Periodically variable star light variable curve classification method based on neural network

Abstract

The invention discloses a periodic variable star light variable curve classification method based on a neural network, and relates to the field of astronomical photometric data classification and identification, and the method comprises the steps: employing an intelligent neural network composition principle, training a plurality of small networks, enabling each small network to be responsible for the identification of a variable star type, enabling all small networks to form a large intelligent neural network, and enabling all small networks to be responsible for the identification of a variable star type; and all variable star types are identified. According to the method, the amplitude of the harmonic wave in the Fourier spectrum of the optical variation curve is used as a characteristic value, supervised learning is performed on the small network, and the learning and identification efficiency of the whole network is improved by combining the symbol logic of the intelligent neural network. In addition, the method has good expandability, for example, when a to-be-recognized variable star type needs to be newly added in the future, only a corresponding small net needs to be added, the small net is added into a large net, and then a small amount of training is iteratively carried out.

Description

Technical Field

[0001] The present invention relates to the field of astronomical photometric data classification and recognition, and specifically to a method for classifying the light curves of periodic variable stars based on a neural network. Background Art

[0002] Photometric measurement is an important observation method in astronomy. This method generates light curves by continuously sampling the luminosity of celestial bodies, which are used to characterize the variation of the luminosity of celestial bodies over time. The light curves of different types of celestial bodies exhibit different characteristics. Different physical processes are involved behind these characteristics, revealing the internal structure and evolution process of celestial bodies. Therefore, classifying light curves is a very important and fundamental task. Periodic variable stars refer to those celestial bodies whose light curves show certain periodic variations. The variation periods can be long or short, and the characteristics appear periodically. They are different from celestial bodies such as supernovae, novae, recurrent novae, and transient sources that do not have significant variation periods.

[0003] With the continuous release of photometric data from various space telescopes, astronomy has entered the big data era. The traditional method of manually classifying light curves can no longer meet the actual needs. Therefore, it is necessary to introduce computer technology and use an automated classification method to classify a large amount of sky survey data. Among them, applying machine learning technology to identify and classify photometric data is an important application. Existing classification methods only identify the main categories of variable stars and do not cover some subtypes or uncommon types of variable stars, such as: heartbeat stars, optical pulsars, multiple star systems, and exoplanet transits.

[0004] On the other hand, the existing light curve feature extraction methods in machine learning applications can be mainly divided into three categories: 1. Mathematical formula calculation method; 2. Non-mathematical formula extraction method; 3. Neural network internal processing method. The first category of methods calculates feature values through a set of specific mathematical formulas, such as amplitude ratio, number of zero crossings, and flux ratio. The second category of methods develops specific non-mathematical algorithms for specific recognition objects to extract light curve features. The third category of methods implicitly completes the feature extraction work inside the neural network without using an explicit feature extraction method. However, these methods all have a certain degree of pertinence and are used to identify the main categories of variable stars, and do not cover some subtypes or uncommon types. Summary of the Invention

[0005] To address the deficiencies in the above-mentioned existing methods, the present invention proposes a method for automatically classifying the light curves of periodic variable stars based on the composition principle of an intelligent neural network. First, Fourier transform is performed on the light curve samples of known types, and the harmonics in the Fourier spectrum are used as the eigenvalue of the light curve. Then, these eigenvalues are used to train several independent small neural networks (hereinafter referred to as small networks), and each small network is responsible for identifying one type of variable star. After all the small networks are trained, they are combined to form a large intelligent neural network (hereinafter referred to as a large network) to identify all types of periodic variable stars. At the same time, symbolic logic is added to improve the learning and recognition efficiency of the entire network. In addition, the present invention also has good scalability. For example, when a new type of variable star to be identified needs to be added in the future, only one corresponding small network needs to be added, and after adding it to the large network, the large network is iteratively trained.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] Training samples: The training samples use real light curve data or synthetic light curve data generated by software model tools;

[0008] Feature extraction: Perform Fourier transform on the light curve data points, then identify the orbital frequency from the Fourier spectrum, and then extract the amplitude values of the first 100 orbital harmonics according to the orbital frequency. After normalizing this set of amplitude values, it is used as the eigenvalue of the light curve;

