Multi-band acoustic topological insulator based on deep learning algorithm and inverse design method thereof

Abstract

The application discloses a multi-band sound topology insulator reverse design method based on a deep learning algorithm, and comprises the following steps: 1) obtaining original structure information data of an insulator; 2) running the insulator in a simulation environment according to the step 1), updating structure information data, and calculating energy band frequency values; 3) combining the original structure information data of the insulator, the updated structure information data and the energy band frequency values into experimental data, training the experimental data by using a deep learning algorithm, and predicting insulator structure parameters; 4) re-modeling the obtained optimal structure parameters, and obtaining an optimal insulator structure. Meanwhile, the application provides a multi-band sound topology insulator. The application uses the deep learning algorithm, uses a trained neural network to reversely predict structure parameters corresponding to an insulator structure model at any desired frequency, and can more quickly realize optimal structure design of the sound topology insulator at the desired frequency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of topological properties of acoustic metamaterials. BACKGROUND

[0002] In recent years, there has been a surge of interest in the study of topological acoustics, with efforts being made to design more complex acoustic topological insulators and expand their range of applications. The performance of phonon topological insulators depends mainly on the geometric parameters of the phonon structure. In traditional design, the geometric parameters are adjusted repeatedly through empirical methods, and a large number of simulation tests are used to observe whether the model achieves good target performance. The performance of phonon topological insulators designed by this method is greatly limited, such as the narrow frequency range in which topological edge states can be achieved and the small quality factor of topological corner states.

[0003] Currently, many scholars have proposed using inverse design methods to solve the technical problems of insulators caused by traditional design, i.e., using algorithm technology to assist in completing the optimal material structure design according to the target performance requirements. Common inverse design techniques include gradient-based methods, evolutionary methods, and deep learning methods. In the past few years, inverse design techniques have been widely used in the design of new photonic and phononic structures, such as photonic and phononic crystals, metamaterials, metasurfaces, and metastructures, and have proven their superiority over traditional empirical design structures in many application scenarios.

[0004] Recently, researchers have begun to apply inverse design techniques to the design of phonon topological insulators, among which deep learning technology is a new design method and physical framework that can be deeply integrated with acoustic topological materials, providing new ideas and approaches for the study and exploration of phonon topological insulators. Currently, inverse design methods have been used in the design of acoustic topological insulators, and the inverse design of phonon topological insulators based on quantum spin Hall effect and quantum valley Hall effect has been used to widen the operable bandwidth of topological edge states. Although some researchers have used inverse design methods to effectively widen the bandwidth of topological edge states, they have not completely abandoned traditional topological optimization methods and still require a large number of training instances, which are created through electromagnetic simulations, requiring a large amount of computing resources and being unable to complete the design of acoustic topological insulators at any desired frequency. SUMMARY

[0005] The present application aims to provide a multi-band acoustic topological insulator inverse design method based on deep learning algorithm, and to provide a multi-band acoustic topological insulator as another object of the present application.

[0006] To achieve the above object, the present application adopts the following technical solutions:

[0007] A multi-band phononic topological insulator reverse design method based on a deep learning algorithm, comprising the following steps:

[0008] 1) obtaining original structure information data of the insulator;

[0009] 2) running the insulator in step 1) in a simulation environment, updating the structure information data, and calculating the energy band frequency value;

[0010] 3) combining the original structure information data of the insulator, the updated structure information data, and the energy band frequency value into experimental data, and adopting a deep learning algorithm to train the experimental data and predict the insulator structure parameters;

[0011] 4) combining the obtained optimal structure parameters to re-model the optimal insulator structure.

[0012] The deep learning algorithm is a CSA-LSTM model algorithm.

