A plasmonic metamaterial spectrum prediction method based on equivalent circuit deep learning
By employing the method of deep learning based on equivalent circuits, a deep learning neural network model based on equivalent circuits was constructed, which solved the problems of high computational cost and low spectral accuracy in the design of plasmonic metamaterials, and achieved fast and accurate spectral prediction and improved generalization performance.
Patent Information
- Application Number
- CN202310047640.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-31
- Publication Date
- 2025-12-12
- Estimated Expiration
- 2043-01-31
AI Technical Summary
In the design of plasmonic metamaterials, existing technologies suffer from high computational costs and long processing times due to traditional methods, and the spectral accuracy of equivalent circuit designs is limited, making it impossible to achieve efficient spectral prediction and generalization performance.
We employ the equivalent circuit deep learning method, generate data samples through RCWA and divide them into training and validation sets, construct a deep learning neural network model based on equivalent circuits, train and validate the model, and use the equivalent circuit formula to predict the absorption spectrum of plasmonic metamaterials.
With limited sample data, it significantly reduces design time and hardware costs, enabling accurate prediction of plasmonic metamaterial spectra and improving the generalization performance of neural networks, thereby increasing prediction accuracy by an order of magnitude.
Smart Images
Figure CN116230133B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of plasmonic metamaterials and artificial intelligence algorithms, and in particular to a method for predicting the spectra of plasmonic metamaterials using deep learning of equivalent circuits. Background Technology
[0002] Plasmon metamaterials have wide applications in optics, biomedicine, and chemical sensing. Before application, their spectra need to be predicted. In most research, plasmon metamaterials are designed by solving Maxwell's equations based on classical electromagnetic wave theory. With the significant advancements in computational electromagnetics, full-wave electromagnetic simulations can be used to design and optimize plasmon metamaterials; however, this method requires high computational costs and time, severely limiting the flexibility and intelligence of the design.
[0003] Later, the concept of conceptualizing complex circuits with multiple functions as appropriate combinations of basic lumped circuit elements (such as capacitors and inductors) was introduced into the field of nano-optics, proposing the concept of "optical circuits." This allows for powerful simplification and effective modularization of the function of each lumped element, facilitating the rapid design of plasmonic metamaterials. However, this method also has drawbacks: equivalent circuits can only be designed using known physical models, and the device parameters in the equivalent circuit cannot be fully and accurately known, requiring verification through simulation and debugging. Therefore, the equivalent circuit method provides vague and limited guidance for the design of plasmonic metamaterials, and the spectral accuracy obtained through this method is also very limited.
[0004] In recent years, with the continuous enhancement of neural network learning capabilities, machine learning has developed rapidly and is widely applied in many fields. By training on large amounts of data, neural networks can express complex nonlinear mapping relationships between data. Once the model is trained, prediction results can be obtained quickly, greatly saving numerical computation time and hardware resource consumption. Commonly used machine learning models include deep neural networks, autoencoders, convolutional neural networks, and generative adversarial networks. However, data-driven machine learning models often require a large number of samples. When the sample size for numerical computation is limited, the prediction accuracy and generalization performance of the model are often severely limited. Therefore, there is an urgent need to construct machine learning models based on physical cognition to perform spectral prediction of plasmon metamaterials, thereby achieving high-precision prediction and improved generalization performance with limited sample data. Summary of the Invention
[0005] To address the aforementioned technical problems in the existing technology, the inventors have proposed a method and device for predicting the spectroscopic spectra of plasmonic metamaterials using deep learning of equivalent circuits.
[0006] In a first aspect, this application proposes a method for predicting the spectra of plasmonic metamaterials using deep learning of equivalent circuits, characterized by comprising the following steps:
[0007] S1: RCWA is used to calculate and generate data samples within the range of structural parameters of a given plasmonic metamaterial physical model. The data samples are divided into training set and validation set.
[0008] S2: Construct a neural network model based on deep learning of equivalent circuits;
[0009] S3: Input the training set into the neural network model for training, use the validation set to verify the performance of the neural network model, and use the training set and validation set to train and test the neural network model to obtain the trained neural network model;
[0010] S4: Based on the trained neural network model, predict the absorption spectrum corresponding to the structural parameters of the plasmonic metamaterial physical model.
