Sensitivity-considered deep learning low-frequency sound absorption metamaterial step-by-step inverse design method

Abstract

The present application belongs to the field of inverse design of acoustic metamaterials, and discloses a deep learning low-frequency sound-absorbing metamaterial step-by-step inverse design method with sensitivity, specifically comprising the following steps: step 1, sensitivity analysis is performed on the structure parameters to be designed; step 2, a data set of acoustic metamaterial structure parameters and corresponding sound absorption coefficients in a fixed frequency band is established; step 3, different prediction modules are trained for parameters with different sensitivities, and the different prediction modules are cascaded and optimized; step 4, the prediction models after cascaded optimization constitute a complete cascaded step-by-step prediction model A; and step 5, the generalization ability and performance of the cascaded step-by-step prediction model A are evaluated using a test model. The present application enhances the generalization ability of the model and improves the prediction accuracy through the step-by-step physical parameter method.

Description

Technical Field

[0001] This invention belongs to the field of reverse design of acoustic metamaterials, specifically involving a step-by-step reverse design method for low-frequency sound-absorbing metamaterials based on deep learning, taking sensitivity into account. Background Technology

[0002] Acoustic metamaterials, by adjusting their structure and shape, achieve precise control over sound wave propagation and reflection, opening up new directions for research in the field of acoustics. In practical scenarios, researchers often expect to quickly obtain the geometric parameters of acoustic metamaterials based on their sound absorption properties. The core issue in acoustic metamaterial design is how to design high-performance artificial structures like acoustic metamaterials to achieve the desired acoustic performance. Traditional forward design methods involve obtaining acoustic response data of the device through simulation or experimentation based on an initial structure, then modifying the parameters of the initial structure based on the response data, and gradually designing the target device through trial and error. However, as the complexity of the device increases, the computational cost and time consumption of the design also increase significantly, making traditional forward design methods insufficient to handle the computational complexity of practical design problems.

[0003] Reverse engineering directly generates the corresponding working structure based on the desired 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, possessing powerful feature extraction, generalization, and complex data processing capabilities. These advantages make them a powerful tool for solving reverse engineering 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 directly affect the impedance characteristics of the device and its effect on sound wave modulation. The interaction between multiple parameters can cause different geometries to have the same sound absorption response curve. This multi-mapping situation can lead to the trained network not always converging, which is a typical problem in reverse 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 cascaded neural network architecture to train the model using the error between the target and predicted absorption spectra in the inverse design of three-dimensional hybrid-sized cavity aqueous acoustic metamaterials. However, the generator part of the cascaded model does not incorporate real structural data during training, which affects the final prediction results. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes an inverse design method for acoustic metamaterials based on sensitivity-enhanced physical mechanisms. Compared to traditional methods, this method enhances the model's generalization ability and improves prediction accuracy through stepwise physical parameter allocation. To achieve the above objectives, this invention is implemented through the following technical solution:

[0005] This invention is a stepwise inverse design method for low-frequency sound-absorbing metamaterials based on deep learning, taking sensitivity into consideration. The method specifically includes the following steps:

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

[0007] Step 2: Establish a dataset of acoustic metamaterial structural parameters and their corresponding sound absorption coefficients within a fixed frequency band;

[0008] Step 3: Train different prediction modules for parameters with different sensitivities, and optimize the network parameters of different prediction modules;

[0009] Step 4: The cascaded optimized prediction models are combined to form a complete cascaded stepwise prediction model A;

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

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

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

[0013] Step 1.2: Calculate the sensitivity for each set of data points generated in Step 1.1;

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

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

[0016] Step 1.2.1: For each generated set of data points (x1, x2, ..., x...), ... i ,x i+1 ,...,x n), calculate the absorption coefficient spectrum α(x1,x2,...,x) within a fixed frequency range. i ,x i+1 ,...,x n () as the benchmark solution;

[0017] Step 1.2.2: Set the structural parameter x of the structure to be designed. i Given a small perturbation Δx, calculate α using a difference scheme with respect to the design variable parameter x. i The approximate derivative, Where 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 0-700Hz, with a step size of 0.5.

