Relative entropy as model selection tool in cluster expansions

Jesper Kristensen, Ilias Bilionis, and Nicholas Zabaras
Phys. Rev. B 87, 174112 – Published 28 May 2013

Abstract

Cluster expansions are simplified, Ising-like models for binary alloys in which vibrational and electronic degrees of freedom are coarse grained. The usual practice is to learn the parameters of the cluster expansion by fitting the energy they predict to a finite set of ab initio calculations. In some cases, experiments suggest that such approaches may lead to overestimation of the phase transition temperature. In this work, we present a novel approach to fitting the parameters based on the relative entropy framework which, instead of energies, attempts to fit the Boltzmann distribution of the configurational degrees of freedom. We show how this leads to T-dependent parameters.

  • Received 16 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.174112

©2013 American Physical Society

Authors & Affiliations

Jesper Kristensen1,2, Ilias Bilionis1, and Nicholas Zabaras1,*

  • 1Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H. T. Rhodes Hall, Cornell University, Ithaca, New York 14853-3801, USA
  • 2School of Applied and Engineering Physics, 271 Clark Hall, Cornell University, Ithaca, New York 14853-3501, USA

  • *Corresponding author: nzabaras@gmail.com; URL: http://mpdc.mae.cornell.edu/

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Vol. 87, Iss. 17 — 1 May 2013

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