A continuous dependence result in the analytic continuation problem

1999 ◽  
Vol 11 (6) ◽  
Author(s):  
S. VESSELLA
Keyword(s):  
Analytic Continuation ◽  
Continuous Dependence ◽  
Continuation Problem ◽  
Dependence Result ◽  
Analytic Continuation Problem

scholarly journals Analytic continuation of noisy data using Adams Bashforth residual neural network

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xuping Xie ◽  
Feng Bao ◽  
Thomas Maier ◽  
Clayton Webster
Keyword(s):  
Neural Network ◽  
Analytic Continuation ◽  
Spectral Function ◽  
Prior Information ◽  
Grand Challenge ◽  
Computational Data ◽  
Continuation Problem ◽  
Deep Learning Network ◽  
High Level ◽  
Analytic Continuation Problem

<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>

scholarly journals A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2255
Author(s):  
Xuemin Xue ◽  
Xiangtuan Xiong
Keyword(s):  
Error Estimate ◽  
Analytic Continuation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Parameter Selection ◽  
Tikhonov Regularization Method ◽  
A Posteriori ◽  
Numerical Result ◽  
Continuation Problem ◽  
Analytic Continuation Problem

In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.

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