Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case  

作　　者：Xilong Fan Peizheng Wang Jin Li Nan Yang 

机构地区：[1]School of Physics and Technology,Wuhan University,Wuhan 430072,China [2]School of Software Technology,Zhejiang University,Ningbo 315048,China [3]Department of Physics,Chongqing University,Chongqing 401331,China [4]Department of Electronical Information Science and Technology,Xingtai University,Xingtai 054001,China

出　　处：《Research in Astronomy and Astrophysics》2023年第12期252-262,共11页天文和天体物理学研究（英文版）

基　　金：supported by the National Natural Science Foundation of China(grant No.11922303);the Natural Science Foundation of Chongqing(grant No.CSTB2023NSCQ-MSX0103);the Key Research Program of Xingtai 2020ZC005;the Fundamental Research Funds for the Central Universities(grant No.2042022kf1182)。

摘　　要：The error propagation among estimated parameters reflects the correlation among the parameters.We study the capability of machine learning of"learning"the correlation of estimated parameters.We show that machine learning can recover the relation between the uncertainties of different parameters,especially,as predicted by the error propagation formula.Gravitational lensing can be used to probe both astrophysics and cosmology.As a practical application,we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters(effective lens mass ML and Einstein radiusθ_(E))in accordance with the theoretical formula for the singular isothermal ellipse(SIE)lens model.The relation of errors of lens mass and Einstein radius,(e.g.,the ratio of standard deviations F=σ_(ML)/σ_(θ_(E)))predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model.As a proof-of-principle test,a toy model of linear relation with Gaussian noise is presented.We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise.Error propagation plays a crucial role in identifying the physical relation among parameters,rather than a coincidence relation,therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

关 键 词：gravitational lensing strong-methods data analysis-Galaxy fundamental parameters 

分 类 号：P14[天文地球—天体物理] TP18[天文地球—天文学]