[0013] The CSA-LSTM model algorithm comprises the following steps:

[0014] a) data preprocessing;

[0015] b) determining the optimization hyperparameters: initializing the parameters and structure required for the LSTM neural network, including one layer of LSTM hidden layer and one layer of dropout layer; at the same time, determining the optimization hyperparameters and optimization range in the LSTM network model, and selecting the hyperparameters to be optimized;

[0016] c) adopting the CSA algorithm to optimize the hyperparameters to be optimized to obtain the optimal hyperparameters;

[0017] d) automatically assigning the optimal hyperparameters to the LSTM neural network for modeling, and training and predicting the insulator structure parameter data.

[0018] Step a) data preprocessing: after data cleaning and normalization of the insulator structure parameter data, the data is divided into training set and test set.

[0019] A multi-band phononic topological insulator, the insulator comprising a plurality of unit cells uniformly distributed on the same circumference and a cell frame connected to the inside of each unit cell, the cell frame comprising a plurality of base frames, and the tangent point of the unit cell to the circumference coincides with the intersection point of the extension lines of the two sides of the base frame connected to the unit cell.

[0020] The insulator comprises three identical circular structure unit cells and three base frames, and the center of the circumference of the insulator coincides with the center of the cell frame in the scatterer structure.

[0021] The unit cell and the cell frame are in a star-shaped structure.

[0022] A phononic crystal formed by a multi-band acoustic topological insulator includes arrays of unit cells, each array of unit cells being formed by several star-shaped arrays of insulators.

[0023] The rotation angle of each unit cell is θ, and the range of θ is -60° to 60°.

[0024] There are two sets of unit cells, and the rotation angles of the two sets of unit cells are different.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1) This invention uses deep learning algorithms and a trained neural network to reverse predict the structural parameters of the insulator structure model at any desired frequency. This solves the problems of long time required for traditional acoustic topology material design, high loss, and strong dependence on analytical theory and models. It can realize the optimal structural design of acoustic topology insulators at desired frequencies more quickly and has the potential to explore more acoustic characteristics and a larger parameter space in acoustic design tasks, so as to design acoustic transmission devices with ultra-high performance factors.

[0027] 2) This invention uses CSA, which has strong optimization capabilities and good global search capabilities, to improve the defects of LSTM parameter selection. By optimizing hyperparameters such as the learning rate and the number of neurons in the LSTM neural network, the problem of complex parameter optimization in LSTM neural networks is solved, and the accuracy of model prediction is also improved.

[0028] 3) The acoustic topological insulator of this invention has the advantages of a single-structure design with multiple frequency bands, and possesses a wealth of adjustable parameters, including cell radius R and rotation angle. Due to its structural system having C... 3v Symmetry, the deterministic degeneracy caused by band gap closure at the high symmetry point in the first Brillouin zone, the scatterer in the rotating phononic crystal breaks the structural symmetry, thus realizing the Valley Hall phase transition. By flexibly adjusting the valley pseudospin state by rotating the scatterer, when the rotation angle of the scatterer is rotated clockwise from -60° to 60°, the band gap goes through the process of opening-closing-opening, and band inversion occurs, realizing the topological phase transition;

[0029] 4) The acoustic topology insulator designed by the reverse design method of this invention utilizes the principle of bulk-boundary state correspondence to construct boundary states through the connection of different structural systems to simulate edge acoustic transmission protected by the topology. The acoustic transmission characteristics of the topological boundary states are verified by the finite element algorithm, which verifies the effectiveness of the insulator structure designed by the reverse design method of this invention. Moreover, the structure of this invention is simple to process and has a wide range of applications, providing ideas and methods for designing multi-frequency and multi-functional acoustic topology devices with relatively simple single structures. Attached Figure Description

[0030] Figure 1 (a) Honeycomb topological unit of an insulator; (b) Detailed internal structure of an insulator; (c) Multiband energy band structure.

[0031] Figure 2 A conceptual diagram illustrating the design process.

[0032] Figure 3 The sample distribution and learning curve of LSTM, (a) low frequency f1 and high frequency f2 of the target band I after normalization; the color of each square represents the number of data in the frequency range; (b) Loss curve.

[0033] Figure 4 CSA-LSTM model prediction flowchart.