[0019] A further improvement of this invention lies in the following: the method for generating the dataset in step 2 includes a formula analysis method based on acoustic-electric analogy and a batch generation method using COMSOL numerical calculations. Acoustic-electric analogy is a method that compares acoustic problems with electromagnetic problems. This method studies acoustic vibration phenomena using circuit theory and circuit diagram analysis. However, the formula analysis method based on acoustic-electric analogy is not suitable for all sound-absorbing structures, especially for some sound-absorbing structures with irregularly shaped sound-absorbing units. For some irregular sound-absorbing structures, COMSOL Multiphysics with MATLAB co-simulation is used: a MATLAB script is used to load the COMSOL model and perform batch scanning. This script's functions include iterating through parameter values, running the COMSOL model solver for each parameter value, generating the required data, integrating and exporting the dataset.

[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: Based on the sensitivity analysis results from Step 1, determine the prediction task of each prediction module. For the parameter with the lowest sensitivity, its corresponding prediction module is set as the most basic prediction unit. This prediction module only accepts known features as input and does not require the introduction of additional auxiliary prediction parameters. As the parameter sensitivity increases, auxiliary prediction parameters, i.e., the output results of the previous stage prediction module, are 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: Train each prediction module using the same training set, and adjust the hyperparameters for different modules to obtain a network module with the lowest validation error for each parameter.

[0024] A further improvement of the present invention is that: in step 4, the cascaded stepwise prediction model A is composed of prediction modules M1, M2, M3...Mn for each parameter. The process of obtaining the cascaded stepwise prediction model A is as follows: write a MATLAB script to implement the cascading of each prediction module. A set of features is predicted by the first-level prediction module M1 to obtain the parameter with the lowest sensitivity. The next level module adds the output parameter of the previous level module to the input data of the previous level module as the input data of the current module, and so on, to complete the cascading of all modules.

[0025] A further improvement of the present invention is that: step 5, evaluating the generalization ability and performance of the cascaded step prediction model A, refers to using the mean absolute error (MAE) as an indicator to measure the difference between the prediction results of the 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, the mean absolute error (MAE) is used as an indicator to measure the difference between the model prediction results and the actual parameters, and multiple sets 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 For actual parameters, x i ' is the prediction parameter.

[0028] The beneficial effects of this invention are as follows: This invention proposes a method for step-by-step inverse design of acoustic metamaterials by analyzing the sensitivity of design parameters and assisting a convolutional neural network. Sensitivity analysis assesses the sensitivity of different parameters to the acoustic response of the model, providing the prediction network with prior knowledge about the acoustic metamaterial. Based on this, a step-by-step superposition of auxiliary parameter inputs is used, avoiding the non-uniqueness of predictions and significantly improving the accuracy of inverse design. Especially in practical applications, it can more clearly guide designers in designing structural parameters under specific requirements, realizing on-demand design applications and greatly improving the flexibility of design. Attached Figure Description

[0029] Figure 1 The flowchart shows the step-by-step acoustic metamaterial inverse design method based on convolutional neural networks provided by this invention.

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

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

[0032] Figure 4 The diagram shows the COMSOL simulation sound absorption coefficient and the sound absorption coefficient calculated by formula derivation in the embodiments of the present invention.

[0033] Figure 5 The above is a sensitivity analysis chart of each parameter in an embodiment of the present invention.

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

[0035] Figure 7 This is a schematic diagram of the inverse design cascaded step prediction model A in an embodiment of the present invention.

[0036] Figure 8 The following are comparison charts of MAE of different prediction models under the same task in the embodiments of the present invention; wherein, (a) is a comparison chart of MAE of cascaded step prediction model A and overall prediction model B under the same task in the embodiments, and (b) is a comparison chart of MAE of cascaded step prediction model A and cascaded step prediction model C under the same task in the embodiments.

[0037] Figure 9 The first image shows a comparison between the target sound absorption curve and the model-predicted sound absorption curve in an embodiment of the present invention; (a) shows a comparison between the predicted sound absorption curves of the cascaded step-by-step prediction model A and the overall prediction model B in an embodiment; and (b) shows a comparison between the predicted sound absorption curves of the cascaded step-by-step prediction model A and the cascaded step-by-step prediction model C in an embodiment. Detailed Implementation

[0038] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0039] like Figure 1 As shown, this invention is a stepwise inverse design method for low-frequency sound-absorbing metamaterials based on deep learning, taking sensitivity into account. The method specifically includes the following steps:

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

[0041] Step 2: Establish a dataset of acoustic metamaterial structural parameters and their corresponding sound absorption coefficients within a fixed frequency band;

[0042] Step 3: Train different prediction modules for parameters with different sensitivities, and perform cascade optimization on the different prediction modules;

[0043] Step 4: The cascaded optimized prediction models form a complete cascaded step prediction model A, which includes prediction module M1, prediction module M2, and prediction module M3.