[0011] By incorporating equivalent circuit knowledge into deep learning neural networks, a deep learning neural network model based on equivalent circuits is constructed. This overcomes the cumbersome design process of traditional numerical simulation methods and equivalent circuit design methods, greatly saving the design time of metamaterial structure parameters, the modeling time of equivalent circuits, and hardware costs. It can achieve accurate prediction of plasmonic metamaterial spectra even with limited sample data, effectively improving the spectral prediction accuracy and the generalization performance of neural networks.
[0012] In a specific embodiment, the equivalent circuit formula of the neural network model is:
[0013]
[0014] R, L e and L m These represent the equivalent resistance, dynamic inductance, and Faraday inductance of the metal layer, respectively; C is the equivalent capacitance generated by the dielectric layer; and A and B are dynamic proportional adjustment coefficients.
[0015] The functions of A and B are to normalize the calculated ohmic loss to a range of 0 to 1. The corresponding ohmic loss corresponds to the optical loss. Circuit parameters |I| 2 It is proportional to the light absorption rate in the spectrum, and can transform the prediction of the absorption rate spectrum directly into the prediction of the branch current of the equivalent circuit, that is, the prediction of the circuit parameters.
[0016] In a specific embodiment, the neural network model includes an input layer, a hidden layer, and an output layer;
[0017] The input layer length is 2, meaning it takes two plasmonic metamaterial physical model structural parameters w and t as input. d , td w represents the thickness of the dielectric layer and w represents the width.
[0018] The hidden layer is constructed from four fully connected layers of length 500, which perform nonlinear transformations on the structural parameters of the plasmonic metamaterial physical model of the input layer and extract features.
[0019] The output layer length is 5, which corresponds to the 5 parameters R, L in the equivalent circuit formula. e +L m C, A, B, where L e With L m The sum is considered as a parameter.
[0020] In a specific embodiment, the absorption spectrum corresponding to the structural parameters of the plasmonic metamaterial physical model is predicted based on the trained neural network model. Specifically, two plasmonic metamaterial physical model structural parameters are input, and after passing through four fully connected layers and a nonlinear unit composed of a ReLU activation function, five equivalent circuit parameters are output. These five circuit parameters are then substituted into the equivalent circuit formula to calculate the absorption spectrum.
[0021] The hidden layer is used to process the two plasmonic metamaterial physical model structural parameters w and t input from the input layer. d By performing nonlinear transformations to extract features, the five parameters in the equivalent circuit formula are output. This neural network model thus realizes the nonlinear mapping relationship between the physical model structural parameters of plasmonic metamaterials and the parameters of the equivalent circuit formula.
[0022] In a specific embodiment, the training set is input into the neural network model for training, and the specific training method is as follows:
[0023] Initialize parameters: set batch size to 32, total number of epochs to 400, initial learning rate to 0.0001, learning rate decay strategy to decrease by 60% every 10 epochs, use Adam as gradient descent optimizer, mean squared error (MSE) as loss function, and ReLU as activation function for the entire network model.
[0024] In a specific embodiment, the physical model structure of the plasmonic metamaterial is composed of layered nanostructure units of metal-dielectric-metal, and the geometry is any one of rectangle, triangle, or ellipse. The metal is any one or more composites of gold, silver, aluminum, titanium, and germanium, and the material of the dielectric is any one of magnesium fluoride, aluminum oxide, silicon dioxide, and silicon monoxide.
[0025] In a specific embodiment, RCWA is used to calculate and generate data samples within the given range of structural parameters of the plasmonic metamaterial physical model. The data samples are then divided into a training set and a validation set, as follows:
[0026] Within the given range of structural parameters of the physical model of plasmon metamaterials, RCWA is used to model plasmon metamaterials and calculate the corresponding absorption spectrum.
[0027] RCWA generates datasets in parallel using the parallel computing capabilities of MATLAB software;
[0028] The dataset is divided into training and validation sets according to a set ratio.
[0029] Secondly, this application also proposes a computer system for an electronic device, the electronic device comprising: a processor, and a memory storing computer program instructions; the processor reads and executes the computer program instructions to implement the plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning as described in the first aspect.
[0030] Thirdly, this application also proposes a computer-readable storage medium having one or more computer programs stored thereon, characterized in that the one or more computer programs, when executed by a computer processor, implement the method described in the first aspect of this application.
