Method and system for obtaining parameters of nanomaterials

Abstract

The application relates to a parameter acquisition method and system of nanomaterials. The method comprises the following steps: acquiring a reference scattering angle spectrum of a reference nanomaterial under a reference electromagnetic wave; and based on the reference scattering angle spectrum, calling a first trained model to determine target information of a target nanomaterial under a target electromagnetic wave; wherein the target nanomaterial comprises a central column and at least one layer of shell located outside the central column; wherein the polarization of the target electromagnetic wave is different from that of the reference electromagnetic wave, and the target information comprises at least one of a target structural parameter and a target material parameter. The method can be used to design the target nanomaterial based on the reference scattering angle spectrum and by using an artificial neural network, so as to reduce the design difficulty of an equivalent electromagnetic dual structure.

Description

Technical Field

[0001] This invention relates to the field of nanomaterial design technology, and in particular to a method and system for obtaining parameters of nanomaterials based on machine learning. Background Technology

[0002] Current techniques for studying light scattering angular spectra primarily employ full numerical simulation methods and the derivation of coupled theories. Typically, researchers work with a multi-shelled core particle, fixing certain parameters (such as the type of core metal and the thickness of the shell and core), and then using numerical simulation software to simulate this particle with fixed parameters. Once the simulation generates the desired light scattering angular spectrum, its structural parameters are extracted to determine the particle's identity.

[0003] The traditional design process for equivalent electromagnetic dual structures also typically employs the above method, which undoubtedly increases the simulation task for researchers and is less efficient. Summary of the Invention

[0004] To address at least one of the aforementioned problems, this invention aims to provide a method and system for obtaining parameters of nanomaterials that facilitates reducing the difficulty of designing equivalent electromagnetic dual structures.

[0005] In a first aspect, this application provides a method for obtaining parameters of nanomaterials, including:

[0006] Obtain the reference scattering angle spectrum of the reference nanomaterial under a reference electromagnetic wave;

[0007] Based on the reference scattering angle spectrum, the first trained model is invoked to determine the target information of the target nanomaterial under the target electromagnetic wave; wherein, the target nanomaterial includes a central pillar and at least one shell located outside the central pillar;

[0008] The target electromagnetic wave has a different polarization from the reference electromagnetic wave, and the target information includes at least one of the target structural parameters and the target material parameters.

[0009] The above-mentioned method for obtaining the parameters of nanomaterials can quickly and accurately design the target nanomaterials under the target electromagnetic wave based on the reference scattering angle spectrum using artificial neural networks, thereby realizing the equivalent electromagnetic dual structure and reducing the design difficulty of the equivalent electromagnetic dual structure in traditional methods. At the same time, due to the strong data processing capability of artificial neural networks, the ability of neural networks to provide solutions is not unique, and it has good generalization ability under the same model. In other words, more than one pair of equivalent dual electromagnetic structures can be designed.

[0010] In one embodiment, the first trained model is determined according to a first training process, the first training process including: acquiring at least one set of first training samples under the target electromagnetic wave, each set of first training samples including a sample scattering angle spectrum of a first sample nanomaterial; acquiring a second trained model, the second trained model being configured to determine the scattering angle spectrum of the nanomaterial under the target electromagnetic wave based on information of the nanomaterial; wherein the information includes at least one of structural parameters and material parameters of the nanomaterial; and training a first initial model based on the second trained model and the at least one set of first training samples to generate the first trained model.

[0011] In one embodiment, the second trained model is determined according to a second training process, which includes: acquiring at least one set of second training samples under the target electromagnetic wave, each set of second training samples including sample information of the second sample nanomaterial and the standard scattering angle spectrum of the second sample nanomaterial, the sample information including at least one of sample structure parameters and sample material parameters; and training a second initial model based on the at least one set of second training samples to generate the second trained model.

[0012] In one embodiment, training a first initial model based on the second trained model and the at least one set of first training samples to generate the first trained model includes: inputting the sample scattering angle spectrum of the first sample nanomaterial in the first training samples into the first initial model to generate reference information of the first sample nanomaterial; wherein the reference information includes at least one of reference structural parameters and reference material parameters; inputting the reference information into the second trained model to generate a predicted scattering angle spectrum; and training the first initial model based on the sample scattering angle spectrum and the predicted scattering angle spectrum to generate the first trained model.

[0013] In one embodiment, obtaining the reference scattering angle spectrum of the reference nanomaterial under a reference electromagnetic wave includes: obtaining a third trained model, the third trained model being configured to determine the scattering angle spectrum of the nanomaterial under the reference electromagnetic wave based on information about the nanomaterial; wherein the information includes at least one of structural parameters and material parameters of the nanomaterial; and, based on the information about the reference nanomaterial, calling the third trained model to determine the reference scattering angle spectrum.

[0014] In one embodiment, the reference electromagnetic wave is a transverse electromagnetic wave and the target electromagnetic wave is a transverse magnetic wave; or, the reference electromagnetic wave is a transverse magnetic wave and the target electromagnetic wave is a transverse electromagnetic wave.

