogy is to use the analogy method to correspond the physical phenomena in the acoustic system with the physical phenomena in the electrical system, so as to use circuit theory to analyze the acoustic system. Figure 3 As shown, the neck can be regarded as a mass element M a , the cavity can be regarded as the acoustic volume C a ; When in resonance or resonance, the system will vibrate at a specific frequency. At this time, the neck will play a major role in acoustic energy loss due to viscous damping and heat conduction, which is similar to the resistor R in the circuit. a .

[0057] In this embodiment, the calculation process of the sound absorption coefficient of the sound absorption unit is as follows:

[0058] Acoustic impedance Z HR =R a +jX a

[0059] Resonator acoustic impedance Resonator Acoustic Reactance

[0060] Compliance Sound quality

[0061] Where S n is the cross-sectional area of ​​the neck n =πr n 2 , ρ is the air density, η is the air viscosity, ω is the angular frequency, V is the cavity volume V = π (r c 2 l RC -r n 2 l N ), l RC is the corrected cavity height, l N is the effective length of the neck, l N = l n +1.7r n , is the cross-sectional area of ​​the neck n The cross-sectional area of ​​the cavity S c Ratio

[0062] Z HR You can also use the normalized acoustic resistance R HR =R a S c / z0 and normalized acoustic reactance X HR =X a S c / z0 is as follows:

[0063] Z HR = z0(R HR +jX HR )

[0064]

[0065]

[0066] The characteristic impedance of air z0 = ρc, the wave number in the cavity k = ω / c

[0067] Sound absorption coefficient

[0068] In order to verify the validity of the formula analysis, the numerical results of the sound absorption coefficient curve obtained by finite element simulation are compared with the results of the formula analysis, such as Figure 4 shown.

[0069] Then construct a data set. The data set elements include randomly generated geometric parameters within the parameter size range and the sound absorption coefficient α within a fixed frequency band; in this embodiment, the frequency range is fixed between 0-700Hz, with a step size of 0.5, and the data set is generated through a MATLAB script. Specifically, the sound absorption coefficient at each frequency point is used as a feature, and each set of data contains 1400 sound absorption coefficient features and the corresponding geometric parameters L, l n , l c 、r c 、r n ; Preprocess the input features before network training. Specifically, use the reshape function to reconstruct the one-dimensional input data into a two-dimensional convolutional layer processing format: N×1×1, where N is the number of input features of the network.

[0070] Step 3: Construct a prediction network based on convolutional neural networks; the basic convolutional neural network model structure of each module is as follows: Figure 6 In this embodiment, the cascade step-by-step prediction model A consists of three parts, namely prediction modules M1, M2, and M3; c and l n The sensitivity is significantly lower than r c 、r n , prediction module M1 predicts l n and l c , whose input is the sound absorption coefficient α and L corresponding to the fixed frequency range, the number of input features of the M1 network is N = 1401; the prediction module M2 predicts r c , whose input is the sound absorption coefficient α and l corresponding to the fixed frequency range n , l c , the number of input features of the M2 network is N = 1402; the prediction module M3 predicts r n , whose input is the sound absorption coefficient α and l corresponding to the fixed frequency range n , l c 、r c , the number of input features of the M2 network is N=1403. In this embodiment, detailed information of the component layer parameters of the specific models of M1, M2, and M3 is shown in Table 2.

[0071] Table 2

[0072]

[0073] The network model parameters were adjusted for different parameters to obtain the network model with the lowest validation error for each parameter; the model hyperparameters were set as follows: the optimization algorithm was specified as Adam, the MaxEpochs of training was 50, the number of samples used in each iteration was MiniBatchSize was 256, and the initial learning rate was set to 10 -5, use cycle-by-cycle learning rate reduction, LearnRateDropFactor is 0.2, LearnRateDropPeriod is 20, and set shuffle data before each epoch.

