Search

CN-121996995-A - Gravity lens magnification factor efficient evaluation method based on deep learning

CN121996995ACN 121996995 ACN121996995 ACN 121996995ACN-121996995-A

Abstract

The invention discloses a gravity lens amplification factor high-efficiency assessment method based on deep learning, which comprises the following steps of establishing a diffraction integral model of a gravity lens system, defining dimensionless frequency and dimensionless source position, converting a physical amplification factor into a general amplification factor which only depends on dimensionless parameters so as to realize scale invariance of the model, acquiring a model training data set containing the dimensionless parameters and amplification factor true values corresponding to the dimensionless parameters, constructing a sine representation network as a core calculation model, utilizing the data set to learn and train the sine representation network, converting the frequency and the parameters of a gravity wave signal to be analyzed into the dimensionless form, inputting the trained sine representation network, and directly outputting the corresponding complex amplification factor for modulating and analyzing a gravity wave waveform. Compared with the traditional numerical integration, the neural network reasoning speed is improved by several orders of magnitude, and the real-time gravitational wave data analysis requirement can be met.

Inventors

  • ZHANG QIKAI
  • ZHANG FAN

Assignees

  • 浙江大学

Dates

Publication Date
20260508
Application Date
20260410

Claims (9)

  1. 1. The high-efficiency evaluation method for the gravitational lens magnification factor based on deep learning is characterized by comprising the following steps of: step S1, a diffraction integral model of an attractive lens system is established, dimensionless frequency and dimensionless source position are defined, and a physical amplification factor is converted into a general amplification factor which only depends on dimensionless parameters, so that scale invariance of the model is realized; Step S2, a model training data set containing dimensionless parameters and amplification factor true values corresponding to the dimensionless parameters is obtained; S3, constructing a sine representation network as a core calculation model, and carrying out learning training on the sine representation network by utilizing a data set; and S4, converting the frequency and parameters of the gravitational wave signal to be analyzed into a dimensionless form, inputting a trained sinusoidal representation network, and directly outputting a corresponding complex amplification factor for modulating and analyzing gravitational wave waveforms.
  2. 2. The method according to claim 1, wherein in step S2, for a specific lens model, a corresponding lens mass distribution function is substituted into the established diffraction integration model, and a true value data set of the magnification factor is calculated and generated by a numerical integration method.
  3. 3. The method for efficient evaluation of gravitational lens magnification factor based on deep learning as claimed in claim 2, wherein when the lens model is a point quality lens model, there is no dimensionless frequency Is defined as General amplification factor The method is obtained by integrating a geometric time delay function, and the integral expression is as follows: in the formula, Is a dimensionless coordinate on the source plane; is a dimensionless location on the source plane; is an imaginary unit; Is the red shift quality of the lens; Is gravitational wave frequency.
  4. 4. The method for efficient evaluation of lens magnification factors of gravitation based on deep learning according to claim 1, wherein in step S3, the sinusoidal representation network adopts a multi-layer perceptron architecture, and the activation function of each layer of neurons is a periodic sinusoidal function.
  5. 5. The method for efficient evaluation of gravitational lens magnification factor based on deep learning of claim 4 wherein the sinusoidal activation function is in the form of , As a matrix of weights, the weight matrix, As a result of the offset vector, As an input vector for the neuron(s), Is a super parameter.
  6. 6. The method for efficiently evaluating the gravitational lens amplification factor based on deep learning according to claim 1, wherein in step S3, dimensionless parameters in the data set are used as input, corresponding amplification factors are used as labels, learning training is performed on the sinusoidal representation network, a mean square error is used as a loss function, and the network weight is optimized in combination with an adaptive learning rate strategy.
  7. 7. The method for efficiently evaluating the magnification factor of the gravitational lens based on deep learning of claim 1, further comprising a region decomposition strategy of dividing the parameter space into a low frequency region and a high frequency region; in the low frequency region, performing full wave optical calculation by using a sine representation network; in the high-frequency region, if the prediction error of the sinusoidal representation network exceeds a preset threshold, automatically switching to a geometric optical approximation formula or a semi-classical approximation formula for calculation.
  8. 8. The method according to claim 1, wherein in step S4, for processing complex amplification factors, sine representing network output layers are set to two channels, respectively predicting real part and imaginary part of the amplification factors, or respectively predicting amplitude and phase.
  9. 9. A deep learning based attractive lens magnification factor efficient evaluation system for implementing the method of claim 1, the system comprising: the preprocessing module (1) is used for converting physical parameters in gravitational wave detection data into dimensionless parameters; The reasoning engine module (2) is used for loading a pre-trained sine representation model, carrying out millisecond forward reasoning on the input dimensionless parameters, and calculating an amplification factor; And the waveform generation module (3) is used for acting the deduced amplification factor frequency domain sequence on the original gravitational wave waveform to generate a template waveform containing a lens effect and used for matched filtering searching or parameter estimation.