[0015] In one embodiment, the central pillar is made of metal, the at least one shell comprises alternating layers of metal shells and dielectric shells, and the outer sidewall of the central pillar is in contact with the dielectric shell; the target structural parameters include at least one of the radius of the central pillar, the number of layers of the at least one shell, and the thickness of each shell layer; the target material parameters include at least one of the material of the central pillar and the material of each shell layer.

[0016] In one embodiment, the material of the central pillar includes at least one of gold, silver, and aluminum, the material of the metal casing includes at least one of gold, silver, and aluminum, and the material of the dielectric casing includes titanium dioxide.

[0017] Secondly, this application also provides an equivalent electromagnetic dual structure, obtained by the method described above, comprising: a first cylindrical structure configured to have a first scattering angle spectrum under a first polarized electromagnetic wave; and a second cylindrical structure configured to have a second scattering angle spectrum under a second polarized electromagnetic wave; wherein the first scattering angle spectrum and the second scattering angle spectrum are substantially the same; and the first polarized electromagnetic wave includes a transverse electric wave or a transverse magnetic wave, and correspondingly, the second polarized electromagnetic wave includes a transverse magnetic wave or a transverse electric wave.

[0018] The aforementioned equivalent electromagnetic dual structure allows the scattering angle spectrum of one cylindrical structure under transverse electric waves to be essentially equivalent to that of another cylindrical structure under transverse magnetic waves, thus achieving a better electromagnetic duality effect. This promotes the study of electromagnetic duality.

[0019] Thirdly, this application also provides a parameter acquisition system for nanomaterials, the system comprising at least one processor and at least one memory; the at least one memory is used to store computer instructions; and the at least one processor is used to execute at least a portion of the computer instructions to implement the method described above.

[0020] The above-mentioned nanomaterial parameter acquisition system can execute at least some of the instructions in the memory through a processor to design the target nanomaterial under the target electromagnetic wave more quickly and accurately based on the reference scattering angle spectrum using an artificial neural network, thereby realizing the equivalent electromagnetic dual structure and reducing the design difficulty of the equivalent electromagnetic dual structure in traditional methods. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating a method according to an embodiment of this application is shown;

[0023] Figure 2 A schematic diagram of the structure of the target nanomaterial according to an embodiment of this application is shown;

[0024] Figure 3 This illustration shows a process diagram in the first trained model according to an embodiment of this application;

[0025] Figure 4 Figure (a) shows the curves of the training loss function value and the validation loss function value changing with the training rounds during the training process of a positive prediction network according to an embodiment of this application under TE wave.

[0026] Figure 4 Figure (b) shows the curves of the training loss function value and the validation loss function value changing with the training rounds during the training process of a positive prediction network according to an embodiment of this application under TM wave.

[0027] Figure 4 Figures (c) to (e) show the predicted scattering angle spectra of different nanomaterials under TE and TM waves and the standard scattering angle spectra determined according to scattering theory, respectively, using the forward prediction network of an embodiment of this application.

[0028] Figure 5 Figure (a) shows the curves of the training loss function value and the validation loss function value changing with the training rounds during the training process of the reverse design network of an embodiment of this application under TE wave;

[0029] Figure 5 Figure (b) shows the curves of the training loss function value and the validation loss function value changing with the training rounds during the training process of the reverse design network of an embodiment of this application under TM wave.

[0030] Figure 5 Figures (c) to (e) show the scattering angle spectra of samples of different nanomaterials, and the predicted scattering angle spectra of nanoparticle information under TE and TM waves based on the above sample scattering angle spectra using the reverse design network of an embodiment of this application.

[0031] Figure 6Figure (a) shows a schematic diagram of the structure of a reference nanomaterial according to an embodiment of this application;

[0032] Figure 6 Figure (b) shows a schematic diagram of the structure of the target nanomaterial corresponding to the reference nanomaterial in Figure (a);

[0033] Figure 6 Figure (c) shows the TE scattering angle spectrum of the reference nanomaterial in Figure (a) and the TM scattering angle spectrum of the target nanomaterial in Figure (b);

[0034] Figure 7 Figure (a) shows a TE field diagram of a reference nanomaterial according to an embodiment of this application;

[0035] Figure 7 Figure (b) shows the TM field plot of the nanomaterial obtained by interchanging the relative permittivity and permeability of the reference nanomaterial in Figure (a);

[0036] Figure 7 Figure (c) shows the TM field plot of the target nanomaterial corresponding to the reference nanomaterial in Figure (a). Detailed Implementation

[0037] To make the technical solution and beneficial effects of the present invention more apparent and understandable, a detailed description is provided below by listing specific embodiments. The accompanying drawings are not necessarily drawn to scale, and local features may be enlarged or reduced to more clearly show the details of the local features; unless otherwise defined, the technical and scientific terms used in this application have the same meanings as those in the technical field to which this application pertains.

[0038] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0039] In the fields of physical optics and micro / nano optics, scattering is an important phenomenon and a research and application area. The traditional method for studying scattering angle spectra is numerical simulation, which combines existing human experience with theoretical derivation to change the structural parameters of the scatterer (generally using the controlled variable method) through trial and error. However, because the numerical simulation software currently used takes a long time to traverse the entire data space (even with some parameters specified), the traditional method is extremely inefficient for studying scattering angle spectra with multiple parameter variations.

