Inference of response functions with the help of machine learning algorithms

TL;DR

This paper introduces a neural network-based method to reconstruct response functions in many-body systems, outperforming traditional techniques like GIT when using few Chebyshev series terms.

Contribution

It presents a novel neural network approach for response function inference, improving accuracy over existing methods with limited series terms.

Findings

Neural network method outperforms GIT with few Chebyshev terms.

Response functions are represented as truncated Chebyshev series.

The approach reduces representation error effectively.

Abstract

Response functions are a key quantity to describe the near-equilibrium dynamics of strongly-interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these \emph{ab initio} have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function $S(\omega)$ defined over a range in frequencies $\omega$. We represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian Integral Transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.