[0009] Small network training: The small network is an artificial neural network. As Figure 1 shown, its input layer has 100 neurons, contains 2 hidden layers, and the output layer has 2 neurons. The number of small networks is the same as the number of variable star categories to be identified, and each small network is responsible for identifying one type of variable star. The small network is trained using the supervised learning method. For example, when training the small network responsible for identifying the EA-type eclipsing binary star, several samples of the EA-type eclipsing binary star are selected as "true" samples, and several samples of other types of variable stars are selected as "false" samples. For the "true" samples, the expected output of the small network is (1,1); for the "false" samples, the expected output of the small network is (0,0);

[0010] Large network training: All small networks form a large intelligent neural network. As Figure 2 shown, its input layer has 100 neurons, the first hidden layer contains all small networks, and there is another hidden layer between the output layer of each small network and the output layer of the large network. The output layer of the large network has 8 neurons. After each set of eigenvalues is input into the large network, it is used as the input of all small networks. At this time, all small networks compete for output, and the rules are as follows:

[0011] 1. If only one small network outputs (1,1), then this small network wins the competition and forcibly sets the output of the large network to the corresponding variable star type;

[0012] 2. If the number of small networks with an output of (1, 1) is 0 or greater than 1, then use the output data of all small networks as the activation values of the hidden layer of the large network, and train the large network to output the expected variable star type.

[0013] Variable star type recognition: After all samples are trained, use the large network to identify unknown variable star samples. Input the eigenvalue of the sample to be identified into the large network, and the output value of the large network is the encoding of the corresponding variable star type.

[0014] A method for classifying the light curves of periodic variable stars based on neural networks, including:

[0015] S1. Collect the light curve data of periodic variable stars and divide it into a training set and a test set.

[0016] S2. Perform Fourier transform on each light curve, extract the first several orbital harmonic amplitudes in its spectrum as eigenvalues, normalize them, combine time-domain features and frequency-domain features to construct a multi-dimensional feature vector, and perform dimensionality reduction on the feature vector.

[0017] S3. Design a small neural network for each variable star type separately. Each small neural network is responsible for identifying a specific type of periodic variable star, and use the supervised learning method to train the small network.

[0018] S4. Integrate the output results of all small neural networks into a large neural network. Introduce a competition mechanism and an attention mechanism during the training process, use the cross-validation method to verify the generalization performance of the large network, and adjust the network structure and training parameters according to the verification results.

[0019] S5. Use the test set to evaluate the performance of the trained small neural network and large neural network, check the overfitting situation of the model, and adopt data augmentation methods for optimization.

[0020] S6. Pass the light curve data to be classified through the same preprocessing and feature extraction process, input the extracted eigenvalues into the large network for classification, and post-process the classification results to improve the reliability of the classification results.

[0021] Preferably, collecting the light curve data of periodic variable stars and dividing it into a training set and a test set specifically includes:

[0022] Separate "true" samples and "false" samples for each variable star type in the training set. The "true" samples are the light curve data of variable stars of this type, and the "false" samples are the light curve data of variable stars of other types.

[0023] Preprocess the sample data, including denoising, normalization, and standardization operations, to eliminate noise interference and ensure the consistency of data distribution;

[0024] Ensure the balance of training samples to avoid the model being biased towards a certain category due to uneven sample distribution.

[0025] Preferably, perform Fourier transform on each light curve, extract the amplitudes of the first several orbital harmonics in its spectrum as eigenvalues, and perform normalization on them. Combine time-domain features and frequency-domain features to construct a multi-dimensional feature vector, and perform dimensionality reduction on the feature vector to reduce the computational complexity and improve the feature expression ability. Specifically include:

[0026] Select an appropriate sampling frequency and window size, apply the fast Fourier transform algorithm to transform the light curve, calculate the spectrogram, and display the energy distribution of different frequency components;

[0027] Find the frequency with the highest energy as the fundamental frequency by analyzing the spectrogram, extract the first several harmonics, and record the amplitude values of each harmonic;

[0028] Construct a multi-dimensional feature vector, arrange the time-domain features and frequency-domain features in sequence to form a high-dimensional vector;

[0029] Perform dimensionality reduction, select an appropriate dimensionality reduction algorithm, perform dimensionality reduction on the multi-dimensional feature vector, and verify whether the features after dimensionality reduction retain sufficient information.