[0074] Step 4: Cascade each prediction module; write a MATLAB script to realize the cascade of each prediction module. A specific set of feature inputs 1 is the target sound absorption coefficient spectrum and L. After data preprocessing, input M1 to obtain the prediction parameter l n ' and l c ', then construct input 2, i.e. the target sound absorption coefficient spectrum and l n ' and l c ', similarly, after data preprocessing, input M2 to obtain the prediction parameter r c ', finally construct input 3, i.e. the target sound absorption coefficient spectrum and l n '、l c ' and r c ', after data preprocessing, input M3 to obtain the prediction parameter r n '. The cascaded step-by-step prediction model A is as follows Figure 7 shown.

[0075] Step 5, test the prediction model; input the sound absorption response spectrum of the test set into the overall model for prediction, and use the mean absolute error (MAE) as an indicator to measure the difference between the model prediction results and the actual parameters; where x i is the actual parameter, x i ' is the prediction parameter;

[0076] In this embodiment, a single network is trained to predict the overall prediction model B of all parameters; the prediction model B and the cascaded step-by-step prediction model A have the same basic network structure in each module and are trained using the same data set. The network input is the sound absorption coefficient α and the device height L, and the output is l n , l c 、r c 、r n . Train the step-by-step prediction model C. The step-by-step prediction model C does not predict in sequence according to the parameter sensitivity order; its network model structure is the same as the step-by-step prediction model A. Model M1 predicts r n , whose input is the sound absorption coefficient α and L corresponding to the fixed frequency range, the number of input features of the M1 network is N = 1401; model M2 predicts r n , whose input is the sound absorption coefficient α and r corresponding to the fixed frequency range c , the number of input features of the M2 network is N = 1402; model M3 predicts l n , l c , whose input is the sound absorption coefficient α and r corresponding to the fixed frequency range n、r c , the number of input features of the M2 network is N=1404; each prediction module uses the same network structure and hyperparameters and is trained on the same dataset.

[0077] Compare the MAE of the cascaded step-by-step prediction model A and the overall prediction model B on the same prediction task, such as Figure 8 (a) shows the MAE of the cascaded step-by-step prediction model A and the cascaded step-by-step prediction model C (not predicted in sequence according to parameter sensitivity) on the same prediction task. Figure 8 (b) as shown.

[0078] Comparing the sound absorption curve of the predicted parameters with the sound absorption curve of the actual parameters can intuitively evaluate the prediction performance of the model; the four groups of random parameters are compared. Fig. 9 As shown, Figure (a) is a comparison diagram of the actual sound absorption curve of four random sets of parameters, the sound absorption curve predicted by the cascaded step-by-step prediction model A, and the sound absorption curve predicted by model B; Figure (b) is a comparison diagram of the actual sound absorption curve of four random sets of parameters, the sound absorption curve predicted by the cascaded step-by-step prediction model A, and the sound absorption curve predicted by the cascaded step-by-step prediction model C (not predicted in sequence according to the parameter sensitivity ranking); it can be seen from the figure that the sound absorption curve error is smaller after step-by-step prediction using the same convolutional network model, and is closer to the target sound absorption curve; and the prediction performance of the step-by-step prediction model based on sensitivity is better, and the model prediction value is closer to the actual value.

[0079] The present invention provides a deep learning low-frequency sound absorption metamaterial step-by-step inverse design method considering sensitivity. By performing sensitivity analysis on each structural parameter, multiple network modules are trained to predict structural parameters of different sensitivity levels. The network module that predicts high-sensitivity parameters assists in predicting parameters (low-sensitivity prediction parameters) at the network input end to improve the prediction accuracy, that is, the greater the influence of the parameters on the sound absorption response, the higher the accuracy of the prediction parameter module is ensured. The problem that the inverse design network does not always converge due to multiple mappings is effectively solved, and the rapid prediction of the target sound absorption response structure is effectively achieved to the greatest extent.

[0080] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A deep learning step-by-step inverse design method for low-frequency sound-absorbing metamaterials considering sensitivity, characterized by: The method specifically comprises the following steps: Step 1: Conduct sensitivity analysis on the structural parameters to be designed; Step 2, establishing a data set of acoustic metamaterial structural parameters and the sound absorption coefficient corresponding to the fixed frequency band; Step 3: train different prediction modules according to parameters with different sensitivities, and optimize network parameters of different prediction modules; Step 4: The prediction models after cascade optimization form a complete cascade step-by-step prediction model A; Step 5: Use the test dataset to evaluate the generalization ability and performance of the cascaded step-by-step prediction model A.

