Artificial Neural Network Approach to the Analytic Continuation Problem.

  title={Artificial Neural Network Approach to the Analytic Continuation Problem.},
  author={Romain Fournier and Lei Wang and Oleg V. Yazyev and Quansheng Wu},
  journal={Physical review letters},
  volume={124 5},
Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum… 

Figures from this paper

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

Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent

Analytic Continuation of Noisy Data Using Adams Bashforth ResNet

A novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet) that is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function.

Automatic differentiation approach for reconstructing spectral functions with neural networks

An automatic differentiation framework is proposed as a generic tool for the reconstruction from observable data of spectral functions from Euclidean Green’s functions and set chi-square as loss function to optimize the parameters with backward automatic differentiation unsupervisedly.

Rational function regression method for numerical analytic continuation.

A simple method for numerical analytic continuation is developed. It is designed to analytically continue the imaginary time (Matsubara frequency) quantum Monte Carlo simulation results to the real

Improving the Deconvolution of Spectrum at Finite Temperature via Neural Network

This work introduces a neural network based discretization scheme to solve the deconvolution problem, and replaces the target spectrum by network and can find a better approximation solution through optimization accurate and efficient.

Machine learning spectral functions in lattice QCD

It is shown that the SVAE in most cases is comparable to the maximum entropy method (MEM) in the quality of reconstructing spectral functions and even outperforms the MEM in the case where the spectral function has sharp peaks with insufficient number of data points in the correlator.

Learned Optimizers for Analytic Continuation

A neural network method by convex optimization and replace the ill-posed inverse problem by a sequence of well-conditioned surrogate problems that are able to give a solution of high quality with low time cost and achieve higher parameter efficiency than heuristic full-connected networks.

Extending the average spectrum method: Grid point sampling and density averaging

This paper demonstrates that sampling the grid points, instead of keeping them fixed, also changes the functional integral limit and rather helps to overcome the bias considerably, and provides an efficient algorithm for doing the sampling and shows how the density of thegrid points acts now as a default model with a significantly reduced biasing effect.

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation



Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics

We present a supervised machine learning approach to the inversion of Fredholm integrals of the first kind as they arise, for example, in the analytic continuation problem of quantum many-body

Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data.

A data-science approach to solving the ill-conditioned inverse problem for analytical continuation by means of a modern regularization technique, which eliminates redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise.

Analytic continuation via domain knowledge free machine learning

The machine-learning-based approach to analytic continuation not only provides the more accurate spectrum than the conventional methods in terms of peak positions and heights, but is also more robust against the noise which is the required key feature for any continuation technique to be successful.

Acceleration of the Stochastic Analytic Continuation Method via an Orthogonal Polynomial Representation of the Spectral Function

Stochastic analytic continuation is an excellent numerical method for analytically continuing Green's functions from imaginary frequencies to real frequencies, although it requires significantly more

On the application of numerical analytic continuation methods to the study of quantum mechanical vibrational relaxation processes

A major problem still confronting molecular simulations is how to determine time-correlation functions of many-body quantum systems. In this paper the results of the maximum entropy (ME) and singular

Kernel polynomial representation of imaginary-time Green's functions

An alternate representation for the Green’s functions of quantum impurity models and combine it with the hybridization expansion continuous-time quantum Monte Carlo impurity solver is developed, based on the kernel polynomial method, which introduces various integral kernels to filter fluctuations caused by the explicit truncations ofPolynomial expansion series and improves the computational precision significantly.

Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach

We present a way of combining real-time path integral Monte Carlo simulations with a maximum entropy numerical analytic continuation scheme in a new approach for calculating time correlation

Kernel polynomial representation for imaginary-time Green’s functions in continuous-time quantum Monte Carlo impurity solver*

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green's functions G(τ), we develop an alternate and superior representation for G(τ) and implement

Definitions and examples of inverse and ill-posed problems

Abstract The terms “inverse problems” and “ill-posed problems” have been steadily and surely gaining popularity in modern science since the middle of the 20th century. A little more than fifty years