Nanofiber bidirectional prediction method based on variational auto-encoder deep learning

Abstract

The invention discloses a nanofiber bidirectional prediction method based on deep learning of a variational auto-encoder. The method comprises the steps that macrostructure parameter samples of nanofibers are generated, then the bidirectional mapping relation between macrostructure parameters and sound absorption coefficients is constructed, and a data set containing physical information is generated; a VAE-PINN deep learning integrated model is established, the model comprises a variational self-encoding module and a physical constraint item, the physical constraint item is added into a total loss function, and stable training of bidirectional mapping is achieved; and through the trained model, forward rapid prediction of the nanofiber sound absorption coefficient and physical consistent reverse design of macrostructure parameters under the target sound absorption performance are realized. Compared with a traditional numerical simulation or pure neural network method, the model has the advantages that the stability and interpretability of understanding are remarkably improved while high calculation efficiency is kept, high-precision two-way design can be achieved under the physical constraint condition, and the method is suitable for intelligent optimization and engineering rapid design of multiple types of nanofiber sound absorption materials.

Description

TECHNICAL FIELD

[0001] The application relates to a nanofiber bidirectional prediction method, and relates to the field of nanomaterial acoustic performance prediction and design, in particular to a nanofiber bidirectional prediction method based on a variational autoencoder deep learning. BACKGROUND

[0002] Nanofibers are widely used in noise control, architectural acoustics and other fields due to their large specific surface area, controllable pore structure and excellent sound absorption performance. The sound absorption performance of nanofibers is mainly determined by five macroscopic structure parameters. Different parameter combinations may produce similar sound absorption coefficient curves, resulting in a "multiple solution" problem.

[0003] Existing nanofiber sound absorption coefficient calculation methods mainly include the following two types: 1. Empirical formula method (such as Delany-Bazley model, porous material acoustics JCA (Johnson-Champoux-Allard) model): This method relies on a large number of experimental regression empirical relationships. Although the calculation is fast, the scope of application is limited, and the required macroscopic structure parameters often need to be obtained with the help of precision instruments, increasing the experimental cost. 2. Numerical simulation method (such as finite element method, boundary element method): This method is based on physical modeling and has high accuracy and interpretability, but it needs to construct a complex three-dimensional geometric model and boundary conditions, and the calculation process is time-consuming. A single set of parameters may take several hours to calculate, making it difficult to meet the needs of rapid iteration and large-scale batch design in engineering.

[0004] In recent years, deep learning methods have been gradually applied to material sound absorption performance prediction and design. Existing researches mostly use deep neural network DNN, convolutional neural network CNN or traditional autoencoder AE models. Although certain effects have been achieved in the forward prediction of "structure parameters → sound absorption coefficient", there are still the following shortcomings: 1. Lack of reverse design capability: Most methods can only complete the one-way calculation of "given parameters → predicted sound absorption coefficient", and cannot realize the reverse design of "giving the target sound absorption curve as needed → calculating the optimal parameters", limiting its application value in actual engineering; 2. Difficulty in handling one-to-many problems: The same sound absorption curve often corresponds to multiple sets of parameters. Deep neural networks and other methods can only give a single solution, which cannot cover all potential feasible solutions, resulting in insufficient design flexibility; 3. Low effectiveness of training samples: Existing methods do not fully combine the physical characteristics and parameter constraints of nanofibers, resulting in redundant or physically infeasible samples in the training data, reducing the generalization ability and engineering applicability of the model; 4. Not robust to noise and experimental data: The performance of some methods significantly decreases when facing actual measurement data, making it difficult to directly combine with experiments.

[0005] Therefore, there is an urgent need for a nanofiber sound absorption coefficient prediction and reverse design method that takes into account efficient calculation, bidirectional prediction (forward and reverse), multi-solution processing capability, physical constraint guidance, and strong generalization, in order to overcome the shortcomings of existing technologies in terms of calculation efficiency, design flexibility, and engineering applicability. SUMMARY

