A method for designing a topological phonon crystal structure using a feedback programming topology

Abstract

The present invention relates to a method for designing a topological phononic crystal structure using a feedback programming topology, and the method includes the following steps: (1) establishing a topological phononic crystal database composed of topological phononic crystal data and non-topological phononic crystal data; (2) using the topological phononic crystal database to train a new structure of a phononic crystal by a neural network algorithm to generate a new structure of a phononic crystal; (3) using the topological phononic crystal database to train a known topological phononic crystal and a known non-topological phononic crystal by a neural network algorithm to obtain a preliminary judgment model of a topological phononic crystal; (4) inputting the new structure of the phononic crystal into the preliminary judgment model of the topological phononic crystal to make a preliminary judgment on the new structure of the phononic crystal; (5) judging the new structure of the phononic crystal that passes the judgment by a topological invariant calculation model; (6) judging the new structure of the phononic crystal that passes the judgment by a finite element method calculation model. The present invention can achieve the purpose of improving the output efficiency and accuracy of the design of topological phononic crystals.

Description

Technical Field

[0001] The present invention relates to the technical field of phononic crystals, and particularly to a method for designing a topological phononic crystal structure using feedback programming. Background Art

[0002] A phononic crystal is an artificially fabricated material with special acoustic properties. It is composed of periodically arranged holes or rigid media and can control and manipulate the propagation of sound waves. The structure of a phononic crystal is similar to that of an electronic crystal, but it controls sound waves instead of electrons. Phononic crystals have a wide range of applications in fields such as sound wave filtering, acoustic isolation, and sound wave waveguides.

[0003] A topological phononic crystal is a special type of phononic crystal that has topologically protected acoustic properties. In a topological phononic crystal, special topological phenomena can occur in the propagation of sound waves on the surface or boundary of the material, which is similar to the electron propagation in a topological insulator. Different from ordinary phononic crystals, the acoustic properties of topological phononic crystals do not depend on the local details of the material but are determined by the topological structure of the material.

[0004] Topological phononic crystals have many unique acoustic properties, such as the emergence of boundary acoustic modes, the non-scattering propagation of sound waves, and acoustic topological phase transitions. These properties make topological phononic crystals have potential applications in fields such as acoustic sensing, sound wave processing, and acoustic communication.

[0005] Since the properties of topological phonons are closely related to their structure, in the research of topological phononic crystals, the design of new structures is very important. For the design of traditional topological phononic crystal structures, researchers generally combine topological theory knowledge and experience to design the phononic crystal structure and then use computer simulations such as calculating the topological invariants of the structure or using finite element methods to verify whether it has topological properties, so as to judge whether the newly designed phononic crystal structure by the designer has topological properties. However, because the conditions for a phononic crystal to have topological properties are harsh and accidental, the vast majority of phononic crystal structures do not have topological properties and cannot become topological phononic crystals. Therefore, the traditional topological phononic crystal design method has problems of large test volume and low design output efficiency. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for designing a topological phononic crystal structure using feedback programming that can improve the output efficiency and accuracy.

[0007] To solve the above problems, a method for designing a topological phononic crystal structure using feedback programming according to the present invention includes the following steps:

[0008] (1) Establish a topological phononic crystal database composed of topological phononic crystal data and non-topological phononic crystal data;

[0009] ⑵ Train the new structure of the phononic crystal using the neural network algorithm with the topological phononic crystal database to obtain a new structure generation model of the phononic crystal, and then generate a new structure of the phononic crystal;

[0010] ⑶ Train the known topological phononic crystal and the known non-topological phononic crystal using the neural network algorithm with the topological phononic crystal database to obtain a preliminary judgment model of the topological phononic crystal;

[0011] ⑷ Input the new structure of the phononic crystal into the preliminary judgment model of the topological phononic crystal. This preliminary judgment model of the topological phononic crystal makes a preliminary judgment on the new structure of the phononic crystal based on the mapping relationship between the phononic crystal structure and the specific characteristics of the energy band. The mapping relationship between the phononic crystal structure and the specific characteristics of the energy band is shown as follows:

[0012]

[0013] In the formula: is the high-symmetry point of the Dirac cone; k is a function describing the probability of the topological phononic crystal;

[0014] When the difference between the third energy band and the fourth energy band at the high-symmetry point is less than or equal to 30 Hz, it is preliminarily judged to have topological properties, then this phononic crystal is a topological phononic crystal, the judgment passes and it is input into the topological invariant calculation model;

[0015] When the difference is greater than 30 Hz, it is preliminarily judged to have no topological properties, then this phononic crystal is a non-topological phononic crystal, the judgment fails and it is input into the non-topological phononic crystal data of the topological phononic crystal database;

[0016] ⑸ The new structure of the phononic crystal that passes the judgment is judged by the topological invariant calculation model:

[0017] When the new structure of the phononic crystal passes the topological invariant calculation and proves to meet the requirements of the topological invariant calculation, it is input into the finite element method calculation model;