[0030] Preferably, extracting the amplitudes of the first several orbital harmonics in its spectrum as eigenvalues specifically includes:

[0031] Time-domain features include mean, variance, skewness, kurtosis, change amplitude, and change rate;

[0032] Frequency-domain features include power spectral density, main frequency, frequency bandwidth, harmonic ratio, and total energy.

[0033] Preferably, extracting the amplitudes of the first several orbital harmonics in its spectrum as eigenvalues and performing normalization on them specifically includes:

[0034] Perform normalization on the extracted amplitude values. The normalization formula is:

[0035]

[0036] where a i represents the amplitude of the i-th orbital harmonic, and ||A|| represents the Euclidean norm of vector A;

[0037] The formula for the normalized amplitude is:

[0038]

[0039] where a’ i represents the normalized amplitude, a i represents the amplitude of the i-th orbital harmonic, and ||A|| represents the Euclidean norm of vector A.

[0040] Preferably, a small neural network is designed separately for each type of variable star. Each small neural network is responsible for identifying a specific type of periodic variable star. Using the supervised learning method to train the small network specifically includes:

[0041] Each small network uses a multi-layer perceptron as the basic architecture. The input layer receives the normalized light curve feature vector. The hidden layer is used to extract features and perform non-linear mapping. The number of neurons in the hidden layer can be adjusted according to the data complexity. The output layer contains 2 neurons, which are used to output the binary classification result. 1 represents a "true" sample, and 0 represents a "false" sample;

[0042] Using the supervised learning method, when inputting a "true" sample, the expected output is (1,1); when inputting a "false" sample, the expected output is (0,0), and reasonable training parameters are set;

[0043] To prevent overfitting, a Dropout layer is introduced to enhance the generalization ability of the model. An early stopping mechanism is adopted. When the performance of the validation set does not improve for several consecutive epochs, the training is stopped;

[0044] The performance of the small network is evaluated using accuracy, precision, recall, and F1-score. If the recognition ability of a certain small network is insufficient, the performance can be improved by increasing the number of "false" samples and adjusting the network structure for incremental training.

[0045] Preferably, the output results of all small neural networks are integrated into a large neural network. During the training process, a competition mechanism and an attention mechanism are introduced. The cross-validation method is used to verify the generalization performance of the large network, and the network structure and training parameters are adjusted according to the verification results. Specifically include:

[0046] Determine the output dimension of each small network;

[0047] Design a competition rule. When the outputs of multiple small networks are "1", the final result is selected according to a preset rule. An attention layer is introduced into the large network to weight the outputs of each small network; the attention weights are obtained through training and learning, making the large network pay more attention to the outputs of the better-performing small networks;

[0048] Design the hidden layer structure of the large network. The hidden layer can include multiple fully connected layers, which are used to integrate and process the outputs from each small network; the output layer is designed with the same number of neurons as the number of variable star types, and each neuron represents the encoding of a variable star type;

[0049] Use k-fold cross-validation, using different subsets as the validation set in each iteration to evaluate the generalization performance of the large network. According to the validation results, adjust the network structure and training parameters;

[0050] Use supervised learning methods to train the large network, set the loss function and optimizer, monitor the performance of the validation set during training to avoid overfitting; adjust the model parameters according to the validation results until satisfactory performance is achieved.

[0051] Preferably, use the test set to evaluate the performance of the trained small neural network and large neural network, check for overfitting of the model, and adopt data augmentation methods for optimization, specifically including:

[0052] The test set should contain various types of variable star samples, including edge cases and samples with high noise;

[0053] Compare the performance of the training set and the test set. If the small network or the large network performs excellently on the training set but poorly on the test set, it indicates overfitting. Use k-fold cross-validation to evaluate the stability of the model, plot the learning curves of the training set and the validation set, and observe whether there are high variance or high bias problems.

