Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields

TL;DR

This paper introduces an adaptive Thouless-Anderson-Palmer method for inverse Ising problems with quenched random fields, demonstrating high accuracy in inferring field distributions across various models.

Contribution

The paper develops a novel adaptive TAP approach tailored for inverse Ising problems with quenched randomness, improving inference accuracy over existing mean-field methods.

Findings

Accurately infers quenched random fields in Ising models

Performs well on SK, Hopfield, and orthogonal models

Effective for Gaussian and bimodal field distributions

Abstract

The adaptive Thouless-Anderson-Palmer equation is derived for inverse Ising problems in the presence of quenched random fields. We test the proposed scheme on Sherrington-Kirkpatrick, Hopfield, and random orthogonal models and find that the adaptive Thouless-Anderson-Palmer approach allows surprisingly accurate inference of quenched random fields whose distribution can be either Gaussian or bimodal, compared with other existing mean-field methods.