Coupling system parameter prediction method based on physical-data co-driven deep neural network CMT-NN

Abstract

The invention relates to the technical field of optics and the like, in particular to a coupled system parameter prediction method based on a physical-data co-driven deep neural network CMT-NN. The method comprises the following steps: taking optical response spectral lines of a double-micro-ring coupling system under different physical parameters as the input of a CMT-NN model, and taking the output as the physical parameters of a coupling resonance system; the step of constructing the trained CMT-NN model specifically comprises the following steps: S1, constructing a physical model of a target coupling system; s2, constructing a CMT-NN model, bringing physical constraints and physical parameters of the coupling model into a loss function of CMT-NN at the same time, calculating physical loss in a back propagation process through the loss function through iterative training and back propagation, and if a preset condition is met, completing training to obtain the CMT-NN model for predicting the physical parameters of the coupling resonance system; and S3, verification of the CMT-NN model is completed, and a trained CMT-NN model is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optics, in particular to a coupled system parameter prediction method based on a physics-data co-driven deep neural network CMT-NN. BACKGROUND

[0002] As a cornerstone of modern physics research, the resonant coupling effect has driven the breakthrough development of cutting-edge technologies such as precision sensing, quantum computing, and ultra-narrow linewidth lasers. To deeply analyze the physical nature of complex coupling phenomena and achieve precise control of the system, the coupled mode theory (CMT) has developed into a unified analytical framework for the study of resonant systems across disciplines. Current research methods are mainly based on theoretical formulas derived from CMT, and through optimization algorithms, the system transmission spectrum is numerically fitted to inversely calculate key parameters such as resonant frequency, energy dissipation, and coupling strength. However, when faced with complex coupling systems with highly similar transmission spectrum characteristics and multiple solutions of physical parameters, this method will fail. More seriously, as the system dimension increases, the computational complexity caused by parameter space search grows exponentially, and the existing fitting method faces dual challenges in computational efficiency and parameter identification reliability. These fundamental defects not only restrict the optimization design of new coupling resonator devices, but also limit the cross-disciplinary application ability of CMT in engineering application fields.

[0003] Deep learning technology builds a deep connection between data and physical laws, opening up a new dimension for the solution of scientific inverse problems. Traditional deep learning methods learn the end-to-end mapping relationship of unknown systems in a data-driven way, and their performance is heavily dependent on the quality and coverage of training data, while overfitting and local optimization may also cause low efficiency of the model. In addition, deep learning methods are essentially black box models lacking physical interpretability, and in complex physical systems, the high degree of freedom of the parameter space and strong nonlinearity characteristics pose great challenges to data set construction and model learning. Therefore, the integration of deep learning algorithms and empirical models provides an effective solution to these challenges. SUMMARY

[0004] Therefore, in order to solve the dual challenges of multiple solutions and computational complexity in the parameter inversion of coupled resonant systems, the present application proposes a coupled system parameter prediction method based on a physics-data co-driven deep neural network CMT-NN.

[0005] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0006] A coupled system parameter prediction method based on a physics-data co-driven deep neural network CMT-NN, comprising the following steps:

[0007] The optical responses of the double-micro-ring coupling system under different physical parameters are taken as inputs of the CMT-NN model, and the physical parameters of the coupling resonant system are output. The relevant data include: the frequency detuning amount, the intrinsic resonant frequency, the coupling efficiency between the microcavity and the optical fiber, the coupling coefficient between the modes, and the phase accumulated during the propagation between the microcavities of the double-microcavity coupling system; the specific content of constructing the trained CMT-NN model includes:

[0008] S1. Construct a physical model of the target coupling system;

[0009] S2. Construct a CMT-NN model, and simultaneously include the physical parameters, eigenvalues and spectral errors into the loss function of the CMT-NN. Through iterative training and back propagation, the value of the loss function in the back propagation process is calculated. If the preset condition is met, the training is completed, and the CMT-NN model for predicting the physical parameters of the coupling resonant system is obtained;

[0010] S3. Verify the CMT-NN model to obtain the trained CMT-NN model.

