High-throughput Calculations¶

Performing many PyCalphad equilibrium calculations is a common requirement for high-throughput workflows such as training a surrogate model, building an active learning dataset, or screening a large composition-temperature space.

A typical pattern for high-throughput workflows is to perform calculations over a sequence of compositions. PyCalphad Workspace objects are optimized for re-use and tight loop calling patterns.

Here we give two examples of performing high-throughput calculations to produce pandas DataFrame objects, one with a lattice grid and one using random sampling.

[1]:

from itertools import product
from time import perf_counter
from importlib.resources import files

import numpy as np
import pandas as pd

from pycalphad import Database, Workspace, variables as v
import pycalphad.tests.databases

def composition_grid(component_count: int, density: int, eps: float = 1e-6):
    """Helper function to create an evenly spaced lattice of compositions

    component_count : int
        number of components in the system
    density : int
        number of lattice points in each dimension
    eps : float
        Minimum amount of each component to avoid edges of composition space
    """
    rows = []
    for counts in product(range(density + 1), repeat=component_count):
        if sum(counts) == density:
            row = np.asarray(counts, dtype=float) / density
            row = np.clip(row, eps, 1.0 - eps * (component_count - 1))
            rows.append(row / row.sum())
    return np.asarray(rows)


def drop_empty_columns(df: pd.DataFrame):
    return df.dropna(axis="columns", how="all")

Lattice grid¶

[2]:

# Set up the composition grid
components = ["AL", "MG", "SI", "CU", "VA"]
elements = [component for component in components if component != "VA"]
solutes = elements[1:]

temperatures = [1000.0, 1250.0, 1500.0]
pressure = 101325.0
density = 4

composition_rows = composition_grid(len(elements), density)
composition_conditions = [
    {v.X(solute): amount for solute, amount in zip(solutes, composition_row[1:])}
    for composition_row in composition_rows
]
n_points = len(composition_rows) * len(temperatures)

[3]:

# set up a Workspace and perform the calculations
test_database_directory = files(pycalphad.tests.databases)
dbf = Database(test_database_directory / "COST507.tdb")
phases = list(dbf.phases.keys())
wks = Workspace(dbf, components, phases)

data_rows = []
print(f"Evaluating {len(composition_rows)} simplex points × {len(temperatures)} temperatures = {n_points} total")
for temperature in temperatures:
    for comp_conds in composition_conditions:
        conditions = {v.T: temperature, v.P: pressure, v.N: 1, **comp_conds}
        wks.conditions = conditions
        out = {
            str(key): value[()]
            for key, value in wks.get_dict("T", "X(*)", "NP(*)", "X(*,*)").items()
        }
        data_rows.append(out)

/Users/bocklund1/src/calphad-workspace/packages/pycalphad/pycalphad/io/tdb.py:293: UserWarning: The type definition character `C` in `TYPE_DEFINITION C GES AMEND_PHASE_DESCRIPTION CBCC_A12 MAGNETIC -3 0.280, ` is not used by any phase.
  warnings.warn(f"The type definition character `{typechar}` in `TYPE_DEFINITION {typechar} {line}` is not used by any phase.")
/Users/bocklund1/src/calphad-workspace/packages/pycalphad/pycalphad/io/tdb.py:1017: UserWarning: The type definition character `R` was defined in the following phases: ['LIQUID'], but no corresponding TYPE_DEFINITION line was found in the TDB.
  warnings.warn(f"The type definition character `{typechar}` was defined in the following phases: "

Evaluating 35 simplex points × 3 temperatures = 105 total

[4]:

# Build a pandas DataFrame from the results
workspace_df = drop_empty_columns(pd.DataFrame(data_rows))
workspace_df

[4]:

