A few-shot spectral inference method based on cauchy mixed physical information transformer

Abstract

This invention discloses a few-sample spectral inference method based on Cauchy hybrid physical information Transformer. The method includes: acquiring a target spectrum, wherein the target spectrum is a low-frequency spectrum used to characterize the low-frequency optical response; predicting the coefficient vector of the target spectrum in Cauchy space using a Transformer-based model; multiplying the predicted coefficient vector by a Cauchy dictionary to reconstruct high-frequency target spectral features; and outputting the predicted spectral data through a multilayer perceptron. This invention improves the accuracy of spectral inference and enhances noise resistance and generalization ability.

Description

Technical Field

[0001] This invention relates to the field of spectral analysis technology, and more specifically, to a few-sample spectral inference method based on Cauchy mixed physical information Transformer. Background Technology

[0002] Spectroscopic analysis refers to the identification of substances and the determination of their chemical composition and relative abundance based on their spectra. In many fields, including photonics, materials science, and chemistry, inferring elusive spectra using simple measurement methods is a fundamental challenge. Due to cross-band correlations, these correlations can be utilized to avoid expensive iterative simulations or physical experiments. For example, in metasurface photonics, the mesh size for high-frequency simulations must decrease with increasing frequency, leading to a sharp increase in computation time and memory consumption. Although deep learning models such as Transformer have performed well in sequence prediction in recent years, the high cost of acquiring spectral data means that directly applying these models, which require massive amounts of data, easily results in poor generalization ability, and they cannot perceive the inherent physical laws of spectroscopy.

[0003] Therefore, further improvements are needed to the existing technology to enable accurate inference from low-frequency spectra to difficult-to-measure high-frequency spectra using only a small amount of training data. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a few-sample spectral inference method based on Cauchy hybrid physical information Transformer. This method includes the following steps: Acquire the target spectrum, which is a low-frequency spectrum, to characterize the low-frequency optical response of the target system; Using a Transformer-based model, predict the coefficient vector of the target spectrum in Cauchy space; The predicted coefficient vector is multiplied by the Cauchy dictionary to reconstruct the high-frequency targeting spectral features of the target system, and the predicted spectral data is output through a multilayer perceptron.

[0005] In one embodiment, the spectral data is obtained by prediction according to the following steps: Based on coupled-mode theory, a Cauchy-Lorentz atom dictionary is constructed, which is parameterized by the center frequency and linewidth. By solving the regularized least squares problem, the input target spectrum is represented as a sparse superposition of Cauchy basis functions to extract the Cauchy embedding coefficients that reflect the physical resonance mode. The target spectrum is then mapped to a high-dimensional Cauchy mixing space to obtain the embedding sequence. Perform spectral segmentation and positional encoding on the embedded sequence to obtain segmented tags; The segmented tags are input into a stacked Transformer encoder to obtain the latent representation after being output and flattened by the encoder. The encoder employs a bidirectional multi-head attention mechanism to perform synchronous feature interaction along the frequency and channel dimensions in order to deeply capture the inherent physical dependencies between different frequency bands within the same channel and between different spectral channels. For the potential representation, the coefficient vector of the target spectrum in Cauchy space is received and predicted using a Cauchy decoder. The predicted coefficient vector is multiplied by the Cauchy dictionary to reconstruct the high-frequency targeting spectral features of the target system, and the final predicted spectral data is output through a multilayer perceptron.

[0006] Compared with existing technologies, the advantages of this invention are that the few-sample spectral inference method based on Cauchy hybrid physical information Transformer overcomes the high cost of existing ultra-wideband full-wave electromagnetic simulation calculations or experimental data, as well as the shortcomings of traditional data-driven models that are prone to overfitting and lack physical constraints under small sample conditions. This invention, by designing a physically information-driven few-sample spectral inference framework (Cauchyformer), can achieve accurate inference from easily obtainable low-frequency spectra to difficult-to-measure targeted high-frequency spectra using minimal training data.

[0007] Other features and advantages of the invention will become clear from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. Attached Figure Description

[0008] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments of the invention and, together with their description, serve to explain the principles of the invention.

[0009] Figure 1 This is a flowchart of a few-sample spectral inference method based on Cauchy hybrid physical information Transformer according to an embodiment of the present invention; Figure 2 This is a schematic diagram of an encoder structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the prediction result according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the verification results on a real-world fabricated metasurface containing experimental noise and manufacturing errors, according to an embodiment of the present invention. Detailed Implementation

[0010] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0011] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0012] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0013] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0014] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0015] It should be noted that the few-sample spectral inference method based on Cauchy hybrid physics information Transformer provided by this invention can be applied to metasurfaces or for spectral prediction of target systems such as chemical substances and proteins. Target systems include, for example, photonic crystals, photonic metasurfaces, photonic metamaterials, chemical substances, gases, protein molecules, or spectrometers.