[0011] The specific content of S1 includes:

[0012] The two micro-ring resonant cavities in the coupling system are arranged in a cascading manner and are coupled with a waveguide. Four resonant modes are considered in this system, including the clockwise (CW) mode and the counterclockwise (CCW) mode of the first microcavity (Cav1), and the CW mode and the CCW mode of the second microcavity (Cav2). The transient equations corresponding to the four resonant modes of the coupling system can be expressed as:

[0013]

[0014]

[0015]

[0016]

[0017] In order to further analyze the transmission characteristics of the coupling system, we calculate the transmittance equation of the system according to the above equation:

[0018]

[0019] By introducing the transient equations of the four modes, the transmission spectrum of the microcavity coupling resonant system can be expressed as follows:

[0020]

[0021] Where:

[0022]

[0023]

[0024]

[0025] and the effective Hamiltonian representation of the system

[0026]

[0027] where Δ1=ω1-ω0 and Δ2=ω2-ω0 are the frequency detunings of the two microcavities, ω0 is the reference frequency, and ω1 and ω2 represent the intrinsic resonance frequencies of the two microcavities, respectively. γ1(γ2) and γ c1 (γ c2 ) represent the intrinsic loss of the first (second) microcavity and the coupling efficiency between the first (second) microcavity and the waveguide, respectively. g represents the direct decay coupling between the two microcavities, while g1(g2) represents the coupling coefficient between the clockwise (CW) and counterclockwise (CCW) modes in the first (second) microcavity. is the phase accumulated by the light wave propagating between the two microcavities. According to the characteristic equation (where y is the eigenstate of the Hamiltonian H), the eigenvalues corresponding to the coupling model can be calculated.

[0028] To further implement the above technical solutions, the specific content of S2 includes:

[0029] Constructing a CMT-NN network model:

[0030] Input layer: the optical response of the micro-ring coupling system under different physical parameters as the input of the CMT-NN model;

[0031] Encoder: mapped to a high-dimensional space through an embedding process, which reduces the data sampling rate and performs batch normalization on the data.

[0032] Convolution layer (attention extraction and feature learning): a large kernel attention mechanism is used to enhance data processing capability, mainly using dilated convolution and deep convolution technology. The enhanced high-dimensional spectral data are then input into a feedforward module, which is implemented through a deep convolution layer to strengthen the feature learning capability. This process is iterated multiple times until the loss function requirement is met.

[0033] Pooling layer: the data of the convolution layer are passed to the fully connected layer.

[0034] Fully connected layer: ReLu is used as the activation function, and the obtained data are split into eight sub-networks corresponding to the eight physical parameters of the coupling system.

[0035] Output layer: output the predicted physical parameters of the coupled resonator system. The output parameters include: the intrinsic resonant frequencies of the two microcavities, the coupling efficiency between the microcavity and the waveguide, the direct coupling coefficient between the modes, and the phase accumulated before the propagation of the modes.

[0036] It should be noted that:

[0037] The key idea of CMT-NN is to extract the intrinsic response of the system through a feature encoding module constrained by physical mechanism, and then realize the efficient inversion of implicit physical parameters through a neural network guided by CMT equation. The key breakthrough lies in converting the CMT eigenvalue theory into a physical constraint term integrated into the loss function, thereby eliminating the risk of multiple solutions and low precision by constructing a unique mapping between the parameter space and the spectral space.

[0038] In order to further implement the above technical solutions, the loss function Loss in S2 is:

[0039] After the four eigenfrequencies of the coupled system are added to the loss function of the neural network, the loss function of CMT-NN is constructed:

[0040]

[0041]

[0042]

[0043] Loss total =Loss1+Loss2+Loss3

[0044] Where w p,i represents the weight of different loss terms, p i represents the predicted value of the parameter, represents the label value of the parameter, N = 8 is the number of parameters; w e represents the weight of eigenvalue loss, λ j represents the predicted value of the eigenvalue, represents the true value corresponding to the predicted value, M = 4 is the number of eigenvalues; w s represents the weight of spectral loss, s k represents the predicted spectrum, represents the input spectrum. The loss function is composed of three parts: physical parameter error, eigenvalue error and transmission spectrum error, corresponding to the three parts of the loss function.

