Training biases in machine learning for the analytic continuation of quantum many-body Green's functions

Zhang, Rong; Merkel, Maximilian E.; Beck, Sophie; Ederer, Claude

doi:10.1103/physrevresearch.4.043082

Cited by 3 publications

(1 citation statement)

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“…The trained NN performs well in the testing set as the predicted spectra are very close to synthetic testing spectra. Several different network structures [9][10][11][12] trained on similar Gaussian-type datasets are also proposed. In addition to synthetic datasets, NNAC is also examined on some exactly solvable models such as one-dimensional transverse-field Ising model [13] and harmonic oscillator linearly coupled to an ideal environment.…”

Section: Introductionmentioning

confidence: 99%

Neural network analytic continuation for Monte Carlo: Improvement by statistical errors

Sun

Wang

2023

Chinese Phys. B

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This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are carefully synthesized without “data leakage”. We found that the training set should match the input correlation functions in terms of statistical error properties, such as noise level, noise dependence on imaginary time, and imaginary time-displaced correlations. We have developed a systematic method to synthesize such training datasets. Our improved algorithm outperform the widely used maximum entropy method in highly noisy situations. As an example, our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.

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