[0031] Fourthly, this application also proposes an equivalent circuit deep learning-based plasmonic metamaterial spectral prediction device, characterized in that the device comprises:
[0032] Sample generation module: Configured for generating data samples for RCWA calculation, dividing the data samples into training set and validation set;
[0033] Neural Network Training Module: Configured for training a neural network model based on a dataset to obtain a trained neural network model based on equivalent circuit deep learning;
[0034] Neural network prediction module: Configured to obtain the five equivalent circuit parameters required to predict the absorption spectrum of plasmonic metamaterials based on the trained neural network model and the corresponding physical model structural parameters of the plasmonic metamaterial.
[0035] Spectrum Calculation Module: Configured to substitute the five equivalent circuit parameters derived from the neural network model based on equivalent circuit deep learning into the equivalent circuit formula, thereby predicting the absorption spectrum of plasmonic metamaterials.
[0036] This application discloses a method for predicting the spectra of plasmonic metamaterials using deep learning of equivalent circuits. It integrates equivalent circuit knowledge into a deep learning neural network, trains the neural network model, inputs the physical model structural parameters of the corresponding plasmonic metamaterial to obtain the parameters in the equivalent circuit formula, calculates the branch current of the equivalent circuit by substituting the parameters, and then obtains the absorption spectrum by predicting the branch current of the equivalent circuit.
[0037] In summary, this application includes at least the following beneficial technical effects:
[0038] 1. By integrating the knowledge of equivalent circuits into deep learning neural networks, the drawbacks of traditional numerical simulation and equivalent circuit design methods, such as being cumbersome and time-consuming, are overcome.
[0039] 2. Compared with traditional deep neural network models that directly predict spectra, the deep learning neural network model used in this invention further improves the prediction accuracy of spectra under the same training and testing data and network model size conditions. It also reduces the prediction error on the validation set by an order of magnitude. This method can achieve fast and accurate simulation of the optical response of plasmonic metamaterials. Attached Figure Description
[0040] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and, together with the description, serve to explain the principles of this application. Other embodiments and many anticipated advantages of these embodiments will be readily recognized as they become better understood through reference to the following detailed description. Elements in the drawings are not necessarily to scale. The same reference numerals refer to corresponding similar parts.
[0041] Figure 1 The flowchart of the plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning according to this application is shown.
[0042] Figure 2a The diagram shows the equivalent circuit schematic corresponding to the plasmonic metamaterial model unit structure of the plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning according to this application.
[0043] Figure 2b The diagram shows a schematic cross-sectional structure of a unit cell of a plasmonic metamaterial model for a plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning according to this application.
[0044] Figure 2c The diagram shows a schematic of the neural network model structure of a plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning according to this application.
[0045] Figure 3This diagram illustrates the absorption rate spectral prediction based on a trained neural network model, according to a deep learning method for equivalent circuit plasmonic metamaterial spectral prediction proposed in this application.
[0046] Figure 4 This paper illustrates a schematic diagram of the traditional neural network model for absorbance spectral prediction in a plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning, as described in this application.
[0047] Figure 5a The diagram shows a comparison of the spectral prediction results of the neural network model of the plasmonic metamaterial spectral prediction method based on deep learning of equivalent circuits proposed in this application and the traditional neural network model.
[0048] Figure 5b The figure shows a statistical comparison of the mean square error of the validation set samples of the neural network model of the plasmonic metamaterial spectral prediction method based on deep learning of equivalent circuits in this application and the traditional neural network model.
[0049] Figure 6a A schematic diagram of the structure of a computer system 600 of an electronic device according to an embodiment of the present invention is shown;
[0050] Figure 6b A schematic diagram of the structure of a plasmonic metamaterial spectral prediction device based on equivalent circuit deep learning according to this application is shown. Detailed Implementation
[0051] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.
[0052] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0053] Figure 1 This paper presents a flowchart illustrating a plasmonic metamaterial spectral prediction method based on deep learning of equivalent circuits, as described in this application. Figure 1 As shown, the prediction method includes the following steps:
[0054] S1: RCWA is used to calculate and generate data samples within the range of structural parameters of a given plasmonic metamaterial physical model. The data samples are divided into training set and validation set.
[0055] S2: Construct a neural network model based on deep learning of equivalent circuits;
[0056] S3: Input the training set into the neural network model for training, use the validation set to verify the performance of the neural network model, and train the neural network model using the training set and the validation set to obtain the trained neural network model;
[0057] S4: Based on the trained neural network model, predict the absorption spectrum corresponding to the structural parameters of the plasmonic metamaterial physical model.
