Reconstructing spectral functions via automatic differentiation

11/29/2021
by   Lingxiao Wang, et al.
0

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in many-body physics. However, the inversion is proved to be ill-posed in the realistic systems with noisy Green's functions. In this Letter, we propose an automatic differentiation(AD) framework as a generic tool for the spectral reconstruction from propagator observable. Exploiting the neural networks' regularization as a non-local smoothness regulator of the spectral function, we represent spectral functions by neural networks and use propagator's reconstruction error to optimize the network parameters unsupervisedly. In the training process, except for the positive-definite form for the spectral function, there are no other explicit physical priors embedded into the neural networks. The reconstruction performance is assessed through relative entropy and mean square error for two different network representations. Compared to the maximum entropy method, the AD framework achieves better performance in large-noise situation. It is noted that the freedom of introducing non-local regularization is an inherent advantage of the present framework and may lead to substantial improvements in solving inverse problems.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/12/2021

Automatic differentiation approach for reconstructing spectral functions with neural networks

Reconstructing spectral functions from Euclidean Green's functions is an...
research
03/07/2022

Neural network approach to reconstructing spectral functions and complex poles of confined particles

Reconstructing spectral functions from propagator data is difficult as s...
research
12/01/2021

Machine learning Hadron Spectral Functions in Lattice QCD

Hadron spectral functions carry all the information of hadrons and are e...
research
05/10/2019

Spectral Reconstruction with Deep Neural Networks

We explore artificial neural networks as a tool for the reconstruction o...
research
10/26/2021

Machine learning spectral functions in lattice QCD

We study the inverse problem of reconstructing spectral functions from E...
research
03/08/2023

Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation

We present a potent computational method for the solution of inverse pro...

Please sign up or login with your details

Forgot password? Click here to reset