## 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.

Original language | English |
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Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Foundations of Data Science |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2020 |

### Funding

2010 Mathematics Subject Classification. Primary: 49N45; Secondary: 49M37. Key words and phrases. Stochastic optimization, stochastic gradient descent, analytic continuation, physics supervision. The first author is supported by NSF grant DMS-1720222. ∗ Corresponding author: Feng Bao. Acknowledgments. This work is partially supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research through Comp-FUSE project and FASTMath Institute. The first author also acknowledges support by U.S. National Science Foundation under Contract DMS-1720222.

## Keywords

- Stochastic optimization
- analytic continuation
- physics supervision
- stochastic gradient descent