[0058] By incorporating equivalent circuit knowledge into deep learning neural networks, a deep learning neural network model based on equivalent circuits is constructed. This overcomes the cumbersome design process of traditional numerical simulation methods and equivalent circuit design methods, greatly saving the design time of metamaterial structure parameters, the modeling time of equivalent circuits, and hardware costs. It can achieve accurate prediction of plasmonic metamaterial spectra even with limited sample data, effectively improving the spectral prediction accuracy and the generalization performance of neural networks.
[0059] In a specific embodiment, RCWA is used to calculate and generate data samples within the given range of structural parameters of the plasmonic metamaterial physical model. The data samples are then divided into a training set and a validation set, as follows:
[0060] Within the given range of structural parameters of the physical model of plasmon metamaterials, RCWA is used to model plasmon metamaterials and calculate the corresponding absorption spectrum.
[0061] RCWA generates datasets in parallel using the parallel computing capabilities of MATLAB software;
[0062] The dataset is divided into training and validation sets according to a set ratio.
[0063] In a specific embodiment, the physical model of the plasmonic metamaterial was modeled using RCWA and the absorbance spectrum in the wavelength range of 1000nm-2500nm was calculated. Sampling was performed in 15nm steps, and each data sample contained 101 spectral values. Furthermore, the parallel computing function of MATLAB software was used to generate the dataset in parallel to improve the data collection efficiency. Finally, 6000 sets of data were obtained, of which 4500 samples were used as the training set and 1500 samples were used as the validation set.
[0064] Figure 2a The diagram shows the equivalent circuit schematic corresponding to the plasmonic metamaterial model unit structure of the plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning according to this application. Figure 2a As shown, the equivalent circuit in the neural network model is equivalent to the following using circuit theory: Figure 2a The current formula for the equivalent circuit of the RLC circuit shown is:
[0065]
[0066] R, L e and L m These represent the equivalent resistance, dynamic inductance, and Faraday inductance of the metal layer, respectively; C is the equivalent capacitance generated by the dielectric layer; and A and B are dynamic proportional adjustment coefficients.
[0067] The functions of A and B are to normalize the calculated ohmic loss to a range of 0 to 1. The corresponding ohmic loss corresponds to the optical loss. Circuit parameters |I| 2 Proportional to the light absorptivity in the spectrum, the prediction of the absorptivity spectrum can be transformed into the prediction of the branch current of the equivalent circuit, that is, the prediction of the circuit parameters. Therefore, the predicted spectrum can be obtained by substituting the above circuit parameters obtained by the prediction.
[0068] like Figure 2b As shown, the unit cell structure has a period of p, the width of both the upper metal layer and the dielectric layer is w, and the thickness of the dielectric layer is t. d The thickness of the upper metal layer is t1, the thickness of the lower metal layer is t2, and the thickness of the dielectric layer is t. d The sum is the main parameter in the physical model structure of the plasmon metamaterial with width w.
[0069] In a specific embodiment, the physical model structure of the plasmonic metamaterial is composed of layered nanostructure units of metal-dielectric-metal, and the geometry is any one of rectangle, triangle, or ellipse. The metal is any one or more composites of gold, silver, aluminum, titanium, and germanium, and the material of the dielectric is any one of magnesium fluoride, aluminum oxide, silicon dioxide, and silicon monoxide.
[0070] like Figure 2c As shown, the neural network model includes an input layer, a hidden layer, and an output layer;
[0071] The input layer length is 2, meaning it takes two plasmonic metamaterial physical model structural parameters w and t as input. d , t d w represents the thickness of the dielectric layer and w represents the width.
[0072] The hidden layer is constructed from four fully connected layers of length 500, which perform nonlinear transformations on the structural parameters of the plasmonic metamaterial physical model of the input layer and extract features.
[0073] The output layer length is 5, which corresponds to the 5 parameters R, L in the equivalent circuit formula. e +L m C, A, B, where L e With L m The sum is considered as a parameter.
[0074] In a specific embodiment, the training set is input into the neural network model for training, and the specific training method is as follows:
[0075] Initialize parameters: set batch size to 32, total number of epochs to 400, initial learning rate to 0.0001, learning rate decay strategy to decrease by 60% every 10 epochs, use Adam as gradient descent optimizer, mean squared error (MSE) as loss function, and ReLU as activation function for the entire network model.