[0016] See Figure 1 As shown, the proposed metasurface few-sample spectral inference method based on Cauchy hybrid physics information Transformer includes the following steps: Step S1: Collect low-frequency spectral dataset and perform preprocessing.

[0017] The data correspondence in the training set is reflected as a mapping from easily obtainable low-frequency responses to difficult-to-obtain high-frequency target spectra.

[0018] For example, any two optical responses of the metasurface in the low-frequency band can be selected as inputs. and Typically, the absorptivity, reflectivity, or transmittance is selected. The output is the corresponding sample in high-frequency bands (such as...) where higher computational costs are required. Optical response and .

[0019] In one embodiment, these pairs of broadband spectral data in the training set can be generated by full-wave electromagnetic simulation (such as Lumerical FDTD software), with each spectrum discretized into uniformly distributed wavelength data points.

[0020] Step S2: Based on the low-frequency spectrum, extract the Cauchy embedding coefficients that reflect the physical resonance mode to obtain the embedding sequence.

[0021] The Cauchy-Lorentz distribution (or Cauchy distribution) is a continuous probability distribution that is very important in probability theory and physics. In spectroscopy, it can be used to describe the phenomenon of spectral line broadening. For example, the spectral lines emitted by excited atoms broaden due to resonance effects, and their shape conforms to the Cauchy distribution.

[0022] Step S2 performs Cauchy Mixture (MoC) physical embedding to represent the low-frequency spectrum as a sparse superposition of Cauchy basis functions, extracting Cauchy embedding coefficients that reflect the physical resonance modes to obtain the embedding sequence after Cauchy mixture physical embedding. For example, based on Coupled Mode Theory (CMT), a Cauchy-Lorentz atom dictionary D is constructed, parameterized by the center frequency and linewidth. The Cauchy-Lorentz atom dictionary D, constructed based on Coupled Mode Theory, contains a set of basis functions (atoms) with specific physical meanings for sparse encoding of the spectrum. The specific details are as follows: (1) Dictionary matrix construction: A dictionary is represented as a matrix It contains n basis functions, each of which is discretized at m frequency sampling points.

[0023] (2) Definition of basis function: each atom in the dictionary All conform to the Cauchy-Lorentz distribution, and the formula is defined as follows: .

[0024] (3) Physical parameterization: Each atom is uniquely determined by two key parameters: center frequency and line width Among them, the set of all center frequencies. It covers the frequency axes of interest for the inference task; while the linewidth set This encompasses a range of possible values ​​that match the spectral broadening phenomenon caused by the radiation (external) loss rate and the absorption / non-radiation (internal) loss rate in real physical systems.

[0025] By solving the regularized least squares problem, the input low-frequency spectrum is represented as a sparse superposition of Cauchy basis functions, thereby extracting the Cauchy embedding coefficients that reflect the physical resonance mode and mapping the spectrum to a high-dimensional MoC space.

[0026] Step S3: Perform spectral segmentation and position encoding on the obtained embedded sequence to obtain the segmented labels.

[0027] Step S3 performs spectral patching and positional encoding. For example, the embedded sequence is divided into continuous, fixed-length blocks along the frequency dimension to preserve fine-grained local features and expand the receptive field, followed by the addition of learnable positional encoding.

[0028] Step S4: Encode the segmented tags to obtain the corresponding latent representations.

[0029] The encoder can be a stacked Transformer encoder, see [link to documentation]. Figure 2 As shown, the overall structure includes a layer normalization layer, a bidirectional multi-head attention layer, and a feedforward neural network, and employs residual connections.

[0030] For example, the segmented labels are input into a stacked Transformer encoder. After being output and flattened by the encoder, the latent representation is obtained. The encoder can employ a bidirectional multi-head attention mechanism to synchronously interact with features along the frequency and channel dimensions, deeply capturing the inherent physical dependencies between different frequency bands within the same channel and between different spectral channels.

[0031] Step S5: For the latent representation, perform spectral decoding and reconstruction under physical guidance to obtain the predicted spectral data.

[0032] Specifically, for the latent representation output and flattened by the encoder, the Cauchy Decoding Head receives and predicts the coefficients of the target spectrum in Cauchy space. The predicted coefficient vector is multiplied by the Cauchy dictionary D to reconstruct the high-frequency targeted spectral features of the metasurface, and the final predicted spectral data is output through a multilayer perceptron (MLP).