[0018] When the new structure of the phononic crystal fails the topological invariant calculation and proves not to meet the requirements of the topological invariant calculation, it is input into the non-topological phononic crystal data of the topological phononic crystal database;

[0019] ⑹ The new structure of the phononic crystal that passes the judgment is judged by the finite element method calculation model:

[0020] When all the obtained phononic crystal energy band structures meet the characteristics of the topological phononic crystal energy band structure through the finite element method calculation, it is considered that this structure has topological properties and is a topological phononic crystal, and then it is input as the topological phononic crystal data in the topological phononic crystal database;

[0021] When the finite element method calculation model fails to pass the judgment, indicating that it does not meet the requirements of the finite element method calculation, the non-topological phononic crystal data is input into the topological phononic crystal database.

[0022] The present invention has the following advantages compared with the prior art:

[0023] 1. The present invention enables a computer to learn the design rules of topological phononic crystals through deep learning technology. By training a program with a large number of topological phononic crystal structures and non-topological phononic crystal structures, and combining the mature physical judgment methods in the research of topological phononic crystals, the topological properties of the newly generated structures are comprehensively judged. At the same time, the newly generated structures during the process are continuously used for training the program to form a feedback mechanism, thereby achieving the purpose of improving the output efficiency and accuracy of the design of topological phononic crystals.

[0024] 2. Whether the structures judged by the topological invariant calculation model and the finite element method calculation model of the present invention pass the judgment or not, they will all become part of the topological phononic crystal database. The supplemented topological phononic crystal database retrains the phonon crystal new structure generation model and the topological phononic crystal preliminary judgment model, thereby forming a kind of feedback.

[0025] 3. The present invention simplifies the energy band feature extraction process and reduces the calculation amount by means of local feature extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The following further describes in detail the specific embodiments of the present invention with reference to the drawings.

[0027] Figure 1 is a flow chart of the present invention.

[0028] Figure 2 is a schematic diagram of the establishment of the topological phononic crystal database in the present invention.

[0029] Figure 3 is a schematic diagram of a new structure of a phononic crystal obtained by using the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] Based on the topological phononic crystal database, the present invention is used to train the phonon crystal new structure generation model and the topological phononic crystal preliminary judgment model. Then, the structural data screened by the topological phononic crystal preliminary judgment model is distributed. Secondly, the structural data is distributed after being judged by the topological invariant calculation model. Then, the structural data is distributed after being judged and screened by the finite element method calculation. Finally, a new structure of the topological phononic crystal is obtained. At the same time, during the operation of the program, the judged structural data (passed and not passed) is used to train the phonon crystal new structure generation model and the topological phononic crystal preliminary judgment model to form a feedback.

[0031] Such as Figure 1As shown in the figure, a method for designing a topological phonon crystal structure using a feedback programming topology includes the following steps:

[0032] ⑴ Establish a topological phonon crystal database composed of topological phonon crystal data and non-topological phonon crystal data.

[0033] Among them: The initial database analyzes whether it has topological properties through the energy band diagram corresponding to the phonon crystal. When there is a "Dirac cone" at the high-symmetry point in the energy band diagram, the phonon crystal structure may have topological properties, as Figure 2 shown. For the establishment of the preliminary database, based on a simple two-dimensional phonon crystal structure, its energy band structure is calculated by the finite element method, and by changing the structure of these simple two-dimensional phonon crystals, a certain number of basic data (about 4,000) are obtained. These data mainly include two-dimensional phonon crystal structure diagrams and the corresponding energy band structure diagrams.

[0034] ⑵ Use the topological phonon crystal database to train a new structure of the phonon crystal using a neural network algorithm to obtain a new structure generation model of the phonon crystal, and then generate a new structure of the phonon crystal.

[0035] ⑶ Use the topological phonon crystal database to train known topological phonon crystals and known non-topological phonon crystals using a neural network algorithm to obtain a preliminary judgment model for topological phonon crystals.

[0036] ⑷ Input the new structure of the phonon crystal into the preliminary judgment model of the topological phonon crystal. The preliminary judgment model of the topological phonon crystal makes a preliminary judgment on the new structure of the phonon crystal based on the mapping relationship between the phonon crystal structure and the specific characteristics of the energy band; the mapping relationship between the phonon crystal structure and the specific characteristics of the energy band is shown in the following formula:

[0037]

[0038] In the formula: is the high-symmetry point of the Dirac cone; k is a function describing the probability of a topological phonon crystal.

[0039] This mapping relationship indicates that at the high-symmetry point where it is easy to form a Dirac cone, the difference between the frequencies corresponding to the third and fourth energy bands is used as the initial judgment basis.

[0040] When the difference between the third energy band and the fourth energy band at the high-symmetry point is less than or equal to 30 Hz, it is initially judged to have topological properties, then the phonon crystal is a topological phonon crystal, the judgment passes and it is input into the topological invariant calculation model.