[0076] In a further embodiment, validation set samples that have not appeared in the training set are fed into the network model, and the prediction accuracy and generalization performance of the model are tested by calculating the error between the predicted spectrum and the true spectrum using MSE.
[0077] Figure 3 This paper illustrates a schematic diagram of the traditional neural network model for absorbance spectral prediction in a plasmonic metamaterial spectral prediction method based on equivalent circuit deep learning, as described in this application. Figure 3 As shown, the traditional neural network model structure has an output layer length of 101, which means it directly predicts 101 discrete spectral values within the wavelength range.
[0078] Figure 4 This diagram illustrates a method for predicting the spectral absorption rate of plasmonic metamaterials using deep learning of equivalent circuits, based on a trained neural network model. Figure 4 As shown, the specific method is as follows:
[0079] Two plasmonic metamaterial physical model structural parameters are input, and after passing through four fully connected layers and a nonlinear unit composed of ReLU activation functions, five equivalent circuit parameters are output. These five circuit parameters are then substituted into the equivalent circuit formula to calculate the current value, ultimately achieving the prediction of the absorption rate spectrum.
[0080] The structural parameters of the two plasmonic metamaterial physical models are t d and w, t d Where R is the dielectric layer thickness and w is the width, the five equivalent circuit parameters of the output layer are R, L, and W. e +L m C, A, and B correspond to the parameters in the equivalent circuit formula. The hidden layer is used to process the two plasmonic metamaterial physical model structural parameters w and t input from the input layer. d By performing nonlinear transformations to extract features, the five parameters in the equivalent circuit formula are output. This neural network model thus realizes the nonlinear mapping relationship between the physical model structural parameters of plasmonic metamaterials and the parameters of the equivalent circuit formula.
[0081] Depend on Figure 3 and Figure 4As shown, the neural network model for predicting plasmonic metamaterials disclosed in this application, compared with traditional neural network models, outputs equivalent circuit parameters instead of spectral prediction values. It incorporates the powerful simplification and effective modularization of the function of each lumped element by the equivalent circuit method into the construction of deep learning neural networks, thereby promoting the rapid design of plasmonic metamaterials.
[0082] like Figure 5a As shown, in a sample of the validation set, compared with the traditional neural network model, the spectral prediction method disclosed in this invention predicts the spectrum more closely to the true value, especially the reflectance value and wavelength position of the resonance peak. The resonance peak in the spectrum generally contains important physical information, and the prediction of the peak in the spectrum is very critical in spectral prediction. Therefore, the neural network model designed in this invention can obtain more accurate spectral prediction results and has better generalization performance than the traditional neural network model.
[0083] like Figure 5b As shown, traditional deep neural networks have approximately 90% of their sample errors greater than 1×10⁻⁶. -3 The method of this invention has a sample error greater than 1×10⁻⁶ in only 47% of cases. -3 Meanwhile, with an error of 10 -4 At this level, the number of samples in the method of this invention is far greater than that of traditional networks. In summary, this invention can achieve rapid and accurate prediction of optical responses based on the structural parameters of the input plasmon metamaterial physical model.
[0084] The testing showed that the validation set error of the traditional neural network model was 7.2 × 10⁻⁶. -3 The validation set error of the neural network model of this method is 9.9 × 10⁻⁶. -4 The validation set error is an order of magnitude smaller than that of traditional neural network models, indicating that the neural network model based on equivalent circuit deep learning proposed in this method has the advantages of more accurate prediction and better generalization performance compared with traditional neural network models.
[0085] Figure 6a A schematic diagram of the structure of a computer system 600 of an electronic device according to an embodiment of the present invention is shown, as shown in 6a. Figure 6aAs shown, the computer system 600 includes a central processing unit (CPU) 601, which can perform various appropriate actions and processes based on programs stored in read-only memory (ROM) 602 or programs loaded from storage section 608 into random access memory (RAM) 603. The RAM 603 also stores various programs and data required for the operation of the system 600. The CPU 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.
[0086] The following components are connected to I / O interface 605: an input section 606 including a keyboard, mouse, etc.; an output section 606 including a liquid crystal display (LCD) and speakers, etc.; a storage section 608 including a hard disk, etc.; and a communication section 609 including a network interface card such as a LAN card and a modem, etc. The communication section 609 performs communication processing via a network such as the Internet. A drive 610 is also connected to I / O interface 605 as needed. A removable medium 611, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 610 as needed so that computer programs read from it can be installed into storage section 608 as needed.