[0054] Preferably, adopt data augmentation methods for optimization, specifically including:

[0055] Perform time translation, scaling, or adding noise to the time-domain data to simulate data changes under different observation conditions;

[0056] Perform phase rotation, frequency offset, or harmonic enhancement on the frequency-domain features to increase spectral diversity;

[0057] Synthetic data generation, using generative adversarial networks to generate virtual light curve data to expand the training samples;

[0058] Combine the enhancement methods in the time domain and the frequency domain to generate more representative training samples.

[0059] Preferably, the variable star curve data to be classified is processed through the same preprocessing and feature extraction process, and the extracted feature values are input into the large network for classification. Post-process the classification results to improve the reliability of the classification results, specifically including:

[0060] Evaluate the confidence of the classification results, calculate the confidence of each classification result, set a confidence threshold, and consider the results below the threshold as "uncertain" and require further analysis and manual review;

[0061] Identify abnormal samples through statistical analysis and clustering methods, mark the abnormal samples, and perform secondary classification and exclusion in combination with domain knowledge;

[0062] Combine the output results of multiple small networks to improve the classification reliability. Introduce astronomical knowledge to calibrate the classification results.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] Adopt the deep learning method, which can automatically extract complex features in the light curve and reduce the dependence on artificial feature engineering. Through the modular small network design and the global optimization of the large network, the accuracy and classification speed of periodic variable star recognition are significantly improved.

[0065] By designing independent small networks for each type of variable star, dynamic expansion is supported. When a new type of variable star is added, only the corresponding small network needs to be added and the large network needs to be retrained, without reconstructing the entire system, which greatly improves the flexibility and adaptability of the system; the introduced competition mechanism and attention mechanism effectively reduce the risk of misjudgment and improve the robustness of the system; at the same time, through cross-validation and data augmentation methods, the generalization ability of the model is enhanced, enabling it to better handle noise and edge cases. Adopt the distributed computing strategy and modular design, which can efficiently process massive astronomical data; through parallel training and optimized network structure, the processing ability and operation efficiency of the system are significantly improved; the introduction of the competition mechanism reduces unnecessary consumption of computing resources; in addition, the modular network structure makes the system easier to maintain and update, with strong functional independence of different parts, facilitating fault troubleshooting and performance optimization. Description of the Drawings

[0066] Figure 1 It is a flowchart of a method for classifying the light curves of periodic variable stars based on a neural network;

[0067] Figure 2 It is a topology diagram of a small network;

[0068] Figure 3 It is a topology diagram of a large network;

[0069] Figure 4 It is an example diagram of a light curve and its spectrum. Detailed Embodiments

[0070] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments in the following description are only examples, and those skilled in the art can think of other obvious variations.

[0071] For the convenience of narration, the following definitions are made first:

[0072] Definition (1): Let T represent the set of all variable star types to be recognized, T = {"EA", "EB", "RRab",...};

[0073] Definition (2): Name the small network. The small network named a is responsible for identifying variable star type a, where a ∈ T. For example, the small network named EA is used to identify EA-type eclipsing binaries;

[0074] Definition (3): Let a, b ∈ T. Let Va(b) denote the output value of the small network when the sample of b is input to the small network a; let W(b) denote the output value of the large network when the sample of b is input to the large network. From Figure 1 and Figure 2 it can be known that: the value of Va(b) is a 1×2 vector, and the value of W(b) is a 1×8 vector;

[0075] Definition (4): In the identification of the small network, let a, b ∈ T. When the sample of b is input to the small network a, if Va(b) = (1, 1), then the small network a identifies the b sample as type a; otherwise, it cannot be identified;

[0076] Definition (5): Encode the types in T. Let a ∈ T. Let N(a) denote a 1×8 vector corresponding to type a. For example, 0000,0001 represents EA type; 0000,0010 represents EB type;

[0077] Definition (6): In the identification of the large network, let b ∈ T. When the sample of b is input to the large network, if there exists a ∈ T such that W(b) = N(a), then the large network identifies the b sample as type a; otherwise, b is an unidentifiable sample;