[0045] According to the above technical solutions, compared with the prior art, the present application provides a coupled system parameter prediction method based on a physical-data co-driving deep neural network CMT-NN, which has the following Advantages:

[0046] The present application aims at the multi-solution problem in coupled resonance system parameter prediction and the calculation bottleneck of high-dimensional parameter search, and proposes a physical parameter prediction method based on a coupled mode theory and data collaborative driving neural network (CMT-NN). By embedding the physical constraint constraint in the coupled mode theory into the network architecture, a loss function with deep fusion of physical mechanism and data features is constructed, and the compliance and interpretability of the neural network model to the underlying physical law of the coupled system are enhanced. Compared with the traditional data-driven method, the present application can achieve better prediction accuracy under the same data set, and compared with the traditional fitting method, the present application solves the problems of poor real-time performance, the need for a large amount of computing resources and time, and multi-solution of parameter fitting in the prior art. It can be seen that the present application can effectively improve the speed and accuracy of unknown coupled system parameter prediction. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows.

[0048] Figure 1 A flowchart of a coupled system parameter prediction method based on a physical-data co-driving deep neural network CMT-NN is provided for the present application.

[0049] Figure 2 A structure diagram of a CMT-NN model in a coupled system parameter prediction method based on a physical-data co-driving deep neural network CMT-NN is provided for the present application. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0051] The present application provides a coupled system parameter prediction method based on a physical-data co-driving deep neural network CMT-NN, as shown in Figure 1 The method comprises the following steps:

[0052] The optical response of the double-micro-ring coupled system under different physical parameters is taken as the input of the CMT-NN model, and the physical parameters of the coupled resonance system are output. The relevant data includes the frequency detuning amount, the inherent resonance frequency, the coupling efficiency of the microcavity and the optical fiber, the coupling coefficient between the modes, and the accumulated phase between the microcavities in the double-microcavity coupled system; the specific content of the constructed CMT-NN model includes:

[0053] S1. Construct a physical model of the target coupling system;

[0054] S2. Construct a CMT-NN model, simultaneously incorporate the physical constraints of the coupling model and the transmission spectrum into the loss function of the CMT-NN, calculate the value of the loss function in the back propagation process through iterative training and back propagation, and if the preset condition is met, the training is completed, and a CMT-NN model for predicting the physical parameters of the coupling resonant system is obtained;

[0055] S3. Verify the CMT-NN model to obtain a trained CMT-NN model.

[0056] The two micro ring resonant cavities in the coupling system are arranged in a cascading manner and simultaneously coupled with a waveguide. Four resonance modes are considered in this system, including the clockwise (CW) mode and the counterclockwise (CCW) mode of the first microcavity (Cav1), as well as the CW mode and the CCW mode of the second microcavity (Cav2). The transient equations corresponding to the four resonance modes of the coupling system can be expressed as:

[0057]

[0058]

[0059]

[0060]

[0061] According to the transient equations of the four modes, the transmission spectrum of the microcavity coupling resonant system can be expressed as follows:

[0062]

[0063] wherein:

[0064]

[0065]

[0066]

[0067] and the effective Hamiltonian of the system is

[0068]

[0069] To further implement the above technical solutions, the specific content of S2 includes:

[0070] Construct a CMT-NN network model:

[0071] Input layer: The optical response of the micro-ring coupling system under different physical parameters is taken as the input of the CMT-NN model.

[0072] Encoder: Mapped to a high-dimensional space through an embedding process that reduces the data sampling rate and performs batch normalization on the data.

[0073] Convolution layer (attention extraction and feature learning): A large kernel attention mechanism is used to enhance data processing capabilities, mainly using dilated convolution and deep convolution techniques. The enhanced high-dimensional spectral data is then input into a feedforward module that implements deep convolution layers to enhance feature learning capabilities. This stage continues multiple times until the loss function requirements are met.

[0074] Pooling layer: The data from the convolution layer is passed to the fully connected layer.

[0075] Fully connected layer: ReLu is used as the activation function to split the obtained data into eight sub-networks corresponding to the eight physical parameters of the coupling system.

[0076] Output layer: Outputs the predicted physical parameters of the coupling resonator system. The output parameters include: the intrinsic resonance frequencies of the two microcavities, the frequency detuning of the two microcavities, the coupling efficiency between the microcavity and the waveguide, and the coupling coefficient between the modes.

