求解解析延拓问题的随机优化的随机梯度下降算法

IF 1.7 Q2 MATHEMATICS, APPLIED Foundations of data science (Springfield, Mo.) Pub Date : 2020-01-01 DOI:10.3934/fods.2020001
F. Bao, T. Maier
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引用次数: 6

摘要

针对从虚时间量子蒙特卡罗数据中提取实频谱的解析延拓问题,提出了一种基于随机梯度下降的优化算法。解析延拓过程是一个病态逆问题,通常用正则化优化方法求解,如最大熵法或随机优化方法。本文的主要贡献是通过引入有监督的随机梯度下降算法来求解翻转逆系统,从而提高随机优化方法的性能,该算法处理由一种快速有效的随机优化方法得到的随机解。
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Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems
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.
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CiteScore
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