[0034] Figure 5 (a) Comparison of fitness curves for prediction parameter R; (b) Comparison of fitness curves for prediction parameter D; (c) Comparison of prediction results for parameter R; (d) Actual value of parameter R; (e) LSTM prediction result for parameter R; (f) CSA-LSTM prediction result for parameter R.

[0035] Figure 6 (g) Comparison of prediction results for parameter D; (h) True value of parameter D; (i) LSTM prediction result for parameter D; (j) CSA-LSTM prediction result for parameter D.

[0036] Figure 7 (a) Model prediction of band structure I at θ = 30°; (b) Band reversal diagram of structural unit as θ changes.

[0037] Figure 8 (a) shows the modal distribution of the valley supercell, where energy propagates only at the boundary states; (b) shows the band structure of the valley supercell, where red and blue lines represent boundary states and black areas represent bulk states.

[0038] Figure 9 Valley states are propagated in structures with straight boundaries formed by topological and non-topological structures, respectively. Detailed Implementation

[0039] The present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0040] Example

[0041] A multi-band acoustic topological insulator, which is a scatterer, includes several unit cells uniformly distributed on the same circumference and a cell frame connected to the inner side of each unit cell. The cell frame includes several base frames, and the point of tangency between the unit cell and the circumference coincides with the intersection of the extension lines of the two sides of the base frame connected to the unit cell. The insulator includes three circular unit cells and three base frames, and the center of the circumference of the insulator coincides with the center of the cell frame within the scatterer structure. The unit cells and cell frames have a star-shaped structure.

[0042] This application is as follows Figure 1 Taking the I-th energy band shown in (c) as an example, this study establishes a numerical calculation model for the corresponding energy band structure. The correspondence between the basic parameters and energy band characteristics of the multi-band acoustic topological insulator is obtained, and the calculation results are output, thus constructing the sample library required for DL ​​algorithm modeling. The constructed honeycomb topological structure unit is shown below. Figure 1 As shown in (a), the internal details of the cell framework are as follows: Figure 1 As shown in (b). Its lattice constant is a, the gray area represents air, and the white area represents an insulator (scatterer). Draw a circle (dashed line) containing the scatterer with the center of the honeycomb topological unit as the center. Divide the circle into three equal parts. Using the line segment between the dividing point on the circle and the center as the height, and the line segment passing through the center as the base, design three isosceles triangles, such as... Figure 1 As shown in (b), a circular unit cell structure with radius R is drawn using the equidistant points on the circumference as tangent points. Then, using the center of the circumference as the rotation point, the unit cell structure is rotated 120° clockwise or 240° counterclockwise. A Boolean operation is then performed to obtain the insulator of this invention. The rotation angle is defined as θ (the angle between the base of an isosceles triangle and the extension of the altitude of the base in a 120° clockwise direction). The gray area represents air, and the white area represents a rigid body. The air density ρ = 1.21 kg / m³. 3 The speed of sound is c = 343 m / s. The scattering body is made of hard materials, including metals and alloys.

[0043] Due to the symmetry of this structural system, the honeycomb topological unit cells with scatterers exhibit deterministic degeneracy caused by bandgap closure at high-symmetry points in the first Brillouin zone. The scatterers in the rotating phononic crystal break the structural mirror symmetry, thus achieving the Valley-Hall phase transition. To study the band structure and transport characteristics of the designed structure, this patent utilizes the finite element analysis software COMSOL Multiphysics to conduct numerical calculations to study the band structure and transport characteristics of the phononic crystal, fixing the lattice constant a = 10 mm and the air density ρ = 1.21 kg / m³. 3The speed of sound is c = 343 m / s. The four external boundaries of the structural unit are set as periodic boundary conditions for band structure calculation. The band structure is calculated by solving the characteristic frequency equation and scanning wave k in the first Brillouin zone of the honeycomb lattice in reciprocal lattice space.

