ESPEI has two different fitting modes: parameter generation and Bayesian parameter estimation, which uses Markov Chain Monte Carlo (MCMC). You can run either of these modes or both of them sequentially.
To run either of the modes, you need to have a phase models 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 that ESPEI should fit to.
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 Make ESPEI Datasets 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), an array of the steps in the MCMC trace (defaults to
trace.npy), and the an array of the log-probabilities for each iteration and chain (defaults to
Parameter Generation only¶
If you have only non-equilibrium thermochemical data, e.g. heat capacity, entropy and enthalpy data and mixing data from first-principles calculations, you may want to see the starting point for your MCMC calculation.
Create an input file called
system: phase_models: my-phases.json datasets: my-input-datasets generate_parameters: excess_model: linear ref_state: SGTE91
Then ESPEI can be run by running
espei --input espei-in.yaml
Bayesian Parameter Estimation (MCMC) only¶
If you have a database already and want to do a Bayesian parameter estimation, you can specify a starting TDB file (named
system: phase_models: my-phases.json datasets: my-input-data mcmc: iterations: 1000 input_db: my-tdb.tdb
The TDB file you input must have all of the degrees of freedom you want as FUNCTIONs with names beginning with
Restart from previous run-phase only¶
If you’ve run an MCMC fitting already in ESPEI and have a trace file called
my-previous-trace.npy , then you can resume the calculation with the following input file
system: phase_models: my-phases.json datasets: my-input-data mcmc: iterations: 1000 input_db: my-tdb.tdb restart_trace: my-previous-trace.npy
A minimal full run of ESPEI is done by the following
system: phase_models: my-phases.json datasets: my-input-data generate_parameters: excess_model: linear ref_state: SGTE91 mcmc: iterations: 1000
ESPEI lets you control many aspects of your calculations with the input files shown above. See ESPEI YAML input files for a full description of all possible inputs.
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.
Many mistakes are found with ESPEI’s
espei check-datasets my-input-datasets on your directory
Q: How do I analyze my results?¶
A: By default, ESPEI will create
lnprob.npy for the MCMC chain at the specified save interval and according to the save interval (defaults to ever iteration).
These are created from arrays via
numpy.save() and can thus be loaded with
Note that the arrays are preallocated with zeros.
These filenames and settings can be changed using in the input file.
You can then use these chains and corresponding log-probabilities to make corner plots, calculate autocorrelations, find optimal parameters for databases, etc..
Some examples are shown in the Recipes page.
Finally, you can use
espei.plot functions such as
espei.plot.dataplot() in concert with pycalphad to plot phase diagrams
with your input equilibria data. The
espei.plot.plot_interaction() functions can be
used to compare single-phase data (e.g. formation and mixing data) with the
properties calculated from your database.
Q: Can I run ESPEI on a supercomputer supporting MPI?¶
A: Yes! ESPEI has MPI support. See the Advanced Schedulers page for more details.
Q: How is the log probability reported by ESPEI calculated?¶
MCMC simulation requires determining the probability of the data given a set of parameters, \(p(D|\theta)\). In MCMC, the log probability is often used to avoid floating point errors that arise from multiplying many small floating point numbers. For each type of data the error, often interpreted as the absolute difference between the expected and calculated value, is determined. For the types of data and how the error is calculated, refer to the ESPEI paper [Bocklund2019].
The error is assumed to be normally distributed around the experimental data point that the prediction of a set of parameters is being compared against.
The log probability of each data type is calculated by the log probability density function of the error in this normal distribution with a mean of zero and the standard deviation as given by the data type and the adjustable weights (see
data_weights in ESPEI YAML input files).
The total log probability is the sum of all log probabilities.
Note that any probability density function always returns a positive value between 0 and 1, so the log probability density function should return negative numbers and the log probability reported by ESPEI should be negative.
Q: Why is the version of ESPEI ‘0+unknown’?¶
A: A version number of
'0+unknown' indicates that you do not have git installed.
This can occur on Windows where git is not in the PATH (and the Python interpreter cannot see it).
You can install git using
conda install git on Windows.
Q: I have a large database, can I use ESPEI to optimize parameters in only a subsystem?¶
A: Yes, if you have a multicomponent CALPHAD database, but want to optimize or determine the uncertainty for a constituent unary, binary or ternary subsystem that you have data for, you can do that without any extra effort.
You may be interested in the symbols input parameter to specify which parameter subset to optimize.
Note that if you optimize parameters in a subsystem (e.g. Cu-Mg) that is used in a higher order description (e.g. Al-Cu-Mg), you may need to reoptimize the parameters for the higher order system as well.