[0040] Based on the above shortcomings, researchers are currently using deep learning methods to build artificial neural networks to train and match the scattering angle spectrum prediction rules from the scattering structure parameters to the quantized light scattering angle spectrum. This has already achieved some results.

[0041] For example, Peurifoy et al. studied the forward prediction and reverse structural design of the scattering spectrum of multilayer nanospheres based on deep learning algorithms. By comparing with traditional optimization algorithms, they found that the reverse structural design speed of deep learning algorithms was several orders of magnitude faster than that of traditional optimization algorithms. So et al. considered different geometric dimensions and material choices of multilayer nanospheres simultaneously, and found that deep learning algorithms could quickly reverse design corresponding multilayer nanospheres based on the required scattering spectral lines, including geometric dimensions and material selection. Sheverdin et al. applied deep learning algorithms to the reverse design of weakly scattering multilayer nanospheres. Luo et al. further combined phase change materials and reverse-designed a special multilayer nanosphere using deep learning algorithms, which can achieve dynamic transitions between weak scattering and superscattering for multiple wavelengths simultaneously. However, previous studies have mostly been limited to the analysis of scattering spectra, and how to achieve forward prediction of scattering angle spectra based on deep learning algorithms, as well as how to customize specific scattering angle spectra, remain unsolved problems.

[0042] This application proposes a method based on deep learning algorithms to study the light scattering angle spectrum, investigating the scattering angle spectra of metal-dielectric multilayer cylinders under transverse electric (TE) and transverse magnetic (TM) waves. Specifically, this application establishes and trains corresponding artificial neural networks for TE and TM scattering angle spectra, respectively. This not only allows for accurate prediction of the scattering angle spectra of different cylinders under different polarized waves, but also enables rapid reverse design of the corresponding cylinders based on the required scattering angle spectra, including the structural geometric and material parameters. Furthermore, by combining neural networks for TE and TM waves, this application reverse designs a pair of cylinders that satisfy equivalent electromagnetic duality, making the TE scattering angle spectrum of one cylinder essentially equivalent to the TM scattering angle spectrum of the other cylinder.

[0043] like Figure 1 and Figure 2As shown, this application provides a method 100 for obtaining parameters of a target nanomaterial 200 based on deep learning. The target nanomaterial 200 may include a central pillar 210 and at least one shell 220 located outside the central pillar 210. The material of the central pillar 210 may be a metal, such as at least one of gold (Au), silver (Ag), and aluminum (Al), and the material of the at least one shell 220 may be at least one of a metal and a dielectric. The reference nanomaterial may have a similar structure to the target nanomaterial; for example, the reference nanomaterial may also have a central pillar and at least one shell located outside the central pillar, but at least one of the structural parameters and material parameters of the reference nanomaterial differs from that of the target nanomaterial.

[0044] Furthermore, such as Figure 1 As shown, method 100 of this application includes:

[0045] S110. Obtain the reference scattering angle spectrum of the reference nanomaterial under the reference electromagnetic wave;

[0046] S120. Based on the reference scattering angle spectrum, call the first trained model to determine the target information of the target nanomaterial 200 under the target electromagnetic wave.

[0047] The target electromagnetic wave has a different polarization from the reference electromagnetic wave, and the target information includes at least one of the target structural parameters and the target material parameters. The target structural parameters include at least one of the following: the radius of the central pillar 210, the number of at least one shell layer 220, and the thickness of each shell layer 220. The target material parameters include at least one of the following: the material of the central pillar 210 and the material of each shell layer 220. The reference electromagnetic wave can be a TE wave, and correspondingly, the target electromagnetic wave can be a TM wave; alternatively, the reference electromagnetic wave can also be a TM wave, and correspondingly, the target electromagnetic wave can be a TE wave.

[0048] In some embodiments, for S110, the structural and material parameters of the reference nanomaterial are typically known, allowing the reference scattering angle spectrum of the reference nanomaterial under a reference electromagnetic wave to be obtained through software simulation or model prediction (e.g., a third trained model). On the other hand, for S120, based on the determined reference scattering angle spectrum, the information required for designing the target nanomaterial 200 (such as at least one of the target structural and material parameters) can be inversely obtained through a trained neural network model (e.g., a first trained model). Both the first and second trained models can be machine learning models, such as convolutional neural network (CNN), recurrent neural network (RNN), deep neural network (DNN), fully convolutional neural network (FCN), generative adversarial network (GAN), etc.

[0049] In some embodiments, such as Figure 2 As shown, the target nanomaterial 200 has four shells 210 surrounding the outer wall of the central pillar 210. The first shell can be a dielectric shell with a thickness of t2, the second shell can be a metal shell with a thickness of t3, the third shell can be a dielectric shell with a thickness of t4, and the fourth shell can be a metal shell with a thickness of t5. In some embodiments, the target nanomaterial 200 can be represented as {t1,t2,t3,t4,t5,m1,m2,m3}, where m1 can represent the material of the central pillar, m2 can represent the material of the second shell, and m3 can represent the material of the fourth shell. In some embodiments, the material of the metal shell can be at least one of gold (Au), silver (Ag), and aluminum (Al), and the material of the dielectric shell can be titanium dioxide (TiO2).

