Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

Bao, Feng; Maier, Thomas

doi:10.3934/fods.2020001

Title: Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

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Abstract

We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.

Authors:

Bao, Feng ^[1];

^[2]

Florida State Univ., Tallahassee, FL (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: 2020-03-01

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1632071

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Foundations of Data Science

Additional Journal Information:: Journal Volume: 2; Journal Issue: 1; Journal ID: ISSN 2639-8001

Publisher:: AIMS

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Bao, Feng, and Maier, Thomas. Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems.  United States: N. p., 2020. 
Web.  doi:10.3934/fods.2020001.

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                    Bao, Feng, & Maier, Thomas. Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems.  United States.  https://doi.org/10.3934/fods.2020001

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                    Bao, Feng, and Maier, Thomas. Sun .  
"Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems".  United States.  https://doi.org/10.3934/fods.2020001.  https://www.osti.gov/servlets/purl/1632071.

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@article{osti_1632071,

  title        = {Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems},

  author       = {Bao, Feng and Maier, Thomas},

  abstractNote = {We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.},

  doi          = {10.3934/fods.2020001},

  journal      = {Foundations of Data Science},

  number       = 1,

  volume       = 2,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

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