[0078] The network topologies of the small network and the large network are respectively as Figure 1 and Figure 2 shown. The small network is an artificial neural network (ANN). Its input layer has 100 neurons, receiving the eigenvalue input from the first layer of the large network. The first hidden layer has 80 neurons, the second hidden layer has 40 neurons, and the output layer has 2 neurons. The identification method of the small network refers to Definition (4); the large network is an intelligent neural network. Its input layer has 100 neurons, receiving the eigenvalue input of the sample. The hidden layer contains several small networks. There is a hidden layer with 60 neurons between the output layer of each small network and the output layer of the large network. The output layer of the large network has 8 neurons, used to output the encoded variable star type after identification. The identification method of the large network refers to Definition (6); in addition, the input-output function from the hidden layer to the output layer of the large network and the input-output functions between the layers of the small network are all sigmoid functions: f(x) = 1 / (1 + e - x).

[0079] The following will combine with Figure 1 the working process to detail the specific implementation manners of the present invention:

[0080] Step (1): Prepare 5000 - 10000 samples for each type of variable star to be identified. The samples can be real light curve data or synthetic light curve data generated by a model tool. Randomly select 80% of the samples as training samples and the remaining 20% as test samples;

[0081] Step (2): Perform Fourier transform on each sample and extract the first 100 orbital harmonic amplitudes in its Fourier spectrum as the eigenvalue of the sample, that is: the eigenvalue of each sample is defined as A = (a1, a2,..., a100), where ai is the amplitude of the i-th orbital harmonic, and normalize it with the following formula: ai = ai / ‖A‖, ‖A‖ = (Σai2)1 / 2. For example Figure 4 As shown, the left side is the phase-folded light curve, and the right side is the corresponding Fourier spectrum, where the red numbers above mark the harmonic numbers;

[0082] Step (3): Use the error backpropagation (BP) algorithm to train each small network so that each small network can identify the type of variable star it is responsible for. For example, when training the small network named EA, use two groups of samples to train it. One group is the "true" samples, and the other group is the "false" samples. The "true" samples are composed of variable star samples of type EA, and the "false" samples are composed of variable star samples of other non-EA types (randomly select several samples from other type samples so that the total number is equivalent to the number of "true" samples). When training with "true" samples, the expected output of the small network is (1, 1); when training with "false" samples, the expected output of the small network is (0, 0);

[0083] Step (4): After all small networks are trained, train the large network with all training samples. After each eigenvalue is input into the large network, all small networks compete for output. The rules are as follows:

[0084] Rule 1: If only one small network outputs (1, 1), then this small network wins the competition, and forcefully set the output of the large network to the value N(x) corresponding to the name of this small network. For example: Let x ∈ T, y = {y|y ∈ T and y ≠ x}. If Vx(x) = (1, 1), and for any y, Vy(x) ≠ (1, 1), then set W(x) = N(x);

[0085] Rule 2: If the number of small networks with an output of (1, 1) is greater than 1 or equal to 0, then use the output values of all small networks as the activation values of the hidden layer of the large network, train the large network, and adjust the weights from the hidden layer to the output layer and the threshold of the output layer of the large network so that its output is the expected type code. For example: Let the input be x, x ∈ T, and after the large network learns, make W(x) = N(x);

[0086] Step (5): After all the training samples are trained, use the test samples to evaluate the performance of the large network. If the recognition ability of the network is poor, the small network can be retrained. The specific method is as follows: Let a = "EA", b = "EB", c = "RRab". When a is the input sample, if Va(a) = (1, 1), Vb(a) = (1, 1), Vc(a) = (1, 1), then several learning samples of the EA type can be selectively extracted and added to the "false" samples of EB and RRab respectively, and then the small networks of EB and RRab are trained again. This method can improve the recognition ability of the network;

[0087] Step (6): Use the trained large network to classify the variable star samples. Input the eigenvalue of the light curve into the large network. The recognition method of the large network is shown in Definition (6). At this time, the output value of the large network is the code corresponding to the recognized variable star type.