[0050] In some embodiments, at least a portion of method 100 may be executed by a processor. For example, method 100 may be stored in a storage device as instructions and invoked and / or executed by a processor. The steps shown above are for illustrative purposes only. In some embodiments, method 100 may be performed using one or more additional steps not described and / or without one or more steps discussed.

[0051] The above-mentioned method for obtaining the parameters of nanomaterials can quickly and accurately design the target nanomaterials under the target electromagnetic wave based on the reference scattering angle spectrum using artificial neural networks, thereby realizing the equivalent electromagnetic dual structure and reducing the design difficulty of the equivalent electromagnetic dual structure in traditional methods. At the same time, due to the strong data processing capability of artificial neural networks, the ability of neural networks to provide solutions is not unique, and it has good generalization ability under the same model. In other words, more than one pair of equivalent dual electromagnetic structures can be designed.

[0052] In some embodiments, the first trained model can be determined according to a first training process, which may also be referred to as the reverse design network training process of the target nanomaterial 200. The first training process includes:

[0053] Acquire at least one set of first training samples under the target electromagnetic wave, each set of first training samples including the sample scattering angle spectrum of the first sample nanomaterial; acquire a second trained model, the second trained model being configured to determine the scattering angle spectrum of the nanomaterial under the target electromagnetic wave based on the information of the nanomaterial; wherein the information of the nanomaterial includes at least one of the structural parameters and material parameters of the nanomaterial; and, based on the second trained model and the at least one set of first training samples, train a first initial model to generate the first trained model.

[0054] Optionally, the first sample nanomaterial may refer to the nanomaterial used to train the first initial model. The first sample nanomaterial may have a structure similar to the target nanomaterial 200. For example, the first sample nanomaterial may be columnar nanoparticles. The sample scattering angle spectrum may refer to the scattering angle spectrum of the first sample nanomaterial used to train the first initial model.

[0055] In some embodiments, the second trained model is determined according to a second training process, which may also be referred to as the training process for a positive prediction network of nanomaterials. The second training process includes:

[0056] Acquire at least one set of second training samples under the target electromagnetic wave. Each set of second training samples includes sample information of the second sample nanomaterial and the standard scattering angle spectrum of the second sample nanomaterial. The sample information may include at least one of the sample structure parameters and sample material parameters. Based on at least one set of second training samples, train a second initial model to generate a second trained model.

[0057] Optionally, the second sample nanomaterial may refer to the nanomaterial used to train the second initial model. The first sample nanomaterial and the second sample nanomaterial may be the same or different. On the other hand, the initial model (e.g., the first initial model and the second initial model) may refer to the machine learning model that needs to be trained. Exemplary training algorithms may include gradient descent, Newton's algorithm, quasi-Newton algorithm, Levenberg-Marquardt algorithm, conjugate gradient algorithm, generative adversarial learning algorithm, etc. In some embodiments, one or more parameter values ​​of the first initial model and the second initial model may be iteratively updated by performing multiple iterations to determine the first trained model and the second trained model. Exemplary parameters of the first initial model and the second initial model may include the kernel size of the layer, the total number of layers, the number of nodes in each layer, the learning rate, the connection weight between two connected nodes, the bias vector associated with the node, etc.

[0058] Optionally, the standard scattering angle spectrum can be obtained by solving the scattering cross-section of the cylindrical structure using scattering theory. Specifically, the scattering cross-section under TE wave incidence can be expressed as:

[0059]

[0060] The scattering cross section under TM wave incidence can be expressed as:

[0061]

[0062] Where E i and H i E represents the electric and magnetic fields of the incident wave, respectively. s and H sLet be the electric field and magnetic field of the scattered wave, respectively, and λ0 be the wavelength of the incident wave in vacuum. Let s be the angle between the direction from the origin to the observation point and the x-axis. n Let be the scattering coefficient, and n be the order of the coefficient. When n = 0, w n =1, otherwise w n =2.

[0063] After the second trained model is determined, the first trained model can be determined based on the second trained model. Specifically, this can include:

[0064] The scattering angle spectrum of the first sample nanomaterial in the first training sample is input into the first initial model to generate reference information of the first sample nanomaterial; wherein, the reference information includes at least one of reference structural parameters and reference material parameters; the reference information is input into the second trained model to generate a predicted scattering angle spectrum; based on the sample scattering angle spectrum and the predicted scattering angle spectrum, the first initial model is trained to generate the first trained model.

[0065] by Figure 3 For example, the sample scattering spectrum 310 of the sample nanomaterial under TE / TM waves can be input into a first initial model 320. Based on the sample scattering spectrum 310, the first initial model 320 can output reference information 330 of the sample nanomaterial. Then, the reference information 330 is input into a second trained model 340. Based on the reference information 330, the second trained model 340 can output a predicted scattering spectrum 350 of the sample nanomaterial under TE / TM waves. Finally, the first initial model 320 can be trained based on the sample scattering spectrum 310 and the predicted scattering spectrum 350 to generate a first trained model. For example, one or more parameter values ​​of the first initial model 320 can be updated by performing multiple iterations to determine the first trained model. In each iteration, the value of the loss function can be determined based on the sample scattering spectrum 320 and the predicted scattering spectrum 350, and the parameter values ​​of the first initial model 320 can be adjusted to reduce the value of the loss function (i.e., reduce the difference between the sample scattering spectrum 310 and the predicted scattering spectrum 350).

