ESPEI, or Extensible Self-optimizing Phase Equilibria Infrastructure, is a tool for automated thermodynamic database development within the CALPHAD method.

The ESPEI package is based on a fork of pycalphad-fitting and uses pycalphad for calculating Gibbs free energies of thermodynamic models. The implementation for ESPEI involves first fitting single-phase data by calculating parameters in thermodynamic models that are linearly described by the single-phase input data. Then Markov Chain Monte Carlo (MCMC) is used to optimize the candidate models from the single-phase fitting to multi-phase zero-phase fraction data. Single-phase and multi-phase fitting methods are described in Chapter 3 of Richard Otis’s thesis.

The benefit of this approach is the automated, simultaneous fitting for many parameters that yields uncertainty quantification, as shown in Otis and Liu High-Throughput Thermodynamic Modeling and Uncertainty Quantification for ICME. Jom 69, (2017).

The name and idea of ESPEI are originally based off of Shang, Wang, and Liu, ESPEI: Extensible, Self-optimizing Phase Equilibrium Infrastructure for Magnesium Alloys Magnes. Technol. 2010 617-622 (2010).


Creating a virual environment is highly recommended. You can install ESPEI from PyPI

pip install espei

or install in develop mode from source

git clone
cd espei
pip install -e .


Run espei -h to see the options in the command utility.

ESPEI has two different fitting modes: single-phase and multi-phase fitting. You can run either of these modes or both of them sequentially.

To run either of the modes, you need to have a fit settings file that describes the phases in the system using the standard CALPHAD approach within the compound energy formalism. You also need to describe the data to fit. You will need single-phase and multi-phase data for a full run. Fit settings and all datasets are stored as JSON files and described in detail at the Writing input files page. All of your input datasets should be validated by running espei --check-datasets my-input-datasets, where my-input-datasets is a folder of all your JSON files.

The main output result is going to be a database (defaults to out.tdb) and an array of the steps in the MCMC chain (defaults to chain.txt).

Full run

A minimal run of ESPEI with single phase fitting and MCMC fitting would involve setting these two files

espei --datasets=my-dataset-folder --fit-settings=my-input.json

Single-phase only

If you have only heat capacity, entropy and enthalpy data and mixing data (e.g. from first-principles), you may want to see the starting point for your MCMC calculation. To do this, simply pass the --no-mcmc flag to ESPEI

espei --no-mcmc --datasets=my-dataset-folder --fit-settings=my-input.json

Multi-phase only

If you have a database already and just want to do a multi-phase fitting, you can specify a starting TDB file with

espei --datasets=my-dataset-folder --fit-settings=my-input.json --input-tdb=my-starting-database.tdb

The TDB file you input must have all of the degrees of freedom you want as FUNCTIONs with names beginning with VV.


In all cases, ESPEI lets you control certain aspects of your calculations from the command line. Some useful options are

  • verbose (or -v) controls the logging level. Default is Warning. Using verbose once gives more detail (Info) and twice even more (Debug)
  • tracefile lets you set the output trace of the chain to any name you want. The default is chain.txt.
  • probfile lets you set the output log-probability of each step in the chain to any name you want. The default is lnprob.txt.
  • output-tdb sets the name of the TDB output at the end of the run. Default is out.tdb.
  • input-tdb is for setting input TDBs. This will skip single phase fitting and fit all parameters defined as FUNCTIONs with names starting with VV.
  • no-mcmc will do single-phase fitting only. Default is to perform MCMC fitting.
  • mcmc-steps sets the number of MCMC steps. The default is 1000.
  • save-interval controls the interval for saving the MCMC chain. The default is 100 steps.

Run espei -h to see all of the configurable options.


Q: There is an error in my JSON files

A: Common mistakes are using single quotes instead of the double quotes required by JSON files. Another common source of errors is misaligned open/closing brackets.

To find the offending files, you can rename the datasets to anything not ending in .json, such as my_datasets.json.disabled. The renamed files will be ignored and it allows you to track down any problematic files.

Q: How do I analyze my results?

A: By default, ESPEI will create chain.txt and lnprob.txt for the MCMC chain at the end of your run and according to the save interval (defaults to every 100 iterations). These are created from arrays via numpy.savetxt and can thus be loaded with numpy.loadtxt(). Note that the arrays are preallocated with zeros. These filenames and settings (e.g. save interval) can be changed using the command line options, see espei -h. You can then use these chains and corresponding log-probabilities to make corner plots, calculate autocorrelations, find optimal parameters for databases, etc.. Finally, you can use py:mod:espei.plot functions such as multiplot to plot phase diagrams with your input equilibria data and plot_parameters to compare single-phase data (e.g. formation and mixing data) with the properties calculated with your database.

Q: Can I run ESPEI on a supercomputer supporting MPI?

A: Yes! ESPEI has MPI support. Currently only single node processing is supported, but fixes are coming soon to support multiple nodes. To use ESPEI with MPI, you simply call ESPEI in the same way as above with mpirun or whichever MPI software you use. You also must indicate to ESPEI that it should create an MPI scheduler by passing the option --scheduler='MPIPool' to ESPEI.

Module Hierarchy

  • is the main entry point
  • is where all of the fitting happens. This is the core.
  • contains specialized utilities for ESPEI.
  • are utilities with reuse potential outside of ESPEI.
  • holds plotting functions

Indices and tables