[0044] Traditional acoustic structure design methods require a considerable amount of simulation data. These simulations cannot be completed in parallel at once but require multiple iterations, making it a process-driven approach. Deep learning, on the other hand, is a data-driven approach. The advantage of a data-driven approach is that once the data is created, it does not continuously consume computational resources like process optimization methods. The key to inverse design lies in establishing the functional relationship between the input and output data. Since the analytical solution of the function is unknown, an algorithm model suitable for solving numerical methods needs to be selected. Considering that the acoustic topology inverse design problem involves multiple strongly coupled parameters, and that the relevant parameters of the model are scanned during dataset preparation, there is a certain time series between the data, and the data sample distribution is as follows... Figure 3 As shown in (a), this application uses LSTM to solve the inverse design problem of acoustic topology parameters. The design process of using LSTM to solve the inverse design problem of acoustic topology insulators is as follows: Figure 2 The learning curve of LSTM is as follows Figure 3 As shown in (b).

[0045] To address the complexity of LSTM neural network parameter optimization and considering the tendency of traditional heuristic search algorithms to get trapped in local optima, this patent proposes using CSA (Computer-Assisted Algorithm) to improve the shortcomings of LSTM parameter selection. This is achieved by optimizing hyperparameters such as the learning rate and the number of neurons in the LSTM neural network, thereby improving the model's prediction accuracy. Furthermore, to demonstrate the effectiveness and superiority of CSA-LSTM, three optimization algorithms—PSO, WOA, and HWBOA—were used to optimize the LSTM. Prediction models for acoustic topology parameters were constructed using five algorithms: standard LSTM, PSO-LSTM, WOA-LSTM, HWBOA-LSTM, and CSA-LSTM. The performance of these models was analyzed and compared. The results show that the CSA-LSTM algorithm significantly outperforms the others in all performance metrics, improving the accuracy of acoustic topology parameter prediction.

[0046] A multi-band acoustic topology insulator reverse design method based on deep learning algorithms, such as Figure 2 As shown, it includes the following steps:

[0047] 1) Obtain the original structural information data of the above-mentioned insulators;

[0048] 2) Run the insulator from step 1) in a simulation environment, update the structural information data, and calculate the band frequency value;

[0049] 3) Combine the original structural information data, the updated structural information data, and the band frequency values ​​of the insulator into experimental data, and use deep learning algorithms to train the experimental data and predict the structural parameters of the insulator.

[0050] 4) Remodel the obtained optimal parameter combination to obtain the optimal insulator structure.

[0051] The deep learning algorithm is the CSA-LSTM model algorithm, such as Figure 4 As shown, it includes the following steps:

[0052] a) Data preprocessing: The parameter data of the insulator structure is cleaned and normalized, and then the standardized data is divided into training set and test set;

[0053] b) Determine the hyperparameters for optimization: Initialize the parameters and structure required for the LSTM neural network, including one LSTM hidden layer and one dropout layer; simultaneously determine the hyperparameters and optimization range in the LSTM network model, and select the hyperparameters [L, I] to be optimized. r ], representing the number of neurons in the hidden layer and the learning rate, respectively;

[0054] c) Initialize the CSA algorithm parameters and define relevant parameter indicators, set the number of participants to n, the maximum number of iterations to G, the number of excellent participants to EC, the number of participants who withdraw after each round of the competition to RC, and the thresholds L1 and L3 representing the learning ability intensity in different participating groups.

[0055] d) Sort and group, calculate the fitness of all participants, and sort and group the participants according to their fitness levels;

[0056] e) Participant position update: The search range of participants in different groups is different. Formulas (1), (2) and (3) can be used to conduct a more comprehensive search of the environment around the participants and improve the search accuracy. During the iteration process, the optimal solution is gradually approached. After the participant position is updated and grouped, each participant will learn and update their own indicators according to their own group.

[0057] f) The "reference" behavior of the participants: After all participants' positions have been updated, when a participant's learning ability is greater than L3, i.e. the best participant in the previous iteration, the participant will have reference behavior to continue learning.