[0066] Optionally, the parameters of the second trained model can be fixed. For example, one or more parameter values ​​of the first initial model can be iteratively updated by performing multiple iterations to determine the first trained model. In each iteration, the value of the loss function can be determined based on the sample scattering spectrum and the predicted scattering spectrum. If the value of the loss function exceeds a threshold in the current iteration, the parameter values ​​of the first initial model can be adjusted to reduce the value of the loss function (i.e., reduce the difference between the sample scattering spectrum and the predicted scattering spectrum). In some embodiments, the parameter values ​​of the first initial model can be updated by performing multiple iterations until a termination condition is met. It is understood that the method of performing multiple iterations to update model parameters is also applicable to other trained models in this application. On the other hand, the loss function for network training is in the form of Mean Squared Error (MSE), and the loss function formula can be expressed as follows:

[0067]

[0068] in, For discrete scattering cross-section data predicted by a neural network, σ i The data represents discrete scattering cross-sections obtained from rigorous scattering theory, and the loss function is the mean square error of both.

[0069] In some embodiments, obtaining the reference scattering angle spectrum of the reference nanomaterial under a reference electromagnetic wave may also include:

[0070] A third trained model is obtained, configured to determine the scattering angle spectrum of the nanomaterial under a reference electromagnetic wave based on the nanomaterial's information; wherein the nanomaterial's information includes at least one of the nanomaterial's structural parameters and material parameters; based on the reference nanomaterial's information, the third trained model is invoked to determine the reference scattering angle spectrum. The third trained model can be determined according to a third training process, which can also be referred to as the forward prediction network training process for nanomaterials. Therefore, obtaining the third trained model may further include: obtaining at least one set of third training samples under a reference electromagnetic wave, each set of third training samples including sample information of the third sample nanomaterial and the standard scattering angle spectrum of the third sample nanomaterial; the sample information may include at least one of the sample's structural parameters and sample's material parameters; based on at least one set of third training samples, a third initial model is trained to generate the third trained model.

[0071] Optionally, the third sample nanomaterial can refer to the nanomaterial used to train the third initial model. The third training sample can be the same as or different from the first and second training samples. The third training process can be substantially the same as the second training process.

[0072] In some embodiments, a forward prediction network and a reverse design network for nanomaterials under TE waves can be established, as well as a forward prediction network and a reverse design network for nanomaterials under TM waves; wherein the reverse design network may include the forward prediction network. Thus, regardless of whether the reference electromagnetic wave is a TE wave or a TM wave, target information of the target nanomaterial based on the reference scattering angle spectrum can be obtained through the reverse design network of the nanomaterial under the corresponding target electromagnetic wave.

[0073] This application also provides an equivalent electromagnetic dual structure, which can be based on Figure 2 cylindrical structure and Figure 3 The reverse design network was obtained.

[0074] Electromagnetic duality is an important characteristic of classical electromagnetic phenomena. For example, for a pair of cylinders that satisfy equivalent electromagnetic duality, the TE scattering angle spectrum of one cylinder is almost completely equivalent to the TM scattering angle spectrum of the other cylinder, and the electromagnetic parameters of the two cylinders usually satisfy... The interchangeability relationship.

[0075] The design of the equivalent electromagnetic dual structure in this application may specifically include the following steps:

[0076] A. Creating a dataset

[0077] This application generates datasets for network training and validation based on rigorous scattering theory. Each sample in the dataset consists of two parts: material structure data and quantized standard scattering angle spectrum. The material structure data includes information on three metal materials and their corresponding thicknesses, which are independently encoded. The three metal materials are: (1) Au, with a relative permittivity of -27.276 + 1.089i; (2) Ag, with a relative permittivity of -29.465 + 0.858i; and (3) Al, with a relative permittivity of -45.281 + 25.649i. The dielectric TiO2 has a relative permittivity of 4.389, and their corresponding relative permeability is 1. The thickness of each metal layer is randomly generated within the range of 5-150 nm. The quantized standard scattering angle spectrum is represented by 362 discrete data points from the scattering width angle spectrum of TE and TM waves from 0-180 degrees. The final dataset consists of 60,000 samples. This application divides the dataset into a training set, a validation set, and a test set in an 8:1:1 ratio. The training set is used to train the network, the validation set is used to verify the training effect of the network, and the test set is used to evaluate the final generalization effect of the network.

[0078] B. Construction of a positive prediction network

[0079] The forward prediction network employs a fully connected network, consisting of an input layer, hidden layers, and an output layer. The input layer uses independent encoding and has 8 nodes, where the first 5 nodes represent the thickness of each layer of a metal-dielectric multilayer cylinder, and the last 3 nodes represent different metals. The output layer is a 181-dimensional TE or TM scattering angle spectrum from 0 to 180 degrees. The number of neurons in each layer from the input to the output layer is (8, 100, 400, 800, 400, 181). This application constructs two separate forward prediction networks for TE and TM and trains them independently. The batch size of the training data (the number of samples injected into the network each time) is 128. To enhance the nonlinear expressive power of the neural network, the hidden layer uses the Leaky ReLU activation function. The AdamW optimizer is used during training, with a learning rate of 10. -3 The weight decays to 10. -5 .