[0087] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 609, and / or installed from removable medium 611. When the computer program is executed by central processing unit (CPU) 601, it performs the functions defined in the methods of this application. It should be noted that the computer-readable storage medium described in this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable storage medium other than a computer-readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on a computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.
[0088] Computer program code for performing the operations of this application can be written in one or more programming languages or a combination thereof, including object-oriented programming languages such as Java, Smalltalk, and C++, and conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).
[0089] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.
[0090] The modules described in the embodiments of this application can be implemented in software or hardware. The described units can also be located in a processor, and the names of these units do not necessarily limit the unit itself.
[0091] Embodiments of the present invention also relate to a computer-readable storage medium storing a computer program that, when executed by a computer processor, performs the methods described above. The computer program includes program code for performing the methods shown in the flowchart. It should be noted that the computer-readable medium of this application may be a computer-readable signal medium, a computer-readable medium, or any combination of the two.
[0092] Figure 6b This paper presents a schematic diagram of the structure of a plasmonic metamaterial spectral prediction device based on equivalent circuit deep learning, as described in this application. Figure 6b As shown, the device includes a sample generation module 701, a neural network training module 702, a neural network prediction module 703, and a spectral calculation module 704, specifically:
[0093] Sample generation module: Configured for generating data samples for RCWA calculation, dividing the data samples into training set and validation set;
[0094] Neural Network Training Module: Configured for training a neural network model based on a dataset to obtain a trained neural network model based on equivalent circuit deep learning;
[0095] Neural network prediction module: Configured to obtain the five equivalent circuit parameters required to predict the absorption spectrum of plasmonic metamaterials based on the trained neural network model and the corresponding physical model structural parameters of the plasmonic metamaterial.
[0096] Spectrum Calculation Module: Configured to substitute the five equivalent circuit parameters derived from the neural network model based on equivalent circuit deep learning into the equivalent circuit formula, thereby predicting the absorption spectrum of plasmonic metamaterials.
[0097] This application discloses a deep learning method for predicting the spectra of plasmonic metamaterials based on equivalent circuits. This method integrates equivalent circuit knowledge into a deep learning neural network, overcoming the drawbacks of traditional numerical simulation and equivalent circuit design methods, which are complex and time-consuming. The neural network model is trained, and the parameters in the equivalent circuit formula are obtained by inputting the physical model structural parameters of the corresponding plasmonic metamaterial. The branch currents of the equivalent circuit are calculated by substituting these parameters, and the absorbance spectrum is obtained through the prediction of the equivalent circuit branch currents. This further improves the prediction accuracy of the spectrum, resulting in an order-of-magnitude reduction in prediction error on the validation set. This method can quickly and accurately simulate the optical response of plasmonic metamaterials, achieving prediction results with smaller errors and closer to the true spectrum compared to traditional neural network models, thus realizing high-precision prediction and improved generalization performance.
[0098] In the description of this application, it should be understood that the terms "upper," "lower," "inner," "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are used only for the convenience of describing this application and for simplification, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The simple fact that certain measures are recited in mutually different dependent claims does not indicate that combinations of these measures cannot be used for improvement. Any reference signs in the claims should not be construed as limiting the scope.
Claims
1. A method for predicting the spectra of plasmonic metamaterials using deep learning of equivalent circuits, characterized in that, Includes the following steps: S1: RCWA is used to calculate and generate data samples within the range of structural parameters of a given plasmonic metamaterial physical model. The data samples are divided into training set and validation set. S2: Construct a neural network model based on deep learning of equivalent circuits; The equivalent circuit formula in the neural network model is: ； R, L e and L m are the equivalent resistance, kinetic inductance and Faraday inductance of the metal layer respectively, C is the equivalent capacitance generated by the dielectric layer, and A and B are dynamic proportional adjustment coefficients; The neural network model includes an input layer, a hidden layer, and an output layer; The input layer has a length of 2, meaning it has two physical model structural parameters w and t. d , t d w represents the thickness of the dielectric layer and w represents the width. The hidden layer consists of four fully connected layers of length 500, which perform nonlinear transformations on the physical model structural parameters of the input layer and extract features. The output layer length is 5, which corresponds to the 5 parameters R, L in the equivalent circuit formula. e +L m C, A, B, where L e With L m The sum is considered as a parameter; S3: Input the training set into the neural network model for training, use the validation set to verify the performance of the neural network model, and use the training set and validation set to train and test the neural network model to obtain the trained neural network model; S4: Based on the trained neural network model, predict the absorption spectrum corresponding to the structural parameters of the plasmonic metamaterial physical model.