[0058] g) Random elimination, update X(i) according to formula (4), randomly eliminate RC participants and randomly generate RC participants;

[0059] h) Determine if the termination iteration condition has been met. If the termination iteration condition is met, the optimal value of the optimization objective can be obtained; otherwise, return to c) and continue the calculation until the termination condition is met.

[0060] i) The optimal hyperparameters obtained through optimization are automatically assigned to the LSTM neural network for modeling, and the acoustic topology insulator structure parameter data are trained and predicted.

[0061]

[0062]

[0063]

[0064]

[0065] Where S1 and S2 are the search range functions for participants with strong learning abilities and those with average learning abilities, respectively; t is the current iteration number; j is the number of dimensions in which X exists, j = 1, 2, 3, 4, ..., d; X i,j This represents the value of the j-th evaluation metric for the i-th contestant, i.e., the position information in the j-th dimension. and L represents the upper and lower bounds of the function within the search range of the j-th dimension, respectively; B and U B All are constants; ρ is a value randomly extracted from the matrix [-1,0,1]; A(i) is the learning ability of the current participant; L1 is the threshold representing the learning ability intensity of the excellent group, and L1 belongs to the matrix (0,1).

[0066] In equation (3), F is the negative factor; α is a random number in matrix [-1,1]; Q is a random number in [0,2]; D and L2 are 1×d matrices, but all elements in matrix D are 1, and the elements in L2 are randomly distributed with -1 and 1; P is a standard normal distribution with mean 0 and variance 1; o is a random factor that updates the position of each contestant and randomly selects [0.1, 0.2, 0.3, 0.4, 0.5] from the matrix.

[0067] In equation (4), L1 is the index value of the j-th dimension of the best contestant in the t-th iteration; L3 is the reference threshold, which belongs to the interval (0,1).

[0068] The CSA optimization algorithm is used to optimize the hyperparameters of the LSTM neural network, aiming to improve the model's prediction performance and reduce the mean squared error on the test set. Simultaneously, we analyze and compare the prediction results. Figure 5 (a) and (b) show the comparison results of the fitness curves of the four optimization algorithms. Figure 5(c)-(f) are comparison results between the prediction curves of LSTM and CSA-LSTM for the acoustic topology parameters R and D and their actual values, respectively. Figure 5 (d)-(f) is Figure 5 (c) Curve splitting diagram; Figure 6 (g)-(j) represent the comparison results between the prediction curves of LSTM and CSA-LSTM for the acoustic topology parameter D and the actual values, respectively. Figure 6 (h)-(j) is Figure 6 (g) curve splitting plot).

[0069] Depend on Figure 5 (c)-6(g) show that the prediction results of the LSTM network model optimized by CSA are significantly closer to the actual parameter values. Therefore, the prediction performance of the CSA-LSTM algorithm is significantly better than other comparative algorithms, proving that the prediction accuracy of the model can be greatly improved after using the CSA algorithm to optimize the hyperparameters of LSTM.

[0070] To achieve multi-band acoustic transmission by maximizing the bandgap width of the target band, the low-frequency f1 = 10500Hz and the high-frequency f2 = 19500Hz of the target band were input. Using the CSA-LSTM algorithm model, the structural radius R and the long side length D of the trapezoid were predicted. The predicted results were R = 1.44mm and D = 0.19mm. Based on these parameter combinations, they were substituted into the multi-band acoustic topological insulator system model, and the simulation results are as follows. Figure 7 As shown in (a).

[0071] Depend on Figure 7 (a) It was found that the target band of the model reached the desired frequency range, verifying the effectiveness of the inverse design method of this invention. Simultaneously, we studied the acoustic topological transmission characteristics of the model. A method was adopted to achieve the valley-Hall phase transition by changing θ to break the mirror symmetry of the crystal system while keeping other structural parameters of the honeycomb structure unit constant. The valley pseudospin state was flexibly adjusted by rotating the scatterer without reconstructing the phononic crystal. When the scatterer rotated clockwise from -60° to 60°, the band gap underwent an on-off-on process, resulting in band reversal and a topological phase transition, as shown in the results. Figure 7 As shown in (b). To verify the properties of topologically protected boundary states, a supercell with the interface in the middle was constructed by combining topologically trivial and non-trivial structures, as shown in (b). Figure 8 As shown in (a). Figure 8 (b) is the dispersion relation of the supercell of the valley topological acoustic waveguide near the Dirac point.

