Extrapolating Quantum Observables with Machine Learning: Inferring Multiple Phase Transitions from Properties of a Single Phase

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 po...

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Bibliographic Details
Published in:Physical review letters 2018-12, Vol.121 (25), p.255702, Article 255702
Main Authors: Vargas-Hernández, Rodrigo A, Sous, John, Berciu, Mona, Krems, Roman V
Format: Article
Language:English
Subjects:
Extrapolation
Gaussian process
Kernels
Machine learning
Phase diagrams
Phase transitions
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.121.255702