[0088] The above is the specific implementation manner of the present invention, which has good scalability. For example, if a new type of variable star "X" to be recognized needs to be added in the future, only a small network named X needs to be newly added and trained, and then added to the large network. At this time, only a small amount of incremental training is required for the large network, and incremental training is also required for some of the original small networks, which will effectively reduce the training cost of the entire network.

[0089] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the description in the specification only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection required by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for classifying light curves of periodic variable stars based on neural networks, characterized in that: include: S1. Collect the light curve data of periodic variable stars and divide them into training set and test set; S2. Perform Fourier transform on each light curve, extract the amplitudes of the first several orbital harmonics in its spectrum as eigenvalues, normalize them, combine the time domain features and frequency domain features, construct a multidimensional feature vector, and perform dimensionality reduction on the feature vector; S3. Design a small neural network for each type of variable star. Each small neural network is responsible for identifying a specific type of periodic variable star. Use supervised learning methods to train the small network. S4. Integrate the output results of all small neural networks into a large neural network, introduce competition mechanism and attention mechanism in the training process, use cross-validation method to verify the generalization performance of the large network, and adjust the network structure and training parameters according to the verification results; S5. Use the test set to evaluate the performance of the trained small neural network and large neural network, check the overfitting of the model, and use data enhancement methods to optimize it; S6. The light curve data to be classified are subjected to the same preprocessing and feature extraction process, the extracted feature values ​​are input into the large network for classification, and the classification results are post-processed to improve the reliability of the classification results.

2. The method for classifying light curves of periodic variable stars based on neural networks according to claim 1, characterized in that: The collecting of light curve data of periodic variable stars and dividing the data into a training set and a test set specifically includes: For each type of variable star in the training set, prepare "true" samples and "false" samples separately. The "true" samples are the light curve data of this type of variable star, and the "false" samples are the light curve data of other types of variable stars. Preprocess the sample data, including denoising, normalization and standardization operations, to eliminate noise interference and ensure the consistency of data distribution; Ensure the balance of training samples to avoid the model being biased towards a certain category due to uneven sample distribution.

3. The neural network-based periodic variable star light curve classification method according to claim 2, characterized in that: The Fourier transform is performed on each light curve, the amplitudes of the first several orbital harmonics in its spectrum are extracted as characteristic values, and normalized, and a multi-dimensional characteristic vector is constructed by combining the time domain features and the frequency domain features, and the characteristic vector is reduced in dimension to reduce the computational complexity and improve the characteristic expression capability. Specifically, the following steps are performed: Select appropriate sampling frequency and window size, apply fast Fourier transform algorithm to transform light curve, calculate spectrum diagram, and show the energy distribution of different frequency components; By analyzing the spectrum, find the frequency with the highest energy as the fundamental frequency, extract the first several harmonics, and record the amplitude value of each harmonic; Construct a multi-dimensional feature vector, arrange the time domain features and frequency domain features in order to form a high-dimensional vector; Dimensionality reduction processing: Select a suitable dimensionality reduction algorithm to reduce the dimensionality of the multi-dimensional feature vector and verify whether the features after dimensionality reduction retain sufficient information.

4. The neural network-based periodic variable star light curve classification method according to claim 3, characterized in that: The step of extracting the first several orbit harmonic amplitudes in the spectrum as characteristic values ​​specifically includes: Time domain characteristics include mean, variance, skewness, kurtosis, amplitude of change, and rate of change; Frequency domain features include power spectral density, main frequency, frequency bandwidth, harmonic ratio, and total energy.

5. The neural network-based periodic variable star light curve classification method according to claim 4, characterized in that: The extracting of the first several orbit harmonic amplitudes in the spectrum as characteristic values ​​and normalizing the characteristic values ​​specifically includes: The extracted amplitude value is normalized, and the normalization formula is: In the formula, a i represents the amplitude of the i-th orbital harmonic, ||A|| represents the Euclidean norm of vector A; The normalized amplitude calculation formula is: In the formula, a′ i Expressed as the normalized amplitude, a i represents the amplitude of the i-th orbital harmonic, and ||A|| represents the Euclidean norm of vector A.

