Author:
Xie Xuping,Bao Feng,Maier Thomas,Webster Clayton
Abstract
<p style='text-indent:20px;'>We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). The advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference45 articles.
1. L.-F. Arsenault, R. Neuberg, L. A. Hannah and A. J. Millis, Projected regression methods for inverting fredholm integrals: Formalism and application to analytical continuation, arXiv preprint arXiv: 1612.04895, 2016.
2. L.-F. Arsenault, R. Neuberg, L. A. Hannah and A. J. Millis, Projected regression method for solving fredholm integral equations arising in the analytic continuation problem of quantum physics, Inverse Problems, 33 (2017), 115007.
3. U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, volume 61, SIAM, Philadelphia, PA, 1998.
4. F. Bao, Y. Tang, M. Summers, G. Zhang, C. Webster, V. Scarola and T. A. Maier, Fast and efficient stochastic optimization for analytic continuation, Physical Review B, 94 (2016), 125149.
5. K. S. D. Beach, Identifying the maximum entropy method as a special limit of stochastic analytic continuation, arXiv preprint arXiv: cond-mat/0403055, 2004.
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