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

[0045] This embodiment uses the inverse design of a low-frequency sound-absorbing metamaterial unit structure as an example to illustrate the proposed design method. The structure is as follows: Figure 2 As shown, the parameter to be designed is the neck length l n Cavity length l c Cavity radius r c Neck radius r n The height of the unit structure device is L = l. n +l c Given geometric parameters;

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

[0047] Step 1: Determine the design parameters l n l c r c r n Sensitivity analysis was performed; the specific sensitivity analysis process in this embodiment is as follows:

[0048] Step 1.1: Perform finite element simulation of the target structure using COMSOL to determine the design parameters l. n l c r c r n The range is determined by randomly generating 100 sets of data points within the space of the input parameters.

[0049] The range of values ​​for the geometric parameters is shown in Table 1:

[0050]

[0051] Set Δx to 0.01 mm, for each set of data points (l n ,l c ,r c ,r n The sound absorption coefficient curves α(l) within the range of 0-700Hz were obtained in batches using COMSOL Multiphysics with MATLAB co-simulation. n ,l c,r c ,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).

[0052] Step 1.3: Perform sensitivity analysis using a custom MATLAB script; specifically, calculate the sensitivity coefficients of the four parameters in each data point group; then, statistically calculate the average of the 100 sensitivity results for each parameter and create a graphical report; the sensitivity analysis in this embodiment is as follows: Figure 5 As shown, the sensitivity levels from low to high are l c l n r c r n .

[0053] Step 2: Construct a dataset for the training process: Establish a dataset of acoustic metamaterial structural parameters and their corresponding sound absorption coefficients within a fixed frequency band.

[0054] First, the design calculations are performed using the acoustic-electric analogy formula analysis method. Acoustic-electric analogy refers to the method of correlating physical phenomena in an acoustic system with physical phenomena in an electrical system through analogy, thereby utilizing circuit theory to analyze the acoustic system. The acoustic-electric circuit in this embodiment is as follows: Figure 3 As shown, the neck can be considered as a mass element M. a The cavity can be considered as the acoustic volume C. a During resonance or harmonic resonance, the system vibrates at a specific frequency. At this time, due to viscous damping and thermal conduction, the neck region plays a major role in sound energy loss, analogous to the resistance R in a circuit. a .

[0055] In this embodiment, the calculation process of the sound absorption coefficient of the sound-absorbing unit is as follows:

[0056] Acoustic impedance Z HR =R a +jX a

[0057] resonator acoustic impedance resonator acoustic impedance

[0058] Tone order sound quality

[0059] Where S n S is the cross-sectional area of ​​the neck. n =πr n 2 ρ is the air density, η is the air viscosity coefficient, ω is the angular frequency, and V is the cavity volume V=π(r c 2 l RC -r n 2 l N ), l RC It is the correction cavity height. l N It is the effective length of the neck, l N =l n +1.7r n , S is the cross-sectional area of ​​the neck. n With the cross-sectional area S of the cavity c ratio

[0060] Z HR Normalized acoustic impedance R can also be used HR =R a S c / z0 and normalized acoustic impedance X HR =X a S c / z0 is as follows:

[0061] Z HR =z0(R HR +jX HR )

[0062]

[0063]

[0064] Air characteristic impedance z0 = ρc, wavenumber in the cavity k = ω / c

[0065] sound absorption coefficient

[0066] To verify the effectiveness of the formula analysis, the numerical results of the sound absorption coefficient curve obtained from finite element simulation were compared with the results of formula analysis, such as... Figure 4 As shown.

[0067] Then, a dataset is constructed. The dataset elements include randomly generated geometric parameters within a parameter size range and sound absorption coefficients α within a fixed frequency band; in this embodiment, the frequency range is fixed between 0-700Hz with a step size of 0.5. The dataset is generated using a MATLAB script. Specifically, the sound absorption coefficient at each frequency point is considered as a feature, and each dataset contains 1400 sound absorption coefficient features and corresponding geometric parameters L and l. n l c r c r n Before training the network, the input features are preprocessed. Specifically, the reshape function is used 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.

[0068] 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 As shown. In this embodiment, the cascaded stepwise prediction model A consists of three parts: prediction modules M1, M2, and M3; among the design parameters, l c and l n The sensitivity is significantly lower than r c r n Prediction module M1 predicts l n and l c Its inputs are the absorption coefficients α and L within a fixed frequency range, and the number of input features of the M1 network is N = 1401; the prediction module M2 predicts r. c Its inputs are the sound absorption coefficients α and l corresponding to a fixed frequency range. n l c The number of input features N = 1402 for the M2 network; the prediction module M3 predicts r n Its inputs are the sound absorption coefficients α and l corresponding to a fixed frequency range. n l c r c The number of input features of the M2 network is N = 1403. In this embodiment, the detailed information of the component layer parameters of the specific models M1, M2, and M3 is shown in Table 2.

