Rapid inversion method for Ia type super-novelty star spectral parameters based on KAN (Karan Area Network)

Abstract

The invention discloses an Ia type super-novelty star spectral parameter rapid inversion method based on a KAN network, and the method comprises the following steps: S1, carrying out data preprocessing, generating simulation spectral data, including spectral lines and parameters, and carrying out the normalization; s2, building a KAN (Kernel Area Network) network model by using a python framework and a pytorch framework; s3, designing a loss function; s4, training the model, and testing the error of each parameter in the stage; s5, performing learning rate adjustment by using an Adam optimizer and a StepLR scheduler in the training process, and optimizing the model; s6, performing Gaussian sampling on an actually measured spectrum, and inputting the actually measured spectrum into the trained KAN model for prediction; s7, analyzing the result, and calculating the standard deviation of the output parameter data; by using the deep learning technology of the KAN network, key physical and chemical parameters are efficiently predicted from the celestial body spectrum, the problems that in the prior art, the calculation amount is too large, and an accurate calculation result cannot be efficiently obtained are solved, and the method has remarkable advantages in the aspects of improving the calculation efficiency and the processing capacity and is suitable for spectrum data analysis in the field of astronomical observation.

Description

Technical Field

[0001] The invention belongs to the field of astronomical technology, and in particular relates to a method for fast inversion of type Ia supernova spectral parameters based on a KAN network. Background Art

[0002] Supernova spectra are derived from the interaction of multiple complex processes, and simulating these spectra requires the use of expensive radiative transfer codes to explore high-dimensional posterior probabilities. Even simple models of supernovae contain more than 10 parameters, and detailed exploration of these parameter spaces requires at least millions of function evaluations. Physically realistic models require at least tens of CPU minutes per evaluation, making it impractical to reconstruct the explosion process using traditional methods; the problem with existing technologies is how to efficiently process and analyze complex data involving a large number of parameters and high-dimensional posterior probabilities. There are several major problems. The first is the high computational cost: traditional radiative transfer models, such as TARDIS, are used to simulate supernova spectra and require huge computing resources. Each parameterized supernova model may require millions of function evaluations, each taking minutes to tens of minutes, making comprehensive parameter space exploration impractical. Second, the parameter space is huge: even relatively simple supernova models contain more than 10 parameters; detailed exploration of these parameter spaces requires huge computational loads that traditional computational methods cannot cope with.

[0003] By using a neural network as a proxy and training on simulated data, the evaluation can be performed much faster than directly evaluating the radiation transfer model. The KAN network can accurately predict spectral parameter data with fewer resources and faster speed. Both the simulation data and the measured data have verified that this network can effectively predict spectral parameter data through spectral line data; for the parameter inversion of spectral data, in addition to the fast inversion method of type Ia supernova spectral parameters based on the KAN network, there is also an MLP network model that can realize the inversion of spectral parameters. However, MLP may require a large amount of data and parameters to learn complex function mappings, while KAN can more naturally capture the complex nonlinear relationships in the data. At the same time, the KAN network can achieve more accurate prediction effects with the same number of parameters. Therefore, it is necessary to design a fast inversion method for type Ia supernova spectral parameters based on the KAN network to solve the above problems. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for fast inversion of type Ia supernova spectral parameters based on a KAN network, aiming to solve the problem that the existing technology has too much calculation and cannot efficiently obtain accurate calculation results.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: A method for fast inversion of type Ia supernova spectral parameters based on a KAN network comprises the following steps: S1, data preprocessing, generating simulated spectrum data, including spectral lines and parameters, and normalizing them; S2, use python and pytorch framework to build KAN network model; S3, design loss function; S4, train the model and calculate the error of each parameter in the test phase; S5, during training, the Adam optimizer and StepLR scheduler are used to adjust the learning rate and optimize the model; S6, the measured spectrum is input into the trained KAN model for prediction after Gaussian sampling; S7, result analysis, calculate the standard deviation of the output parameter data.

[0006] Preferably, in step S1, the method for generating simulated spectral data, including spectral lines and parameters, and normalizing them is: Select inner boundary velocities and temperatures, determine element abundances and exclude low-brightness models with brightness below a set threshold Set the TARDIS spectrum to 3400 to 7600 Resample on a logarithmic grid between , so that the line structures on the spectrum have equal pixels on each structure; Multiple spectra were divided into training and test sets in proportion and normalized by removing the mean and scaling to unit variance.

[0007] The generated data set has 1000 input spectra and 13 parameter data points. The input TARDIS file, parameters (abundance, inner boundary velocity / temperature) are generated uniformly within the specified range.