[0006] In order to solve the problems in the background art, the present application provides a nanofiber bidirectional prediction method based on variational autoencoder deep learning. The present application is suitable for rapid prediction of the performance of nanofiber sound absorption materials and reverse structural parameter design, solving the problems of low calculation efficiency, lack of reverse design capability, and poor physical consistency in traditional nanofiber sound absorption performance prediction methods. Based on the variational autoencoder VAE deep learning architecture, the present application innovatively introduces the acoustic physical constraint module PINN, embeds the acoustic theoretical equation in the loss function, and embeds the acoustic equation and boundary conditions in the network training process, realizing the physical consistency constraint of the model learning process, thereby effectively solving the problems of solution space divergence and unstable reverse design in pure data-driven models. The method establishes a bidirectional mapping relationship between "macroscopic structural parameters and sound absorption coefficients", combines the "data-driven learning" and "physical law guidance" mechanisms, and can realize both forward rapid prediction of nanofiber sound absorption performance and physically consistent reverse design of structural parameters under the target sound absorption curve.

[0007] The technical scheme adopted by the present application is: The nanofiber bidirectional prediction method based on variational autoencoder deep learning of the present application is characterized by comprising: First, generate a number of nanofiber macroscopic structural parameter samples that satisfy physical feasibility; obtain the theoretical sound absorption coefficient of each macroscopic structural parameter sample based on a simplified flexible frame model, thereby establishing a bidirectional mapping relationship between macroscopic structural parameters and sound absorption coefficients, and generating a data set containing physical information.

[0008] Second, establish a deep learning integrated model based on the physically informed variational autoencoder VAE-PINN (Variational AutoEncoder-Physics Informed Neural Networks), introduce the acoustic physical equation residual as the physical constraint loss term of the deep learning integrated model to construct the total loss function, input the data set into the deep learning integrated model for bidirectional mapping training, realize physically consistent bidirectional mapping model training through joint optimization, until the total loss function converges, and obtain the trained deep learning integrated model.

[0009] In the third step, the macrostructure parameters of the nanofiber to be predicted are input into the trained deep learning integrated model for forward prediction, and the sound absorption coefficient curve is output after processing; the sound absorption coefficient range and frequency interval of the nanofiber to be predicted are input into the trained deep learning integrated model for reverse prediction, and the optimal macrostructure parameters meeting the acoustic physical constraints are output after processing, so as to design the nanofiber, and finally realize the bidirectional prediction of the nanofiber.

[0010] In the first step, the macrostructure parameters include the tortuosity of the nanofiber α , the porosity φ , the viscous characteristic length , the flow resistance rate σ , and the bulk density ρ .

[0011] In the first step, in the simplified flexible frame model, the dynamic density and the bulk modulus used to obtain the theoretical sound absorption coefficient are as follows: ; ;

[0012] ; wherein, is the angular frequency; is the equivalent density of the nanofiber; is the equivalent fluid mass; ρ f is the air density; α is the tortuosity of the nanofiber; φ is the porosity of the nanofiber; σ is the flow resistance rate of the nanofiber; i is the imaginary unit; µ is the dynamic viscosity of air; is the viscous characteristic length of the nanofiber; ρ is the bulk density of the nanofiber; p A is the standard atmospheric pressure; γ is the specific heat ratio of air; is the Planck number.

[0013] In the first step, the data set containing physical information generated according to the bidirectional mapping relationship of the macrostructure parameters and the sound absorption coefficient includes a forward mapping data set and a reverse mapping data set, the forward mapping data set takes the macrostructure parameters as input and takes the theoretical sound absorption coefficient curve in the preset frequency interval as output during training, and the reverse mapping data set takes a plurality of characteristic frequency points uniformly distributed in the theoretical sound absorption coefficient curve in the preset frequency interval as input and takes the macrostructure parameters as output during training.

[0014] In the second step, the deep learning integrated model based on the physical information constraint variational autoencoder VAE-PINN includes an input layer, an encoder, a hidden latent layer, a decoder and an output layer connected in sequence.

[0015] In the second step, the total loss function L As follows: ; Wherein, L recon The mean square error MSE reconstruction loss is And The first and second weights are respectively L KL The K divergence term is L phys The physical constraint loss term is the acoustic equation residual of the simplified flexible framework model, and is used to ensure the physical consistency of the prediction result.