Description

Gravity lens magnification factor efficient evaluation method based on deep learning Technical Field The invention relates to the technical field of gravitational wave data processing, in particular to a gravitational lens magnification factor efficient evaluation method based on deep learning. Background In gravitational wave astronomy, the gravitational lens effect occurs when gravitational waves pass near large mass astronomical objects (e.g., black holes, stars). The gravitational wave acts as a space-time ripple, and the propagation path is influenced by the gravitational field to generate bending, so that signals sent by the same gravitational wave source reach the earth along multiple paths to form interference phenomena. In order to accurately analyze this effect, particularly in the "wave optics" region of long wavelength or lenslet quality, the diffraction integral (Diffraction Integral) must be calculated to obtain the magnification factor F. However, the direct calculation of the diffraction integral faces great challenges that the integral kernel contains a plurality of terms with high oscillation, so that the numerical integral converges very slowly, the calculation cost is very high, for the gravity wave data analysis task needing to process massive parameter spaces, the conventional numerical integral method is difficult to meet the real-time processing requirement, the conventional table look-up method grows exponentially with the increase of parameter dimensions, the memory consumption is not expandable, and a common deep learning model (such as MLP using a ReLU activation function) is difficult to fit the high-frequency oscillation characteristics in the diffraction integral due to the 'spectrum deviation' problem, so that the accuracy is insufficient. Aiming at the problems, the invention provides a deep learning method based on a sine representation network, which utilizes a periodic activation function to match oscillation characteristics of diffraction integral so as to realize rapid and high-precision calculation. Disclosure of Invention The invention aims to overcome the defects of the prior art, and provides a gravity lens amplification factor high-efficiency evaluation method based on deep learning, which utilizes the periodic activation function characteristic of a sine representation network to match the inherent oscillation characteristic of a diffraction integral kernel so as to realize rapid high-precision calculation of the amplification factor. In order to achieve the above purpose, the present invention adopts the following technical scheme: a gravity lens magnification factor high-efficiency evaluation method based on deep learning comprises the following steps: step S1, a diffraction integral model of an attractive lens system is established, dimensionless frequency and dimensionless source position are defined, and a physical amplification factor is converted into a general amplification factor which only depends on dimensionless parameters, so that scale invariance of the model is realized; Step S2, a model training data set containing dimensionless parameters and amplification factor true values corresponding to the dimensionless parameters is obtained; S3, constructing a sine representation network as a core calculation model, and carrying out learning training on the sine representation network by utilizing a data set; and S4, converting the frequency and parameters of the gravitational wave signal to be analyzed into a dimensionless form, inputting a trained sinusoidal representation network, and directly outputting a corresponding complex amplification factor for modulating and analyzing gravitational wave waveforms. Further, in step S2, for a specific lens model, the corresponding lens mass distribution function is substituted into the established diffraction integration model, and the amplification factor true value data set is generated through calculation by a numerical integration method. Further, when the lens model is a point quality lens model, the dimensionless frequency is zeroIs defined asGeneral amplification factorThe method is obtained by integrating a geometric time delay function, and the integral expression is as follows: in the formula, Is a dimensionless coordinate on the source plane; is a dimensionless location on the source plane; is an imaginary unit; Is the red shift quality of the lens; Is gravitational wave frequency. Further, in step S3, the sinusoidal representation network adopts a multi-layer perceptron architecture, and the activation function of each layer of neurons is a periodic sinusoidal function. Further, the sinusoidal activation function is in the form of,As a matrix of weights, the weight matrix,As a result of the offset vector,As an input vector for the neuron(s),Is a super parameter. Further, in step S3, dimensionless parameters in the data set are used as input, corresponding amplification factors are used as labels, l