[0077] It should be noted that:

[0078] The key idea of CMT-NN is to extract the system's intrinsic response through a feature encoding module constrained by physical mechanisms, and then use a decoupling reasoning network guided by a differentiable CMT equation to efficiently invert the implicit physical parameters. The key breakthrough lies in converting the CMT eigenvalue theory into a physical regularization term integrated into the loss function, thereby eliminating the multi-solution problem by constructing a tight mapping between the parameter space and the spectral space.

[0079] To further implement the above technical solution, the loss function Loss in S2 is:

[0080] After obtaining the four eigenfrequencies of the coupling system, they are added to the loss function of the DNN. In neural network (NN) and multi-layer perceptron (MLP) models, the following loss function is used:

[0081]

[0082] By adding relevant parameters to this loss function, the loss function of CMT-NN is constructed:

[0083]

[0084]

[0085]

[0086] Loss total =Loss1+Loss2+Loss3

[0087] where w p,i represents the weight of different loss terms, p i represents the predicted value of the parameter, represents the label value of the parameter, N is the number of parameters; λ j represents the predicted value of the real part and the imaginary part of a certain eigenvalue, represents the true value corresponding to the predicted value, M is the sum of the number of real parts and imaginary parts in all eigenvalues; w s represents the weight of spectral loss, s k represents the predicted spectrum, represents the input spectrum; w e represents the weight of eigenvalue loss. The loss function is composed of three parts: physical parameter error, eigenvalue error and average transmission spectrum error, which correspond to the three parts of the loss function respectively.

[0088] In the method of the application, when training the neural network, the total loss function Loss can be made to approach a set threshold by cyclic iteration. When the total loss of the neural network approaches the set threshold, the network can be considered to be completed for predicting the physical parameters of the target coupled system.

[0089] In order to prove the excellent performance of CMT-NN, the transmission spectrum simulated by solving Maxwell equation using finite element method (FEM) is used as the input of CMT-NN to test the universality and robustness of the neural network. For the coupling of two different microcavity sizes, the spectrum reconstructed by the physical parameters predicted by CMT-NN is highly consistent with the FEM result, indicating that the physical parameter prediction has excellent accuracy for transmission spectra not belonging to the training and verification data set. These results show that the CMT-NN model can accurately capture spectral features, accurately and universally predict the physical parameters of the system, and realize accurate spectral reconstruction of the resonant system in different coupling scenarios.

[0090] The application proposes a coupled system parameter prediction method based on a physical-data co-driving deep neural network CMT-NN to solve the dual challenges of multiple solutions and computational complexity in coupled resonant system parameter identification.

[0091] Experimental verification shows that CMT-NN can realize high-precision prediction of the hidden physical parameters of the coupled resonance system by inputting the transmission spectrum. The core innovation lies in embedding the physical eigenvalues of the resonance system as regularization constraints into the loss function, which fundamentally eliminates the multi-solution dilemma in existing methods. In the batch spectrum processing scene, compared with the traditional fitting method, it shows revolutionary advantages: the calculation efficiency is improved by 3 orders of magnitude (the time consumption is reduced to 1 / 1000), and the prediction accuracy is improved by 2 orders of magnitude (the error is reduced to 1 / 100). The engineering practicability of the model is further verified in the displacement sensing experiment, highlighting its breakthrough value in intelligent analysis of complex coupled systems.

[0092] The above examples are only used to illustrate the technical solutions of the present application, but not limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A method for predicting parameters of a coupled system based on a physics-data co-driven deep neural network (CMT-NN), characterized in that, Includes the following steps: The optical response of the dual-micro-ring coupled system under different physical parameters is used as the input to the CMT-NN model, and the output is the physical parameters of the coupled resonant system. The relevant data include: the frequency detuning of the two microcavities in the dual-microcavity coupled system, the inherent resonant frequency, the coupling efficiency between the microcavities and the waveguide, the direct coupling strength between the microcavity modes, and the phase accumulated during propagation between the microcavities. The specific content of constructing the trained CMT-NN model includes: S1. Construct a physical model of the target coupled system; S2. Construct a CMT-NN model, incorporating both the physical constraints and physical parameters of the coupled model into the loss function of the CMT-NN. Through iterative training and backpropagation, calculate the value of the loss function during backpropagation. If the preset conditions are met, the training is complete, and a CMT-NN model for predicting the physical parameters of coupled resonant systems is obtained. S3. Complete the validation of the CMT-NN model to obtain the trained CMT-NN model.