[0016] In the third step, during forward prediction, the macrostructure parameters of the nanofiber to be predicted are input, the macrostructure parameters are within the preset parameter range, are normalized after being processed in the deep learning integrated model after training, are mapped into a latent space vector by the encoder, and the sound absorption coefficient values of a plurality of characteristic frequency points are output by the decoder, and then the sound absorption coefficient curve is generated after the sound absorption coefficient values of the plurality of characteristic frequency points are recovered to the physical order of magnitude through inverse normalization; during reverse prediction, the sound absorption coefficient range and the frequency interval of the nanofiber to be predicted are input, the sound absorption coefficient values of a plurality of characteristic frequency points are selected in the hidden latent through a grid search method in the deep learning integrated model after training, and then the sound absorption coefficient values of the plurality of characteristic frequency points are mapped into a plurality of groups of candidate macrostructure parameters by the decoder, the plurality of groups of candidate macrostructure parameters are input into the simplified flexible framework model for processing, so that the optimal macrostructure parameters are screened out, and the physical consistent reverse design from the sound absorption performance to the structure parameters is realized.

[0017] The beneficial effects of the present application are: The method of the application is based on a physical information constraint variational autoencoder VAE-PINN architecture, realizes the integration function of "sound absorption coefficient forward prediction + macro structure parameter reverse design" of nanofiber, and has high precision and physical consistency. Compared with the traditional numerical simulation method which only relies on empirical formula or one-way calculation, the acoustic equation of the flexible framework model is embedded in the network training process in the application, and the prediction results of the model are optimized by "reconstruction error + KL divergence + physical constraint residual" joint optimization, so that the model prediction results are more consistent with the acoustic law, and the reverse design is more stable. The parameter calculation time of the method is less than 0.1 s, which is significantly faster than the traditional numerical simulation method, and can support batch design and parameter optimization; the prediction error MSE of the model is less than 0.001, the determination coefficient R 2 >0.98, and good generalization ability and scalability are shown in different material and structure parameter ranges. At the same time, the VAE-PINN model has self-adaptive error correction ability, which can dynamically balance the data-driven and physical constraint terms in the training process, and can maintain the prediction stability without manual intervention. The application can be directly integrated into the sound absorption material design and simulation platform, and provides reliable technical support for efficient intelligent design and performance prediction of nanofiber sound absorption structure, and has significant engineering application value.

[0018] Compared with the traditional numerical simulation or pure neural network method, the model of the application can realize high-precision bidirectional design under the condition of physical constraint while maintaining high computational efficiency, and is suitable for intelligent optimization and engineering rapid design of multiple types of nanofiber sound absorption materials. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The figure is a flowchart of the method of the application; Figure 2 The figure is a schematic diagram of the forward prediction neural network architecture of the application; Figure 3 The figure is a schematic diagram of the reverse design neural network architecture of the application; Figure 4 The figure is a flowchart of the model training process of the application; Figure 5 The figure is a loss value change graph in the training process of the application; Figure 6 The figure is a comparison graph of the nanofiber sound absorption coefficient results and theoretical values predicted by the model of the application selected from four groups of structure parameters, wherein, Figure 6 (a) of the figure is a comparison graph of the first group of structure parameter model prediction results and theoretical values of the application, Figure 6 (b) of the figure is a comparison graph of the second group of structure parameter model prediction results and theoretical values of the application, Figure 6 (c) of the figure is a comparison graph of the third group of structure parameter model prediction results and theoretical values of the application, Figure 6(d) is a comparison chart of the fourth group of structural parameter model prediction results and theoretical values of the application; Figure 7 is a comparison chart of the target curve and the reverse designed nanofiber sound absorption coefficient curve of the application. DETAILED DESCRIPTION

[0020] The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] As shown in Figure 1 , the bidirectional prediction method of nanofiber based on variational autoencoder deep learning of the application is as follows: First, generate a number of macro-structure parameter samples of nanofiber that meet physical feasibility by randomly generating and logically arranging and combining acoustic theory constraints; obtain the theoretical sound absorption coefficient of each macro-structure parameter sample based on the simplified flexible framework model, thereby constructing the bidirectional mapping relationship between macro-structure parameters and sound absorption coefficient, and generating a data set containing physical information.