[0080] The training results of the network are as follows Figure 4 As shown. It can be seen that TE( Figure 4 (a) and TM ( Figure 4 (b) The positive prediction network (see Figure 1) shows good training performance and fast convergence speed. The training and validation set losses of the TE positive prediction network are 0.007 and 0.019, respectively, while those of the TM positive prediction network are 0.006 and 0.011. To further verify the training effect of the positive network, this application randomly selected three sets of data for Au, Ag, and Al metals from the test set for testing. The test results are shown below. Figure 4 Figures (c) to (e) show the results. The dots represent the angular spectrum output by the forward prediction network, and the solid line represents the angular spectrum calculated numerically based on scattering theory. It can be seen that, for both TE and TM waves, with the three metals serving as the central pillars, the output of the forward prediction network and the numerically calculated data remain consistent, at 0.0003, 0.0005, and 0.0005 respectively. This demonstrates that the forward prediction network constructed in this application can predict the correct scattering angular spectrum based on given arbitrary structural parameters, exhibiting extremely high accuracy and generalization.

[0081] C. Reverse engineering network construction

[0082] The reverse network is constructed by connecting two fully connected networks in series (see [reference]). Figure 3The network structure consists of two parts: one is the aforementioned forward prediction network; the other is a fully connected network, which is part of the reverse design and also consists of an input layer, hidden layers, and an output layer. The input layer uses independent encoding and has 181 nodes. These nodes represent the TE or TM scattering angle spectrum from 0 to 180 degrees. The output layer has 8 nodes, where the first five represent the predicted thickness of the metal-dielectric multilayer cylinder, and the last three represent the predicted metal type. The number of neurons in each layer from the input layer to the output layer is (181, 400, 800, 400, 100, 8), which is structurally symmetrical to the forward network.

[0083] This application trains two inverse design networks built using TE and TM separately. During training, the forward prediction network needs to be pre-trained, and its internal weight parameters are fixed. Only the internal parameters of the inverse design part are trained. Other parameters, such as the learning rate, activation function, and optimizer, are exactly the same as those of the forward network. The loss function is the mean square error between the input angular spectrum and the output angular spectrum of the concatenated network, with the same formal mean square error (MSE).

[0084] The reverse design network implemented in this application does not require the network to output specified structural parameters; it only needs that the scattering angle spectrum corresponding to the output structural parameters and material selection is close to the original scattering angle spectrum. This overcomes the convergence problem of traditional methods due to non-uniqueness. The training and actual prediction results are as follows: Figure 5 As shown in the figure. Calculations revealed that after 500 training iterations, the network exhibited good convergence, as shown in the figure. Figure 5 Figures (a) and (b) show the results. The training and validation set losses for the TE network were 0.013 and 0.012, respectively, while those for the TM network were 0.053 and 0.048. To test the reverse engineering capability of this cascaded network, three scattering angle spectra of three metals were randomly selected from the test set and input into the cascaded network. Based on the structural parameters predicted by the network, the corresponding scattering angle spectra were calculated according to scattering theory. These scattering angle spectra were then compared with the original scattering angle spectra, as shown in the comparison figure. Figure 5 Figures (c) to (e) show the results. In the figures, the dots represent the scattering angle spectrum corresponding to the structure given by the network, and the solid lines represent the numerical results of the scattering theory. For different polarization and material choices, the network's reverse design capability remains excellent, with good fitting results. The mean square errors of the three sets of data are 0.171, 0.074, and 0.008, respectively. These results demonstrate the effectiveness of the design network in this application for reverse design problems. It is worth mentioning that the reverse design process only takes 0.03 seconds, far faster than traditional numerical design algorithms.

[0085] D. Reverse design verification of equivalent electromagnetic dual structure

[0086] Using the methods described above, it is possible to design, for example Figure 6Cylinder 1 and cylinder 2 are shown. (As shown...) Figure 6 As shown in Figure (a), cylinder 1 has a 5-layer structure of alternating Ag and TiO2 layers, with thicknesses of 5.69 nm, 112.85 nm, 106.45 nm, 128.31 nm, and 5.58 nm, respectively. Its TE scattering angle spectrum is as follows: Figure 6 As shown by curve 1 in figure (c). Cylinder 2 is as follows. Figure 6 Figure (b) shows a five-layer structure consisting of alternating Au and TiO2 layers, plus an outermost air layer. The thicknesses of each layer are 47.89 nm, 58.98 nm, 39.65 nm, 89.03 nm, 16.38 nm, and 106.95 nm, respectively, and its total radius is the same as that of cylinder 1. The TM scattering angle spectrum of cylinder 2 is as follows. Figure 6 As shown in curve 2 of Figure (c), it can be seen that the TM scattering angle spectrum of cylinder 2 matches the TE scattering angle spectrum of cylinder 1 well.

