Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase

TL;DR

This paper introduces a machine learning approach using Gaussian Process regression to predict quantum phase transitions by extrapolating properties from a single phase, enabling the identification of multiple transitions across phase diagrams.

Contribution

The novel method combines kernel optimization with Gaussian Process regression to accurately extrapolate quantum phase transitions from limited data, surpassing previous techniques.

Findings

Successfully predicts multiple phase transitions from data within a single phase.

Capable of extrapolating across phase boundaries to identify sharp transitions.

Applicable to uncharted regions of parameter space where experimental or theoretical data is scarce.

Abstract

We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen through an iterative procedure maximizing the predicting power of the kernels. The method is capable of extrapolating across the transition lines. The calculations within a given phase can be used to predict not only the closest sharp transition, but also a transition removed from the available data by a separate phase. This makes the present method particularly valuable for searching phase transitions in the parts of the parameter space that cannot be probed experimentally or theoretically.