[0069] Table 2

[0070]

[0071] The network model parameters were adjusted for different parameters to obtain a network model with the lowest validation error for each parameter. The model hyperparameters were set as follows: Adam optimization algorithm, MaxEpochs of training set to 50, MiniBatchSize of samples used in each iteration set to 256, and initial learning rate set to 10. -5We used a periodic reduction of the learning rate, with LearnRateDropFactor set to 0.2 and LearnRateDropPeriod set to 20, and set up data shuffling before each epoch.

[0072] Step 4: Cascade the prediction modules; write a MATLAB script to implement the cascading of the prediction modules. Specifically, a set of feature inputs, i.e., the target sound absorption coefficient spectrum and L, are input to M1 after data preprocessing to obtain the prediction parameter l. n 'and l c Next, construct input 2, which is the target sound absorption coefficient spectrum and l n 'and l c Similarly, after data preprocessing, the input to M2 yields the prediction parameter r. c Finally, input 3, namely the target sound absorption coefficient spectrum and l, are constructed. n '、l c 'and r c After data preprocessing, the prediction parameter r is obtained by inputting it into M3. n The cascaded stepwise prediction model A is as follows: Figure 7 As shown.

[0073] Step 5: Test the prediction model; input the 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 true parameters. Where x i For actual parameters, x i ' is the prediction parameter;

[0074] In this embodiment, a single network is trained to predict all parameters of the overall prediction model B. The prediction model B and the cascaded step-by-step prediction model A have the same basic network structure and are trained using the same dataset. Its network inputs are the sound absorption coefficient α and the device height L, and its output is l. n l c r c r n Train a stepwise prediction model C, which predicts sequentially without prioritizing parameter sensitivity; its network model structure is the same as that of the stepwise prediction model A. Model M1 predicts r. n Its inputs are the absorption coefficients α and L within a fixed frequency range, and the number of input features of the M1 network is N = 1401; the model M2 predicts r n Its inputs are the sound absorption coefficients α and r within a fixed frequency range. c The number of input features for the M2 network is N = 1402; the model M3 predicts l n l c Its inputs are the sound absorption coefficients α and r within a fixed frequency range. nr c The M2 network has 1404 input features (N = 1404); each prediction module uses the same network structure and hyperparameters and is trained on the same dataset.

[0075] Comparing the MAE of cascaded stepwise prediction model A and overall prediction model B on the same prediction task, such as... Figure 8 As shown in (a); comparing the MAE of cascaded stepwise prediction model A and cascaded stepwise prediction model C (predicting sequentially without ordering by parameter sensitivity) on the same prediction task, as follows: Figure 8 As shown in (b).

[0076] Comparing the absorption curves of the predicted parameters with those of the actual parameters provides a direct evaluation of the model's predictive performance; four sets of random parameter comparisons, for example... Figure 9 As shown in the figures, Figure (a) is a comparison of the actual sound absorption curves of four random sets of parameters, the sound absorption curves predicted by cascaded step-by-step prediction model A, and the sound absorption curves predicted by model B. Figure (b) is a comparison of the actual sound absorption curves of four random sets of parameters, the sound absorption curves predicted by cascaded step-by-step prediction model A, and the sound absorption curves predicted by cascaded step-by-step prediction model C (predicting in sequence without sorting by parameter sensitivity). It can be seen from the figures that the sound absorption curves with smaller errors and closer to the target sound absorption curves after step-by-step prediction using the same convolutional network model are better. The prediction performance of the step-by-step prediction model based on sensitivity is better, and the model prediction values ​​are closer to the actual values.

[0077] This invention provides a stepwise inverse design method for low-frequency sound-absorbing metamaterials based on deep learning, taking sensitivity into account. By analyzing the sensitivity of various structural parameters, multiple network modules are trained to predict structural parameters at different sensitivity levels. For network modules predicting high-sensitivity parameters, auxiliary prediction parameters (low-sensitivity prediction parameters) are added at the network input to improve prediction accuracy; that is, the greater the influence of a parameter on the sound absorption response, the higher the accuracy of the prediction parameter module. This effectively solves the problem of incomplete convergence of the inverse design network caused by multiple mappings, maximizing the rapid prediction of the target sound-absorbing response structure.