2. The method for predicting plasmonic metamaterial spectra using deep learning of equivalent circuits according to claim 1, characterized in that, The absorption spectrum corresponding to the structural parameters of the plasmonic metamaterial physical model is predicted based on the trained neural network model. The specific method is as follows: Two plasmonic metamaterial physical model structural parameters are input, and after passing through four fully connected layers and a nonlinear unit composed of ReLU activation functions, five equivalent circuit parameters are output. These five circuit parameters are then substituted into the equivalent circuit formula to calculate the absorption spectrum.
3. The method for predicting plasmonic metamaterial spectra using deep learning of equivalent circuits according to claim 1, characterized in that, The training set is input into the neural network model for training. The specific training method is as follows: Initialize parameters: set batch size to 32, total number of epochs to 400, initial learning rate to 0.0001, learning rate decay strategy to decrease by 60% every 10 epochs, use Adam as gradient descent optimizer, mean squared error (MSE) as loss function, and ReLU as activation function for the entire network model.
4. The method for predicting plasmonic metamaterial spectra using deep learning of equivalent circuits according to claim 1, characterized in that, The physical model structure of the plasmonic metamaterial is composed of layered nanostructure units of metal-dielectric-metal, and the geometry is any one of rectangle, triangle, or ellipse. The metal is any one or more composites of gold, silver, aluminum, titanium, and germanium, and the material of the dielectric is any one of magnesium fluoride, aluminum oxide, silicon dioxide, and silicon monoxide.
5. The method for predicting the spectroscopic spectrum of plasmon metamaterials using deep learning of equivalent circuits according to claim 1, characterized in that, Data samples were generated using RCWA within the given range of structural parameters of a plasmonic metamaterial physical model. These samples were then divided into a training set and a validation set, as follows: Within the given range of structural parameters of the physical model of plasmon metamaterials, RCWA is used to model plasmon metamaterials and calculate the corresponding absorption spectrum. RCWA generates datasets in parallel using the parallel computing capabilities of MATLAB software; The dataset is divided into training and validation sets according to a set ratio.
6. A computer system for an electronic device, the electronic device comprising: Processor, and memory storing computer program instructions; The processor reads and executes the computer program instructions to implement the plasmonic metamaterial spectral prediction method based on deep learning of equivalent circuits as described in any one of claims 1-5.
7. A computer-readable storage medium having one or more computer programs stored thereon, characterized in that, When the one or more computer programs are executed by a computer processor, they perform the method according to any one of claims 1 to 5.
8. A plasmonic metamaterial spectral prediction device based on equivalent circuit deep learning, characterized in that, The device includes: Sample generation module: Configured for generating data samples for RCWA calculation, dividing the data samples into training set and validation set; Neural Network Training Module: Configured for training a neural network model based on a dataset to obtain a trained neural network model based on equivalent circuit deep learning; The equivalent circuit formula in the neural network model is: ； R, L e and L m These are the equivalent resistance, dynamic inductance, and Faraday inductance of the metal layer, respectively; C is the equivalent capacitance generated by the dielectric layer; and A and B are dynamic proportional adjustment coefficients. The neural network model includes an input layer, a hidden layer, and an output layer; The input layer has a length of 2, meaning it has two physical model structural parameters w and t. d , t d w represents the thickness of the dielectric layer and w represents the width. The hidden layer consists of four fully connected layers of length 500, which perform nonlinear transformations on the physical model structural parameters of the input layer and extract features. The output layer length is 5, which corresponds to the 5 parameters R, L in the equivalent circuit formula. e +L m C, A, B, where L e With L m The sum is considered as a parameter; Neural network prediction module: Configured to obtain the five equivalent circuit parameters required to predict the absorption spectrum of plasmonic metamaterials based on the trained neural network model and the corresponding physical model structural parameters of the plasmonic metamaterial. Spectrum Calculation Module: Configured to substitute the five equivalent circuit parameters derived from the neural network model based on equivalent circuit deep learning into the equivalent circuit formula, thereby predicting the absorption spectrum of plasmonic metamaterials.