6. The neural network-based periodic variable star light curve classification method according to claim 5, characterized in that: A small neural network is designed for each type of variable star. Each small neural network is responsible for identifying a specific type of periodic variable star. The supervised learning method is used to train the small network, including: Each small network uses a multi-layer perceptron as the basic architecture. The input layer receives the normalized light curve feature vector. The hidden layer is used to extract features and perform nonlinear mapping. The number of neurons in the hidden layer can be adjusted according to the complexity of the data. The output layer contains 2 neurons for outputting binary classification results. 1 represents a "true" sample and 0 represents a "false" sample. Using supervised learning methods, when inputting "true" samples, the expected output is (1,1); when inputting "false" samples, the expected output is (0,0), and reasonable training parameters are set; The Dropout layer is introduced to prevent overfitting. The early stopping mechanism is adopted to enhance the generalization ability of the model. When the performance of the validation set does not improve for several consecutive epochs, the training is stopped. Model evaluation uses accuracy, precision, recall and F1 score to evaluate the performance of the small network. If the recognition ability of a small network is insufficient, incremental training can be performed by increasing the number of "fake" samples and adjusting the network structure.

7. The neural network-based periodic variable star light curve classification method according to claim 6, characterized in that: The output results of all small neural networks are integrated into a large neural network, and the competition mechanism and attention mechanism are introduced in the training process. The cross-validation method is used to verify the generalization performance of the large network, and the network structure and training parameters are adjusted according to the verification results. Specifically, the following are included: Determine the output dimension of each small network; Design competition rules. When multiple small networks output "1", select the final result according to the preset rules. Introduce an attention layer in the big network to weight the output of each small network. The attention weight is learned through training, so that the big network pays more attention to the output of the small network with better performance. Design the hidden layer structure of the large network. The hidden layer can contain multiple fully connected layers to integrate and process the outputs from each small network. The output layer is designed to have the same number of neurons as the number of variable star types, and each neuron represents the code of a variable star type. Use k-fold cross validation, use different subsets as validation sets in each iteration, evaluate the generalization performance of the large network, and adjust the network structure and training parameters based on the validation results; Use supervised learning methods to train the large network, set the loss function and optimizer, monitor the performance of the validation set during training to avoid overfitting; adjust the model parameters according to the validation results until satisfactory performance is achieved.

8. The neural network-based periodic variable star light curve classification method according to claim 7, characterized in that: The test set is used to evaluate the performance of the trained small neural network and large neural network, check the overfitting of the model, and optimize it by taking data enhancement methods, including: The test set should contain a variety of variable star samples, including edge cases and noisy samples; Compare the performance of the training set and the test set. If the small network or the large network performs well on the training set but poorly on the test set, it indicates overfitting. Use k-fold cross-validation to evaluate the stability of the model, draw the learning curves of the training set and the validation set, and observe whether there are high variance or high bias problems.

9. The method for classifying light curves of periodic variable stars based on neural networks according to claim 8, characterized in that: The optimization by using the data enhancement method specifically includes: Time-shift, scale, or add noise to time-domain data to simulate data changes under different observation conditions; Perform phase rotation, frequency shift or harmonic enhancement on frequency domain features to increase spectrum diversity; Synthetic data generation: Generate virtual light curve data using generative adversarial networks to expand training samples; Combine the enhancement methods in time domain and frequency domain to generate more representative training samples.

10. The neural network-based periodic variable star light curve classification method according to claim 9, characterized in that: The light curve data to be classified are subjected to the same preprocessing and feature extraction process, the extracted feature values ​​are input into the large network for classification, and the classification results are post-processed to improve the reliability of the classification results. Specifically, the following steps are performed: Conduct confidence assessment on the classification results, calculate the confidence of each classification result, set a confidence threshold, and consider results below the threshold as "uncertain" and require further analysis and manual review; Identify abnormal samples through statistical analysis and clustering methods, mark abnormal samples, and perform secondary classification and exclusion based on domain knowledge; Combine the output results of multiple small networks to improve the reliability of classification. Introduce astronomical knowledge to calibrate the classification results.

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