[0078] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A stepwise inverse design method for low-frequency sound-absorbing metamaterials based on deep learning, considering sensitivity, characterized in that: The method specifically includes the following steps: Step 1: Perform sensitivity analysis on the structural parameters to be designed; Step 2: Establish a dataset of acoustic metamaterial structural parameters and their corresponding sound absorption coefficients within a fixed frequency band; Step 3: Train different prediction modules for parameters with different sensitivities, and optimize the network parameters of different prediction modules; Step 4: The cascaded optimized prediction models are combined to form a complete cascaded stepwise prediction model A; Step 5: Use the test dataset to evaluate the generalization ability and performance of the cascaded stepwise prediction model A; Step 3 involves training different prediction modules for parameters with different sensitivities, specifically including the following steps: Step 3.1: Based on the sensitivity analysis results in Step 1, determine the prediction task of each prediction module. For the parameter with the lowest sensitivity, its corresponding prediction module is set as the most basic prediction unit. This prediction module only accepts known features as input and does not need to introduce additional auxiliary prediction parameters. As the parameter sensitivity increases, auxiliary prediction parameters, i.e., the output results of the previous level prediction module, are 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: Train each prediction module using the same training set, and adjust the hyperparameters for different modules to obtain a network module with the lowest validation error for each parameter; The calculation process for the sound absorption coefficient of the sound-absorbing unit is as follows: acoustic impedance resonator acoustic impedance acoustic impedance of resonator , sound sound quality ,in The cross-sectional area of ​​the neck , air density, The viscosity coefficient of air. Angular frequency, It is the volume of the cavity. , It is the correction cavity height. , It is the effective length of the neck. , The cross-sectional area of ​​the neck With the cross-sectional area of ​​the cavity ratio , Also using normalized acoustic impedance and normalized acoustic resistance The result is as follows: Air characteristic impedance wavenumber in the cavity sound absorption coefficient .

2. The step-by-step inverse design method for low-frequency sound-absorbing metamaterials based on sensitivity considerations according to claim 1, characterized in that: Step 1, the sensitivity analysis of the structural parameters to be designed, specifically includes the following steps: Step 1.1: Determine the range of input parameters according to specific design requirements, perform finite element simulation on the target structure, and randomly generate multiple sets of parameter value data points within the range of design parameter values; Step 1.2: Calculate the sensitivity for each set of data points generated in Step 1.1; Step 1.3: Calculate the average value of the sensitivity results for all data points to evaluate the overall sensitivity and uncertainty. Use a custom MATLAB script to perform sensitivity analysis and create a graphical report to intuitively obtain the sensitivity relationship between geometric parameters and the structure's sound absorption coefficient. Sort the design parameters according to their sensitivity.

3. The step-by-step inverse design method for low-frequency sound-absorbing metamaterials based on sensitivity considerations according to claim 2, characterized in that: Step 1.2, calculating the sensitivity, specifically includes the following steps: Step 1.2.1: For each generated set of data points Calculate its sound absorption coefficient spectrum within a fixed frequency range. As a benchmark solution; Step 1.2.2: Adjust the parameters of the structure to be designed. There is a perturbation Calculate using the difference scheme For design variable parameters The approximate derivative, ,in, , This represents the sound absorption coefficient spectrum.

4. The stepwise inverse design method for low-frequency sound-absorbing metamaterials based on deep learning, considering sensitivity, as described in claim 1, is characterized in that: In step 4, the cascaded stepwise prediction model A consists of prediction modules M1, M2, M3, ..., Mn for each parameter. The process of obtaining the cascaded stepwise prediction model A is as follows: a MATLAB script is written to implement the cascading of each prediction module. A set of features is predicted by the first-level prediction module M1 to obtain the parameter with the lowest sensitivity. The next-level module adds the output parameter of the previous-level module to the input data of the previous-level module as the input data of this module, and so on, to complete the cascading of all modules.

5. The step-by-step inverse design method for low-frequency sound-absorbing metamaterials based on sensitivity considerations according to claim 1, characterized in that: Step 5, evaluating the generalization ability and performance of the cascaded step prediction model A, refers to using the mean absolute error as an indicator to measure the difference between the prediction results of the 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. The mean absolute error is used as an indicator to measure the difference between the model prediction results and the actual parameters. Multiple sets 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 the cascaded step prediction model A. ， in For actual parameters, These are the prediction parameters.

Images