[0041] When the difference is greater than 30 Hz, it is initially judged that there is no topological property, so the phononic crystal is a non-topological phononic crystal, and the judgment fails and is input into the non-topological phononic crystal data in the topological phononic crystal database.

[0042] ⑸ The newly-structured phononic crystal that passes the judgment is judged by the topological invariant calculation model. The calculation of topological invariants corresponds to the calculation of the Chern number of the phononic crystal structure, and this method is obtained by calculating its Berry curvature and volume integral in the phononic crystal. If there is a non-zero topological invariant in the space of the Berry curvature, then the phononic crystal is a possible topological phononic crystal.

[0043] When the newly-structured phononic crystal passes the calculation of topological invariants and proves to meet the requirements of topological invariant calculation, it is input into the finite element method calculation model.

[0044] When the newly-structured phononic crystal fails to pass the calculation of topological invariants and proves not to meet the requirements of topological invariant calculation, it is input into the non-topological phononic crystal data in the topological phononic crystal database.

[0045] ⑹ The newly-structured phononic crystal that passes the judgment is judged by the finite element method calculation model. The finite element method is based on the physical properties such as the acoustic wave propagation and electron energy band structure of the phononic crystal, and forms the most basic judgment of the phononic crystal starting from physical principles.

[0046] When all the obtained phononic crystal energy band structures meet the characteristics of the topological phononic crystal energy band structure through the finite element method calculation, it is considered that the structure has topological properties and is a topological phononic crystal, and then it is input as the topological phononic crystal data in the topological phononic crystal database.

[0047] When the finite element method calculation model fails to pass the judgment and proves not to meet the requirements of the finite element method calculation, it is input into the non-topological phononic crystal data in the topological phononic crystal database. Embodiment

[0048] Using the method of the present invention to train the data of the two-dimensional rhombic unit cell phononic crystal structure, the phononic crystal structure generation model has realized the generation of such new two-dimensional rhombic unit cell phononic crystal structures. A new "clover" type two-dimensional rhombic unit cell phononic crystal structure generated by the phononic crystal structure generation model is screened by the topological phononic crystal initial judgment model, and then the "clover" type two-dimensional rhombic unit cell phononic crystal structure is calculated by the topological invariant and the finite element method, and it is confirmed that the newly-generated "clover" type two-dimensional rhombic unit cell phononic crystal structure has topological properties. In addition to the clover type, the newly-generated "six-petal plum blossom" type and "triangle windmill" type phononic crystals are also predicted, as Figure 3 shown.

Claims

1. A method for designing a topological phononic crystal structure using a feedback programming topology, comprising the following steps: ⑴ Establish a topological phononic crystal database composed of topological phononic crystal data and non-topological phononic crystal data; ⑵ Use the topological phononic crystal database to train a new structure of the phononic crystal using a neural network algorithm to obtain a generation model for the new structure of the phononic crystal, and then generate a new structure of the phononic crystal; ⑶ Use the topological phononic crystal database to train known topological phononic crystals and known non-topological phononic crystals using a neural network algorithm to obtain a preliminary judgment model for topological phononic crystals; ⑷ Input the new structure of the phononic crystal into the preliminary judgment model for topological phononic crystals, and this preliminary judgment model for topological phononic crystals makes a preliminary judgment on the new structure of the phononic crystal based on the mapping relationship between the phononic crystal structure and specific band characteristics; the mapping relationship between the phononic crystal structure and specific band characteristics is shown in the following formula: Wherein: is the high symmetry point of the Dirac cone; k is a function describing the probability of the topological phononic crystal; When the energy difference between the third energy band and the fourth energy band at the high-symmetry point is less than or equal to 30 Hz, it is initially judged to have topological properties, and then this phononic crystal is a topological phononic crystal. The judgment passes and it is input into the topological invariant calculation model; When the difference is greater than 30 Hz, it is preliminarily judged that there is no topological property, and then the phononic crystal is a non-topological phononic crystal, the judgment fails and it is input into the non-topological phononic crystal data in the topological phononic crystal database; ⑸ The new structure of the phononic crystal that passes the judgment is judged by a topological invariant calculation model: When the new structure of the phononic crystal passes the topological invariant calculation and proves to meet the requirements of the topological invariant calculation, it is input into the finite element method calculation model; When the new structure of the phononic crystal fails the topological invariant calculation and proves not to meet the requirements of the topological invariant calculation, it is input into the non-topological phononic crystal data in the topological phononic crystal database; ⑹ The new structure of the phononic crystal that passes the judgment is judged by a finite element method calculation model: When the obtained phononic crystal band structure meets the topological phononic crystal band structure characteristics through finite element method calculation, it is considered that the structure has topological properties and is a topological phononic crystal, and then it is input as the topological phononic crystal data in the topological phononic crystal database; When the finite element method calculation model fails the judgment and proves not to meet the requirements of the finite element method calculation, it is input into the non-topological phononic crystal data in the topological phononic crystal database.

Images