[0072] A phononic crystal formed by a multi-band acoustic topological insulator includes an array of cells. Each cell array is formed by several star-shaped arrays of insulators (arranged linearly along the x-direction). The rotation angle of each cell array is θ, ranging from -60° to 60°. Clockwise rotation is positive, and counterclockwise rotation is negative. The phononic crystal has two cell arrays, each with 12 rows of cells, consisting of 12 rows of cells with a rotation angle θ = 30° and 12 rows of cells with a rotation angle θ = -30°. The cells with a rotation angle θ = 30° form topological boundary states with their adjacent cells with a rotation angle θ = -30°. The characteristics of the topological boundary state transmission are tested, such as... Figure 9 As shown.

[0073] Depend on Figure 9 It was learned that the phononic crystal exhibits the characteristics of topological boundary state propagation. The sound wave is confined to the topological boundary state formed by the unit cell with a rotation angle of θ = 30° and the unit cell with a rotation angle of -30° adjacent to it (propagation at the boundary), and does not spread to both sides.

[0074] A key property of topological boundary states is their robustness in boundary propagation. Whether the boundary is straight or curved, topologically protected boundary states can propagate with virtually no reflection or loss. For example... Figure 8 As shown, a structure with a straight boundary line is constructed from two types of units: θ = 30° and θ = -30°. When an excitation is applied to the left side, it can be observed that the sound wave propagates along the straight boundary line without obstruction. This is because there are topologically protected boundary states at the boundary between non-trivial and trivial structures. Even if the interface is irregularly shaped, such as curved, the sound wave can still propagate along the interface. At the same time, as the sound wave propagates from the boundary to both sides, its energy attenuates rapidly, allowing the sound wave to propagate only forward along the interface.

Claims

1. A multi-band acoustic topological insulator, characterized in that, The insulator includes three identical circular unit cells evenly distributed on the same circumference and a cell frame connected to the inside of each unit cell. The cell frame includes three base frames. The point of tangency between the unit cell and the circumference coincides with the intersection of the extension lines of the two sides of the base frames connected to the unit cell.

2. The multi-band acoustic topological insulator as described in claim 1, characterized in that, The center of the circumference where the insulator is located coincides with the center of the cell frame within the scatterer structure.

3. The multi-band acoustic topology insulator as described in claim 2, characterized in that, The unit cell and the cell framework have a star-shaped structure.

4. The reverse design method for multi-band acoustic topological insulators as described in any one of claims 1-3, based on deep learning algorithms, is characterized in that... Includes the following steps: 1) Obtain the original structural information data of the insulator; 2) Run the insulator from step 1) in the simulation environment, update the structural information data, and calculate the band frequency value; 3) Combine the original structural information data, the updated structural information data, and the band frequency values ​​of the insulator into experimental data, and use deep learning algorithms to train the experimental data; The deep learning algorithm is the CSA-LSTM model algorithm; The CSA-LSTM model algorithm includes the following steps: a) Data preprocessing; b) Determine the hyperparameters to be optimized: Initialize the parameters and structure required for the LSTM neural network, including one LSTM hidden layer and one dropout layer; at the same time, determine the hyperparameters to be optimized and the optimization range in the LSTM network model, and select the hyperparameters to be optimized; c) Use the CSA algorithm to find the optimal hyperparameters; d) The optimal hyperparameters are automatically assigned to the LSTM neural network for modeling, and the insulator structure parameter data are trained and predicted.

5. The method for reverse design of multi-band acoustic topological insulators based on deep learning algorithms as described in claim 4, characterized in that, Step a) Data preprocessing: The parameter data of the insulator structure is cleaned and normalized, and then divided into training set and test set.

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