[0008] Preferably, in step S2, building a KAN network model includes: The Kolmogorov-Arnold representation theorem is used to build a deep learning network. The theorem states that any multivariable continuous function can be represented as a combination of a series of single-variable functions. Specifically: ; In the formula, Representation vector No. elements, p The value range is 1 arrive n , n is the dimension of the input vector; q Index, used to traverse the external function every component of.

[0009] Preferably, in step S3, the loss function is designed as: ; In the formula, N is the number of samples in the dataset, It is i The actual observed value of samples, It is i The predicted value of a sample.

[0010] Preferably, in step S5, the parameter update formula of the Adam optimizer is: ; In the formula, It's time t Parameters, It's time t The first moment estimate of and is a hyperparameter (usually set to 0.9 and 0.999); It's time t The second moment estimate of is a very small constant used to prevent the denominator from being zero.

[0011] Furthermore, in the deep learning training process, the learning rate (LR) is a very important hyperparameter that controls the magnitude of the model weight update. The StepLR scheduler is a strategy for adjusting the learning rate, which periodically reduces the learning rate at predetermined intervals to help the model converge more effectively during training.

[0012] Preferably, in steps S6 and S7, the measured spectrum is input into the trained KAN model after Gaussian sampling for prediction and then the standard deviation of the output parameter data is calculated. The specific method is: The probability density function of the Gaussian distribution is: ; In the formula, x represents a random variable, is the mean of the distribution, i.e. the center of the distribution; is the standard deviation which indicates the width of the distribution, The variance represents the degree of dispersion of the data; The standard deviation is calculated as follows: ; In the formula s is the sample standard deviation, n is the number of elements in the sample; is the value of each sample element, is the sample mean.

[0013] The beneficial effects of the present invention are as follows: When the present invention adopts the same depth, width and number of parameters, the error fluctuation of the two decreases during the training process. As the number of training rounds increases, after the error of MLP stabilizes in the middle of training, the error of KAN continues to decrease and finally stabilizes when reaching a lower error. The error value distribution of a single parameter of the present invention is significantly smaller than that of MLP in the test phase, proving that the accuracy of the KAN model is higher than that of MLP. The present invention is better than MLP in all aspects. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0015] Embodiment 1: like Figure 1 As shown, a method for fast inversion of type Ia supernova spectral parameters based on a KAN network comprises the following steps: S1, data preprocessing, generating simulated spectrum data, including spectral lines and parameters, and normalizing them; S2, use python and pytorch framework to build KAN network model; S3, design loss function; S4, train the model and calculate the error of each parameter in the test phase; S5, during training, the Adam optimizer and StepLR scheduler are used to adjust the learning rate and optimize the model; S6, the measured spectrum is input into the trained KAN model for prediction after Gaussian sampling; S7, result analysis, calculate the standard deviation of the output parameter data.

[0016] Preferably, in step S1, the method for generating simulated spectral data, including spectral lines and parameters, and normalizing them is: Select inner boundary velocities and temperatures, determine element abundances and exclude low-brightness models with brightness below a set threshold Set the TARDIS spectrum to 3400 to 7600 Resample on a logarithmic grid between , so that the line structures on the spectrum have equal pixels on each structure; Multiple spectra were divided into training and test sets in proportion and normalized by removing the mean and scaling to unit variance.

[0017] The generated data set has 1000 input spectra and 12 parameter data points. The input TARDIS file, parameters (abundance, inner boundary velocity / temperature) are generated uniformly within the specified range.

[0018] In step S2, building a KAN network model includes: The Kolmogorov-Arnold representation theorem is used to build a deep learning network; the theorem states that any multivariable continuous function can be represented as a combination of a series of single-variable functions. Specifically: ; In the formula, Representation vector No. elements, p The value range is 1 arrive n , n is the dimension of the input vector; q Index, used to traverse the external function every component of .

[0019] Preferably, in step S3, the loss function is designed as: ; In the formula, N is the number of samples in the dataset, It is i The actual observed value of samples, It is i The predicted value of a sample.

[0020] Preferably, in step S5, the parameter update formula of the Adam optimizer is: ; In the formula, It's time t Parameters, It's time t The first moment estimate of and is a hyperparameter (usually set to 0.9 and 0.999); It's time t The second moment estimate of is a very small constant used to prevent the denominator from being zero.

