Analytic Continuation of Noisy Data Using Adams Bashforth ResNet

TL;DR

This paper introduces a neural network model called AB-ResNet for the analytic continuation problem in quantum physics, outperforming traditional methods like MaxEnt especially with noisy data, and does not require prior information.

Contribution

The paper presents a novel Adams-Bashforth residual neural network that improves analytic continuation accuracy without needing prior spectral information, especially under high noise conditions.

Findings

AB-ResNet outperforms MaxEnt with noisy data

The model is model independent and does not require prior information

Achieves comparable accuracy to MaxEnt with low noise levels

Abstract

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.