[0087] However, it should be noted that the equivalence of scattering angle spectra is a necessary but not sufficient condition for equivalent electromagnetic duality. This is because the scattering angle spectra only consider the amplitudes of the electric and magnetic fields and do not reflect whether the phases are the same. To further prove that cylinder 1 and cylinder 2 approximately satisfy equivalent duality, Figure 7 Figure (a) shows the distribution of the real part and amplitude of the electric field of cylinder 1 under TE waves. For comparative analysis, in... Figure 7 In Figure (b), by interchanging the relative permittivity and permeability of cylinder 1 and using TM wave excitation, this cylinder satisfies strict electromagnetic duality symmetry with cylinder 1. The magnetic field distribution at this point is essentially identical to that of cylinder 1. Figure 7 The electric field distribution in Figure (a). Furthermore, Figure 7 Figure (c) shows the distribution of the real part and amplitude of the magnetic field of cylinder 2 under TM wave excitation, in comparison with... Figure 7 The electric field distribution in Figure (a) and Figure 7 As can be seen from the magnetic field distribution in Figure (b), the field distributions in the three cases are almost identical. This indicates that cylinder 1 and cylinder 2 do indeed satisfy approximate electromagnetic duality, and also proves the accuracy and efficiency of deep learning algorithms in reverse engineering.

[0088] In summary, the method of this application avoids the cumbersome complexity of traditional numerical simulation calculation methods by training and combining forward prediction networks and reverse design networks. It is fast and efficient in predicting light scattering angle spectra and inversely designing scatterer structures. Furthermore, in the process of realizing the design of equivalent electromagnetic dual structures, it not only overcomes the deficiency of traditional methods in lacking design capabilities, but also, because artificial neural networks have strong data processing capabilities, the ability of neural networks to provide solutions is not unique, and it has good generalization ability under the same model. That is, the method of this patent can design more than one pair of equivalent dual electromagnetic structures of cylinders.

[0089] This application also provides a parameter acquisition system for nanomaterials, the system comprising at least one processor and at least one memory; the at least one memory is used to store computer instructions; and the at least one processor is used to execute at least a portion of the computer instructions to implement the method described above.

[0090] The above-mentioned nanomaterial parameter acquisition system can execute at least some of the instructions in the memory through a processor to design the target nanomaterial under the target electromagnetic wave more quickly and accurately based on the reference scattering angle spectrum using an artificial neural network, thereby realizing the equivalent electromagnetic dual structure and reducing the design difficulty of the equivalent electromagnetic dual structure in traditional methods.

[0091] Optionally, the processor can execute computer instructions (e.g., program code) and perform the function of acquiring parameters of nanomaterials according to the techniques described in this application. Computer instructions may include, for example, routines, programs, objects, components, data structures, procedures, modules, and functions that perform the specific functions described in this application. In some embodiments, the processor may include one or more hardware processors, such as microcontrollers, microprocessors, reduced instruction set computers (RISC), application-specific integrated circuits (ASICs), application-specific instruction set processors (ASIPs), central processing units (CPUs), graphics processing units (GPUs), physical processing units (PPUs), microcontroller units, digital signal processors (DSPs), field-programmable gate arrays (FPGAs), advanced RISC machines (ARMs), programmable logic devices (PLDs), any circuit or processor capable of performing one or more functions, or combinations thereof.

[0092] For illustrative purposes only, only one processor is described in the computing device. However, it should be noted that the computing device disclosed in this application may also include multiple processors. Therefore, the operations and / or method steps disclosed in this application that are executed by one processor may also be executed jointly or separately by multiple processors. For example, if in this application, the processor of the computing device executes operation A and operation B, it should be understood that operation A and operation B may also be executed jointly or separately by two or more different processors in the computing device (e.g., the first processor executes operation A, the second processor executes operation B, or the first processor and the second processor jointly execute operation A and B).

[0093] The memory can store data / information. In some embodiments, the memory may include mass storage, removable memory, volatile read-write memory, read-only memory, etc., or any combination thereof. For example, mass storage may include disks, optical disks, solid-state drives, etc. Removable memory may include flash drives, floppy disks, optical disks, memory cards, compact disks, magnetic tapes, etc. Volatile read-write memory may include random access memory (RAM). RAM may include dynamic RAM (DRAM), double data rate synchronous dynamic RAM (DDR SDRAM), static RAM (SRAM), thyristor RAM (T-RAM), and zero-capacitor RAM (Z-RAM), etc. ROM may include mask ROM (MROM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), optical disc ROM (CD-ROM), and digital multifunction disk ROM, etc. In some embodiments, the memory may store one or more programs and / or instructions to perform the exemplary methods described in this application.

[0094] Input / output can input and / or output signals, data, information, etc. In some embodiments, input / output may include input devices and output devices. Exemplary input devices may include a keyboard, mouse, touchscreen, microphone, etc., or combinations thereof. Exemplary output devices may include display devices, speakers, printers, projectors, etc., or combinations thereof. Exemplary display devices may include liquid crystal displays (LCDs), light-emitting diode (LED) based displays, flat panel displays, curved screens, television equipment, cathode ray tubes (CRTs), touchscreen screens, etc., or combinations thereof. A communication port may be connected to a network to facilitate data communication.

[0095] This application also provides a computer-readable storage medium that stores computer instructions that, when executed by a processor, implement the method described above.