[0021] Furthermore, in the deep learning training process, the learning rate (LR) is a very important hyperparameter that controls the magnitude of the model weight update. The StepLR scheduler is a strategy for adjusting the learning rate, which periodically reduces the learning rate at predetermined intervals to help the model converge more effectively during training.

[0022] Preferably, in steps S6 and S7, the measured spectrum is input into the trained KAN model after Gaussian sampling and then the standard deviation of the output parameter data is calculated. The specific method is: The probability density function of the Gaussian distribution is: ; In the formula, x represents a random variable, is the mean of the distribution, i.e. the center of the distribution; is the standard deviation which indicates the width of the distribution, The variance represents the degree of dispersion of the data; The standard deviation is calculated as follows: ; In the formula s is the sample standard deviation, n is the number of elements in the sample; is the value of each sample element, is the sample mean.

[0023] Embodiment 2: The effectiveness of the model is evaluated by comparing the distribution of parameter errors in the test phase and the measured errors.

[0024] This is verified through experiments, the experimental contents are as follows: The experimental data is derived from the TARDIS spectrum at 3400 to 7600 The data is resampled on the logarithmic grid between , so that the line structures on the spectrum have approximately equal pixels on each structure. The data size is 117941, of which the features of the spectral line data are 1000 and the features of the parameter data are 13. The split ratio of the training set and the test set is 8:2. Set the initial parameters of the model {width = 512, depth = 4, lr = 0.001, }Where width is the model width, depth is the model depth, lr is the model initial learning rate, is the standard deviation of the noise, which determines how different the generated vector is from the original tensor After building the model in step S2, training and testing can be performed to conduct preliminary error analysis.

[0025] After Gaussian sampling of the measured spectral lines and inputting them into the model, the measured error can be calculated. Combined with the previous error analysis, the accuracy of the model can be comprehensively evaluated.

Claims

1. A fast inversion method for type Ia supernova spectral parameters based on KAN network, characterized in that: The following steps are involved: S1, data preprocessing, generating simulated spectrum data, including spectral lines and parameters, and normalizing them; S2, use python and pytorch framework to build KAN network model; S3, design loss function; S4, training model; S5, during training, the Adam optimizer and StepLR scheduler are used to adjust the learning rate and optimize the model; S6, the measured spectrum is input into the trained KAN model for prediction after Gaussian sampling; S7, result analysis, calculate the standard deviation of the output parameter data.

2. The method for rapid inversion of type Ia supernova spectral parameters based on a KAN network according to claim 1, characterized in that: In step S1, the method of generating simulated spectrum data, including spectrum lines and parameters, and normalizing them is as follows: Select inner boundary velocities and temperatures, determine element abundances and exclude low-brightness models with brightness below a set threshold Set the TARDIS spectrum to 3400 to 7600 Resample on a logarithmic grid between , so that the line structures on the spectrum have equal pixels on each structure; Multiple spectra were divided into training and test sets in proportion and normalized by removing the mean and scaling to unit variance.

3. The method for rapid inversion of type Ia supernova spectral parameters based on a KAN network according to claim 1, characterized in that: In step S2, building a KAN network model includes: The Kolmogorov-Arnold representation theorem is used to build a deep learning network, specifically: ； In the formula, Representation vector No. elements, p The value range is 1 arrive n , n is the dimension of the input vector; q Index, used to traverse the external function every component of.

4. The method for rapid inversion of type Ia supernova spectral parameters based on a KAN network according to claim 1, characterized in that: In step S3, the loss function is designed as: ； In the formula, N is the number of samples in the dataset, It is i The actual observed value of samples, It is i The predicted value of a sample.

5. The method for rapid inversion of type Ia supernova spectral parameters based on a KAN network according to claim 1, characterized in that: In step S5, the parameter update formula of the Adam optimizer is: ； In the formula, It's time t Parameters, It's time t The first moment estimate of and is a hyperparameter; It's time t The second moment estimate of is a constant used to prevent the denominator from being zero.

6. The method for rapid inversion of type Ia supernova spectral parameters based on a KAN network according to claim 1, characterized in that: In steps S6 and S7, the measured spectrum is input into the trained KAN model after Gaussian sampling and then the standard deviation of the output parameter data is calculated. The specific method is: The probability density function of the Gaussian distribution is: ； In the formula, x represents a random variable, is the mean of the distribution, i.e. the center of the distribution; is the standard deviation which indicates the width of the distribution, The variance represents the degree of dispersion of the data; The standard deviation is calculated as follows: ； In the formula s is the sample standard deviation, n is the number of elements in the sample; is the value of each sample element, is the sample mean.

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