[0022] The macro-structure parameters include tortuosity α , porosity φ , viscous characteristic length , flow resistance rate σ , and bulk density ρ . When generating the macro-structure parameter samples of nanofiber, first, randomly sample 10000 groups of candidate samples of macro-structure parameters within the preset parameter range of macro-structure parameters, then logically arrange and expand the randomly generated candidate samples, first arrange the parameters based on engineering / manufacturing constraints, for example, limit the porosity to the interval (0, 1), the tortuosity > 1, the bulk density and the flow resistance rate meet the manufacturable range; then delete obviously repeated or non-representative samples, increase the sampling density as needed to enhance the boundary solution performance, which can enhance the sample coverage and model generalization ability of the boundary region, thereby generating the final macro-structure parameter samples. After the above screening and expansion, the effective samples that meet the physical and manufacturing constraints are retained, and the typical number is 50000-80000 groups.

[0023] In the simplified flexible framework model, the dynamic density and bulk modulus used to obtain the theoretical sound absorption coefficient are as follows: ; ;

[0024] ; wherein, is the angular frequency; equivalent density of the nanofiber; equivalent fluid mass; ρ f air density; α tortuosity of the nanofiber; φ porosity of the nanofiber; σ flow resistivity of the nanofiber; i imaginary unit; µ kinetic viscosity of air; viscous characteristic length of the nanofiber; ρ bulk density of the nanofiber; p A standard atmospheric pressure; γ ratio of specific heat of air; Planck number.

[0025] In the data set containing physical information generated according to the bidirectional mapping relationship of the macroscopic structure parameters and the sound absorption coefficient, the forward mapping data set takes the macroscopic structure parameters as the input and the theoretical sound absorption coefficient curve in the preset frequency interval as the output, and specifically, the frequency interval of 500-6400 Hz can be adopted; the reverse mapping data set takes the several characteristic frequency points uniformly distributed in the theoretical sound absorption coefficient curve in the preset frequency interval as the input, and specifically, the sound absorption coefficients at the 256 characteristic frequency points can be adopted, and takes the macroscopic structure parameters as the output. All data are processed by Min-Max standardization to map the parameter values to the interval [0, 1] to eliminate the dimension effect, and finally form the training data set containing physical information.

[0026] Secondly, a deep learning integrated model based on the physical information constraint variational autoencoder VAE-PINN is established, the acoustic physical equation residual is introduced as the physical constraint loss term of the deep learning integrated model to construct the total loss function, the data set is input into the deep learning integrated model for bidirectional mapping training, and the physically consistent bidirectional mapping model training is realized through joint optimization until the total loss function converges, and the trained deep learning integrated model is obtained.

[0027] As Figure 2 and Figure 3As shown, the deep learning integrated model based on the physical information constrained variational autoencoder VAE-PINN includes an input layer, an encoder, a hidden latent layer, a decoder, and an output layer connected in sequence; the input layer is 5 macroscopic structure parameters during forward prediction and 256 frequency points of sound absorption coefficients during reverse prediction; the encoder includes 2 fully connected layers with node numbers of 512 and 128 respectively, and the activation function is ReLU; the dimension of the hidden latent layer is 64, realizing feature mapping of the parameters and the sound absorption coefficients; the decoder includes 2 fully connected layers with node numbers of 128 and 512 respectively, and the activation function is ReLU; the output layer is 256 frequency points of sound absorption coefficients during forward prediction and 5 macroscopic structure parameters during reverse prediction. Among them, μ is the mean of the normal distribution, and log σ 2 is the logarithm of the variance of the normal distribution, ε is a random noise sampled from a standard normal distribution, z is the final latent vector. The VAE-PINN network is built in the structure of “input layer-encoder-latent layer-decoder-output layer-physical constraint module”. In the data preprocessing stage, normalization and cross-validation mechanism are adopted, the initial learning rate of the model is set to 0.001, the batch size is 128, the Adam optimization algorithm is used for training, and learning rate decay is introduced to speed up convergence.

[0028] The loss function is composed of “reconstruction error MSE + KL divergence + physical constraint residual term”, wherein the physical constraint residual term is based on the acoustic equation residual of the simplified flexible frame model, and is used to guide the network prediction result to meet the physical law. The total loss function L is as follows: ; wherein, L recon is the mean square error MSE reconstruction loss; and are the first and second weights respectively; L KL is the K divergence term; L phys is the physical constraint loss term, i.e. the acoustic equation residual of the simplified flexible frame model, which is used to ensure the physical consistency of the prediction result.