2. The method for predicting parameters of a coupled system based on a physical-data co-driven deep neural network (CMT-NN) according to claim 1, characterized in that: The specific content of S1 includes: Two microring resonators in the coupled system are arranged in a cascaded manner and simultaneously coupled to a waveguide. A total of four resonant modes are considered in this system, including the clockwise (CW) and counterclockwise (CCW) modes of the first microcavity (Cav1), and the CW and CCW modes of the second microcavity (Cav2). The transient equations corresponding to the four resonant modes of this coupled system can be expressed as: The transmission spectrum of a microcavity coupled resonant system can be expressed in the following form: in: Energy exchange between microcavities is achieved through direct and indirect coupling: the CW (CCW) mode of Cav1 is indirectly coupled to the CW (CCW) mode of Cav2 via a waveguide, and the CW (CCW) mode of Cav1 can also be directly coupled to the CCW (CW) mode of Cav2. The effective Hamiltonian of this system is expressed as follows: Where Δ1 = ω1 - ω0 and Δ2 = ω2 - ω0 represent the frequency detuning of the two microcavities, ω0 is the reference frequency, and ω1 and ω2 represent the natural resonant frequencies of the two microcavities, respectively. γ1(γ2) and γ c1 (γ c2 ) represent the inherent loss of the first (second) microcavity and the coupling efficiency between the first (second) microcavity and the waveguide, respectively. g represents the direct attenuation coupling between the two microcavities, while g1 (g2) represents the coupling coefficient between the clockwise (CW) and counterclockwise (CCW) modes in the first (second) microcavity. It is the phase accumulated when the light wave propagates between the two microcavities. According to the characteristic equation Hψ=λψ (where y is the eigenstate of the Hamiltonian H), the eigenvalues ​​of the corresponding coupled model can be calculated.

3. The method for predicting parameters of a coupled system based on a physical-data co-driven deep neural network (CMT-NN) according to claim 1, characterized in that: The specific content of S2 includes: Constructing the CMT-NN network model: Input layer: The optical response of the micro-ring coupled system under different physical parameters is used as the input to the CMT-NN model; Encoder: Maps data to a high-dimensional space through an embedding process that reduces the data sampling rate and performs batch normalization on the data. Convolutional layers (attention extraction and feature learning): Employing a large-kernel attention mechanism to enhance data processing capabilities, primarily using dilated convolution and deep convolution techniques, the enhanced high-dimensional spectral data is input into the feedforward module—implemented through deep convolutional layers—to strengthen feature learning capabilities. This process iterates multiple times until the loss function requirements are met. Pooling layer: Passes data from the convolutional layer to the fully connected layer. Fully connected layer: ReLU is used as the activation function to split the obtained data into eight sub-networks, corresponding to the eight physical parameters of the coupled system. Output layer: Outputs predicted physical parameters of the coupled resonant system. These parameters include: the intrinsic resonant frequencies of the two microcavities, the coupling efficiency between the microcavities and the waveguide, the direct coupling coefficient between modes, and the phase accumulated during propagation before the modes.

4. The method for predicting parameters of a coupled system based on a physical-data co-driven deep neural network (CMT-NN) according to claim 1, characterized in that: The loss function Loss in S2 is: Based on the physical constraints of the coupled system's physical model, these constraints are incorporated into the loss function of the deep neural network to construct the loss function of CMT-NN: Among them, w p,i p represents the weights of different loss terms. i This represents the predicted value of the parameter. This represents the label value of the parameter; N=8 is the number of parameters; w e The weight λ represents the eigenvalue loss. j This represents the predicted value of the eigenvalue. This represents the true value corresponding to the predicted value, where M = 4 is the number of eigenvalues, and Im and Re represent the imaginary and real parts, respectively; w s The weights representing the spectral loss, s k Indicates the predicted spectrum, This represents the input spectrum. The loss function consists of three parts: physical parameter error, eigenvalue error, and transmission spectrum error, which correspond to the three parts of the loss function, respectively.

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