2. The step-by-step inverse design method of low-frequency sound-absorbing metamaterials by deep learning considering sensitivity according to claim 1, characterized in that: The step 1 of performing sensitivity analysis on the structural parameters to be designed specifically comprises the following steps: Step 1.1, determine the value range of the input parameters according to the specific design requirements, perform finite element simulation on the target structure, and randomly generate multiple groups of data points of each parameter value within the value range of the design parameters; Step 1.2, for each set of data points generated in step 1.1, calculate its sensitivity; Step 1.3: Calculate the average value of the sensitivity results of all data points to evaluate the overall sensitivity and uncertainty, customize the MATLAB script for sensitivity analysis, and create a graphical report to intuitively obtain the sensitivity relationship between geometric parameters and structural sound absorption coefficient, and sort the design parameters according to sensitivity.

3. The sensitivity-considered deep learning low-frequency sound-absorbing metamaterial step-by-step inverse design method according to claim 2, characterized in that: The step 1.2 of calculating the sensitivity specifically comprises the following steps: Step 1.2.1, for each set of data points (x1, x2, ..., x i ,x i+1 ,...,x n ), calculate the sound absorption coefficient spectrum α(x1,x2,...,x i ,x i+1 ,...,x n ) as the benchmark solution; Step 1.2.2: Let the structural parameter x i There is a perturbation Δx, and the difference format is used to calculate the effect of α on the design variable parameter x i The approximate derivative of Wherein, i=1,2,...,n, and α represents the sound absorption coefficient spectrum.

4. The step-by-step inverse design method of low-frequency sound-absorbing metamaterials by deep learning considering sensitivity according to claim 1, characterized in that: In step 3, different prediction modules are trained for parameters with different sensitivities, specifically including the following steps: Step 3.1: Determine the prediction task of each prediction module based on the results of the sensitivity analysis in step 1. For the parameter with the lowest sensitivity, the corresponding prediction module is set as the most basic prediction unit. This prediction module only accepts known features as input, and no additional auxiliary prediction parameters are required. As the sensitivity of the parameter increases, the auxiliary prediction parameter, i.e., the output result of the previous prediction module, is added to the input of the prediction module to improve the prediction accuracy. Step 3.2: Define the convolutional neural network model and adjust the network layer parameters according to the design tasks of each prediction module; Step 3.3: Use the same training set to train each prediction module, and adjust the hyperparameters for different modules to obtain the network module with the lowest validation error for each parameter.

5. The step-by-step inverse design method of low-frequency sound-absorbing metamaterials by deep learning considering sensitivity according to claim 1, characterized in that: In step 4, the cascaded step-by-step prediction model A is composed of prediction modules M1, M2, M3, ..., Mn for each parameter. The acquisition process of the cascaded step-by-step prediction model A is as follows: a MATLAB script is written to realize the cascade of each prediction module, a set of features is predicted through the first-level prediction module M1 to predict the parameter with the lowest sensitivity, and the next-level module adds the output parameters of the previous-level module as the input data of this module based on the input data of the previous-level module, and the cascade of all modules is completed in sequence.

6. The step-by-step inverse design method of low-frequency sound-absorbing metamaterials by deep learning considering sensitivity according to claim 1, characterized in that: The step 5 of evaluating the generalization ability and performance of the cascaded step-by-step prediction model A refers to selecting the mean absolute error as an indicator to measure the difference between the prediction results of the step-by-step prediction model A and the actual parameters. Specifically, the sound absorption response spectrum of the test data is input into the overall model for prediction, and the mean absolute error is used as an indicator to measure the difference between the model prediction results and the actual parameters, and multiple groups of prediction parameters are randomly selected to compare the sound absorption coefficient curve of the predicted structure with the target sound absorption coefficient curve to verify the actual prediction situation of the cascaded step-by-step prediction model A. where x i is the actual parameter, x′ i is the prediction parameter.

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