[0029] The physical constraint module of the model setting, namely the PINN constraint, is based on the acoustic equation of the established simplified flexible frame model. The physical consistency correction of the network output is realized by introducing the acoustic equation residual term in the loss function. The model parameters are optimized through back propagation to improve the physical consistency of the prediction results and the stability of the inverse design while maintaining high computational efficiency. When the mean square error (MSE) of the training set and the validation set is less than 0.001 and there is no obvious decline in the last 10 batches (epochs), the training is stopped and the optimal model parameters are saved.

[0030] As shown in FIG. 4, the training loss and the validation loss in the model training process are stably decreased with the number of iterations. After about 100 iterations, they tend to converge. The mean square error (MSE) of the training set and the validation set is less than 0.001, as shown in FIG. 4, indicating that the model has high prediction accuracy and stability. Figure 5 In practical applications, the user can input the macro-structure parameters of the designed nanofiber to quickly obtain its sound absorption coefficient curve in the target frequency range through the trained model, realizing forward prediction. Conversely, by inputting the target sound absorption coefficient data, the model can search and output the corresponding macro-structure parameters in the latent variable space, realizing inverse design, and greatly improving the design efficiency and accuracy.

[0031] In the third step, the macro-structure parameters of the nanofiber to be predicted are input into the trained deep learning integrated model for forward prediction, and the sound absorption coefficient curve is output after processing. The sound absorption coefficient range and frequency interval of the nanofiber to be predicted are input into the trained deep learning integrated model for inverse prediction, and the optimal macro-structure parameters that meet the acoustic physical constraints are output after processing, to design the nanofiber. Finally, the bidirectional prediction of the nanofiber is realized.

[0032] In forward prediction, the macrostructure parameters of the nanofiber to be predicted are input, the macrostructure parameters are within the preset parameter range, are normalized after the deep learning integrated model trained is completed, are mapped to a latent space vector by an encoder, are output by a decoder, and then are restored to a physical order of magnitude after inverse normalization to generate an absorption coefficient curve of a plurality of characteristic frequency points. In reverse prediction, the absorption coefficient range and frequency interval of the nanofiber to be predicted are input, the absorption coefficient values of a plurality of characteristic frequency points are selected in the hidden latent by a grid search method in the deep learning integrated model trained, specifically, a step of 0.01 can be used, the characteristic vector closest to the target absorption curve is used as the absorption coefficient value, and then the characteristic vector is mapped to a plurality of groups of candidate macrostructure parameters by the decoder. The plurality of groups of candidate macrostructure parameters are input into the simplified flexible frame model for processing to obtain a deviation of a theoretical absorption coefficient from a target range and an acoustic equation residual value, and a parameter group that simultaneously satisfies the target absorption coefficient interval and has a minimum corresponding physical residual is obtained. If there are multiple groups of solutions that satisfy the condition, the first five groups of candidate parameters are output from high to low according to a prediction correlation coefficient R 2 , and the optimal macrostructure parameters are screened out to realize physical consistent reverse design from the sound absorption performance to the structure parameters.

[0033] In the embodiment of the present application, the nanofiber structure parameter selection range is shown in Table 1 as follows: Table 1

[0034] Now input four groups of structure parameters to compare the model prediction value and the theoretical calculation value, and the four groups of structure parameters are shown in Table 2 as follows.

[0035] In the embodiment of the present application, after the nanofiber deep learning model is trained, the known structure parameters are input into the model, and the output result is the predicted absorption coefficient curve of the nanofiber. After comparison with the theoretical absorption curve, it is proved that the model can correctly predict the absorption coefficient of the nanofiber, as shown in Figure 6 (a) of FIG. 1, Figure 6 (b) of FIG. 1, Figure 6 (c) of FIG. 1, and Figure 6 (d) of FIG. 1.

[0036] According to the trained VAE-PINN deep learning model, the absorption coefficient curve data in the specified range is input into the model. The output result is the macrostructure parameters of the nanofiber, as shown in Table 3. The calculated nanofiber absorption coefficient of the obtained parameters is consistent with the actual absorption coefficient, verifying the reliability of the reverse design, as shown in Figure 7 .

[0037] Table 2

[0038] Table 3

[0039] The above description is merely that of the preferred embodiments of the application, and is not intended to limit the scope of the application. Any changes and modifications that can be made by one of ordinary skill in the art to the applications described herein must be within the spirit and technical scope of the application, and the changes and modifications are intended to be included in the protection range of the application. Therefore, the protection range of the application should be subject to the protection range of the claims. The information disclosed in the background section is merely intended to deepen the understanding of the general background of the application, and should not be regarded as acknowledging or implying in any form that the information constitutes the prior art known to those skilled in the art.