[0096] The aforementioned computer-readable storage medium, when the computer instructions stored therein are executed by a processor, can quickly and accurately design the target nanomaterial under the target electromagnetic wave based on the reference scattering angle spectrum using an artificial neural network, thereby realizing an equivalent electromagnetic dual structure and reducing the design difficulty of the equivalent electromagnetic dual structure in traditional methods.

[0097] Those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0098] It should be noted that the numbers used to describe quantities or properties in certain embodiments of this application should be understood to be modified in some cases by the terms "approximately," "approximately," or "essentially." For example, unless otherwise stated, "approximately," "approximately," or "essentially" can indicate a variation of ±20% of the value they describe. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the desired characteristics of individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of range in some embodiments of this application are approximate values, in specific embodiments, such values ​​are set as precisely as feasible.

[0099] It should be understood that the above embodiments are exemplary and are not intended to encompass all possible implementations included in the claims. Various modifications and changes can be made to the above embodiments without departing from the scope of this disclosure. Similarly, the various technical features of the above embodiments can be arbitrarily combined to form other embodiments of the present invention that may not be explicitly described. Therefore, the above embodiments only illustrate several implementations of the present invention and do not limit the scope of protection of this patent.

Claims

1. A method for obtaining parameters of nanomaterials, characterized in that, include: Obtain the reference scattering angle spectrum of a reference nanomaterial under a reference electromagnetic wave; wherein the reference nanomaterial includes a first pillar structure, the first pillar structure including a central pillar and at least one shell layer located outside the central pillar; Based on the reference scattering angle spectrum, the first trained model is invoked to determine the target information of the target nanomaterial under the target electromagnetic wave; wherein, the target nanomaterial includes a second columnar structure, the second columnar structure includes a central column and at least one shell layer located outside the central column; in, The reference electromagnetic wave is a transverse electromagnetic wave, and the target electromagnetic wave is a transverse magnetic wave; or, the reference electromagnetic wave is a transverse magnetic wave, and the target electromagnetic wave is a transverse electromagnetic wave. The scattering angle spectrum of the second columnar structure under the target electromagnetic wave is the same as the reference scattering angle spectrum of the first columnar structure; The target information includes at least one of the target structural parameters and the target material parameters.

2. The method according to claim 1, characterized in that, The first trained model is determined according to a first training process, which includes: Acquire at least one set of first training samples under the target electromagnetic wave, each set of first training samples including the sample scattering angle spectrum of the first sample nanomaterial; A second trained model is obtained, configured to determine the scattering angle spectrum of the nanomaterial under the target electromagnetic wave based on information about the nanomaterial; wherein the information includes at least one of structural parameters and material parameters of the nanomaterial; and, Based on the second trained model and the at least one set of first training samples, a first initial model is trained to generate the first trained model.

3. The method according to claim 2, characterized in that, The second trained model is determined according to a second training process, which includes: At least one set of second training samples under the target electromagnetic wave is obtained. Each set of second training samples includes sample information of the second sample nanomaterial and the standard scattering angle spectrum of the second sample nanomaterial. The sample information includes at least one of the sample structure parameters and sample material parameters. The standard scattering angle spectrum is obtained by solving the scattering cross section of the column structure using scattering theory. Based on the at least one set of second training samples, a second initial model is trained to generate the second trained model.

4. The method according to claim 2, characterized in that, The step of training a first initial model based on the second trained model and the at least one set of first training samples to generate the first trained model includes: The scattering angle spectrum of the first sample nanomaterial in the first training sample is input into the first initial model to generate reference information of the first sample nanomaterial; wherein, the reference information includes at least one of reference structural parameters and reference material parameters; The reference information is input into the second trained model to generate a predicted scattering angle spectrum; Based on the sample scattering angle spectrum and the predicted scattering angle spectrum, the first initial model is trained to generate the first trained model.

5. The method according to claim 1, characterized in that, The process of obtaining the reference scattering angle spectrum of the reference nanomaterial under a reference electromagnetic wave includes: A third trained model is obtained, the third trained model being configured to determine the scattering angle spectrum of the nanomaterial under the reference electromagnetic wave based on information about the nanomaterial; wherein, the information includes at least one of the structural parameters and material parameters of the nanomaterial; Based on the information of the reference nanomaterial, the reference scattering angle spectrum is determined by calling the third trained model.

6. The method according to claim 1, characterized in that, The material of the central column includes metal, and the at least one shell includes alternating layers of metal shells and dielectric shells, with the outer sidewall of the central column in contact with the dielectric shell; The target structural parameters include at least one of the following: the radius of the central column, the number of the at least one shell layer, and the thickness of each shell layer. The target material parameters include at least one of the materials of the central column and each layer of the shell.

7. The method according to claim 6, characterized in that, The material of the central column includes at least one of gold, silver, and aluminum; the material of the metal shell includes at least one of gold, silver, and aluminum; and the material of the dielectric shell includes titanium dioxide.

8. A parameter acquisition system for nanomaterials, characterized in that, The system includes at least one processor and at least one memory; The at least one memory is used to store computer instructions; and, The at least one processor is configured to execute at least a portion of the computer instructions to implement the method as described in any one of claims 1 to 7.

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