[0033] It should be noted that various types of loss functions can be used during model training. For example, in the end-to-end training phase, the model primarily uses Mean Square Error (MSE) as the loss function. This is achieved by minimizing the high-frequency spectra predicted by the model. With real high frequency spectrum The mean squared error between the two is used to optimize the network weights.

[0034] Furthermore, for the objective function in the Cauchy embedding stage, when constructing the MoC module to extract physical embeddings, it essentially involves solving an L1-regularized least squares problem. Its objective function is: ,in, Represents the original spectrum. Represents the original spectrum Cauchy coefficients after sparse decomposition. This function not only includes the reconstruction error term but also introduces a control for the sparsity of the coefficients. Penalty term (through sparse weights) (Control), thereby achieving noise reduction and feature decoupling guided by physical laws.

[0035] In summary, compared with the prior art, and as shown in Table 1 below, the present invention has the following technical effects: (1) Enhanced data efficiency: Due to the adoption of a Cauchy hybrid mechanism similar to dictionary learning, the spectrum is sparsely encoded on physically meaningful patterns, which reduces noise and improves feature decoupling ability, so that the model can maintain extremely high inference accuracy and training stability even with very few samples (such as 10-20).

[0036] (2) Improved inference accuracy: Compared with traditional mainstream time series forecasting models (such as iTransformer, PatchTST, etc.), this invention achieves optimal performance in terms of mean squared error (MSE) and mean absolute error (MAE). Combined with... Figure 3 As can be seen, the model can accurately predict the high-frequency spectral evolution trends and characteristic peak positions of various types of simulated metasurfaces. This breakthrough in data efficiency is fundamentally attributed to the Cauchy mixing (MoC) mechanism introduced in this invention.

[0037] (3) Enhanced noise resistance and generalization ability: Thanks to the efficient physical representation established in the simulation domain, combined with Figure 4 As can be seen, the model of this invention was directly verified on a real manufactured metasurface containing experimental noise and manufacturing errors. It not only accurately predicted the spectral trend, but also highly reproduced the CIE color chromaticity coordinates in actual applications, and has great potential for industrial application.

[0038] Table 1: Experimental Results

[0039] This invention can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0040] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0041] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0042] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0043] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0044] 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 the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive 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 action, or using a combination of dedicated hardware and computer instructions. It will be known to those skilled in the art that implementation in hardware, implementation in software, and implementation using a combination of software and hardware are equivalent.

[0045] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, and are not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.

Claims

1. A few-sample spectral inference method based on Cauchy hybrid physical information Transformer, comprising the following steps: Acquire the target spectrum, which is a low-frequency spectrum, to characterize the low-frequency optical response of the target system; Using a Transformer-based model, predict the coefficient vector of the target spectrum in Cauchy space; The predicted coefficient vector is multiplied by the Cauchy dictionary to reconstruct the high-frequency targeting spectral features of the target system, and the predicted spectral data is output through a multilayer perceptron.

2. The method of claim 1, wherein, The spectral data is obtained by prediction based on the following steps: Based on coupled-mode theory, a Cauchy-Lorentz atom dictionary D is constructed, which is parameterized by the center frequency and linewidth. By solving the regularized least squares problem, the input target spectrum is represented as a sparse superposition of Cauchy basis functions to extract the Cauchy embedding coefficients that reflect the physical resonance mode. The target spectrum is then mapped to a high-dimensional Cauchy mixing space to obtain the embedding sequence. Perform spectral segmentation and positional encoding on the embedded sequence to obtain segmented tags; The segmented tags are input into a stacked Transformer encoder to obtain the latent representation after being output by the encoder and flattened. For the potential representation, the coefficient vector of the target spectrum in Cauchy space is received and predicted using a Cauchy decoder. The predicted coefficient vector is multiplied by the Cauchy dictionary D to reconstruct the high-frequency targeting spectral features of the target system, and the final predicted spectral data is output through a multilayer perceptron.

3. The method according to claim 1, characterized in that, The low-frequency optical response of the metasurface is selected from two of the following: absorptivity, reflectivity, and transmittance.

4. The method according to claim 1, characterized in that, Performing spectral segmentation and positional encoding on the embedded sequence includes: dividing the embedded sequence into continuous blocks of fixed length in the frequency dimension, and then adding learnable positional codes.

5. The method according to claim 1, characterized in that, The target system includes photonic crystals, photonic metasurfaces, photonic metamaterials, chemical substances, gases, protein molecules, or spectrometers.

6. The method according to claim 2, characterized in that, The encoder employs a bidirectional multi-head attention mechanism to synchronously interact with features along the frequency and channel dimensions, thereby deeply capturing the inherent physical dependencies between different frequency bands within the same channel and between different spectral channels.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

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