Claims

1. A method for bidirectional prediction of nanofibers based on variational autoencoder deep learning, characterized in that, include: The first step is to generate several samples of macroscopic structural parameters for nanofibers that meet physical feasibility requirements. The theoretical sound absorption coefficients of various macroscopic structural parameter samples are obtained based on a simplified flexible framework model, thereby constructing a two-way mapping relationship between macroscopic structural parameters and sound absorption coefficients, and generating a dataset containing physical information. The second step is to establish a deep learning integrated model based on the physical information-constrained variational autoencoder VAE-PINN, introduce the acoustic physical equation residual as the physical constraint loss term of the deep learning integrated model to construct the total loss function, input the dataset into the deep learning integrated model for bidirectional mapping training until the total loss function converges, and obtain the trained deep learning integrated model. The third step involves inputting the macroscopic structural parameters of the nanofiber to be predicted into the trained deep learning integrated model for forward prediction, and outputting the sound absorption coefficient curve after processing. The sound absorption coefficient range and frequency interval of the nanofiber to be predicted are input into the trained deep learning integrated model for inverse prediction, and outputting the optimal macroscopic structural parameters that satisfy acoustic physical constraints after processing, so as to design the nanofiber and ultimately realize the bidirectional prediction of the nanofiber.

2. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the first step, the macroscopic structural parameters include the tortuosity α, porosity φ, viscous characteristic length Ʌ, flow resistance σ, and bulk density ρ of the nanofibers.

3. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the first step, the dynamic density used in the simplified flexible frame model to obtain the theoretical sound absorption coefficient is... and bulk modulus as follows: ； ； ； ； in, Angular frequency; This represents the equivalent density of the nanofibers. For equivalent fluid mass; ρ f ρ is the air density; α is the tortuosity of the nanofiber; φ is the porosity of the nanofiber; σ is the flow resistance of the nanofiber; i is the imaginary unit; µ is the dynamic viscosity of air; Ʌ is the viscous characteristic length of the nanofiber; ρ is the bulk density of the nanofiber; p A γ is the standard atmospheric pressure; γ is the specific heat ratio of air. It is the Planck number.

4. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the first step, the dataset containing physical information generated based on the bidirectional mapping relationship between macroscopic structural parameters and sound absorption coefficient includes a forward mapping dataset and a reverse mapping dataset. The forward mapping dataset takes macroscopic structural parameters as input and the theoretical sound absorption coefficient curve within a preset frequency range as output during training. The reverse mapping dataset takes several characteristic frequency points evenly distributed in the theoretical sound absorption coefficient curve within the preset frequency range as input and the macroscopic structural parameters as output during training.

5. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the second step, the deep learning integrated model based on the physical information constrained variational autoencoder VAE-PINN includes an input layer, encoder, hidden latent layer, decoder and output layer connected in sequence.

6. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the second step, the total loss function L is as follows: ； Among them, L recon The mean square error (MSE) is used to reconstruct the loss. and The first and second weights are respectively; L KL For K divergence term; L phys This is the physical constraint loss term, which is the acoustic equation residual of the simplified flexible frame model.

7. The method for bidirectional prediction of nanofibers based on variational autoencoder deep learning according to claim 1, characterized in that: In the third step, during forward prediction, the macroscopic structural parameters of the nanofiber to be predicted are input, normalized in the trained deep learning integrated model, mapped to a latent space vector by the encoder, and the sound absorption coefficient values ​​of several feature frequency points are output by the decoder. After inverse normalization, the sound absorption coefficient curve is generated. During reverse prediction, the sound absorption coefficient range and frequency interval of the nanofiber to be predicted are input, and the sound absorption coefficient values ​​of several feature frequency points are selected in the hidden latent space by the grid search method in the trained deep learning integrated model. Then, the sound absorption coefficient values ​​of several feature frequency points are mapped to several sets of candidate macroscopic structural parameters by the decoder. Each set of candidate macroscopic structural parameters is input into the simplified flexible framework model for processing, thereby selecting the optimal macroscopic structural parameters.

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