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ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

  • Brandon Bocklund (a1), Richard Otis (a2), Aleksei Egorov (a3), Abdulmonem Obaied (a3), Irina Roslyakova (a3) and Zi-Kui Liu (a1)...
  • Please note a correction has been issued for this article.


The software package ESPEI has been developed for efficient evaluation of thermodynamic model parameters within the CALPHAD method. ESPEI uses a linear fitting strategy to parameterize Gibbs energy functions of single phases based on their thermochemical data and refines the model parameters using phase equilibrium data through Bayesian parameter estimation within a Markov Chain Monte Carlo machine learning approach. In this paper, the methodologies employed in ESPEI are discussed in detail and demonstrated for the Cu–Mg system down to 0 K using unary descriptions based on segmented regression. The model parameter uncertainties are quantified and propagated to the Gibbs energy functions.


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Address all correspondence to Brandon Bocklund <>


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ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

  • Brandon Bocklund (a1), Richard Otis (a2), Aleksei Egorov (a3), Abdulmonem Obaied (a3), Irina Roslyakova (a3) and Zi-Kui Liu (a1)...
  • Please note a correction has been issued for this article.


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