	T	X_AL	X_CU	X_MG	X_SI	NP_ALCU_EPSILON	NP_BCC_B2	NP_CU19SI6_ETA	NP_CUMGSI_SIGMA	NP_CUMGSI_TAU	...	X_LAVES_C15_MG	X_LAVES_C15_SI	X_LIQUID_AL	X_LIQUID_CU	X_LIQUID_MG	X_LIQUID_SI	X_MG2SI_AL	X_MG2SI_CU	X_MG2SI_MG	X_MG2SI_SI
0	1000.0	1.000000e-06	9.999970e-01	1.000000e-06	1.000000e-06	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	1000.0	9.999985e-07	7.499985e-01	9.999985e-07	2.499995e-01	NaN	NaN	0.986806	NaN	NaN	...	NaN	NaN	0.026538	6.892373e-01	2.653855e-02	2.576861e-01	NaN	NaN	NaN	NaN
2	1000.0	9.999977e-07	4.999990e-01	9.999976e-07	4.999990e-01	NaN	NaN	0.657859	NaN	NaN	...	NaN	NaN	0.026533	6.892331e-01	2.654473e-02	2.576892e-01	NaN	NaN	NaN	NaN
3	1000.0	9.999962e-07	2.499995e-01	9.999979e-07	7.499985e-01	NaN	NaN	0.328913	NaN	NaN	...	NaN	NaN	0.026528	6.892290e-01	2.655093e-02	2.576923e-01	NaN	NaN	NaN	NaN
4	1000.0	1.000000e-06	1.000000e-06	9.999999e-07	9.999970e-01	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.140855	2.934158e-01	2.843417e-01	2.813874e-01	0.0	0.0	0.666667	0.333333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
100	1500.0	4.999990e-01	9.999980e-07	4.999990e-01	9.999980e-07	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.499999	9.999980e-07	4.999990e-01	9.999980e-07	NaN	NaN	NaN	NaN
101	1500.0	7.499985e-01	2.499995e-01	9.999980e-07	9.999980e-07	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.749999	2.499995e-01	9.999980e-07	9.999980e-07	NaN	NaN	NaN	NaN
102	1500.0	7.499985e-01	9.999980e-07	9.999980e-07	2.499995e-01	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.749999	9.999980e-07	9.999980e-07	2.499995e-01	NaN	NaN	NaN	NaN
103	1500.0	7.499985e-01	9.999980e-07	2.499995e-01	9.999980e-07	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.749999	9.999980e-07	2.499995e-01	9.999980e-07	NaN	NaN	NaN	NaN
104	1500.0	9.999970e-01	1.000000e-06	1.000000e-06	1.000000e-06	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.999997	1.000000e-06	1.000000e-06	1.000000e-06	NaN	NaN	NaN	NaN

105 rows × 60 columns

Random sampling¶

In high-dimensional composition spaces, lattice grids can produce intractably many compositions. Random sampling from the composition space is attractive to generate training data for these cases, but care should be taken because naïve random sampling approaches in composition simplices can produce highly correlated points in high dimensions. Otis, Emelianenko, and Liu [1] demonstrated the use of scrambled Halton sequences to produce low discrepancy points on an n-simplex and this method is used internally in PyCalphad’s starting point generation.

Here we import PyCalphad’s scrambled Halton sequence sampler to generate low-discrepancy samples from our composition space for high-throughput calculations.

[1] R. Otis, M. Emelianenko, Z.-K. Liu, Computational Materials Science 130 (2017) 282–291

[5]:

from pycalphad.core.utils import point_sample

# Set up the composition grid using PyCalphad's scrambled Halton sequence sampler
components = ["AL", "MG", "SI", "CU", "VA"]
elements = [component for component in components if component != "VA"]
solutes = elements[1:]

temperatures = [1000.0, 1250.0, 1500.0]
pressure = 101325.0
density = 10

composition_rows = point_sample([len(elements)], density)
composition_conditions = [
    {v.X(solute): amount for solute, amount in zip(solutes, composition_row[1:])}
    for composition_row in composition_rows
]
n_points = len(composition_rows) * len(temperatures)

[6]:

# set up a Workspace and perform the calculations
test_database_directory = files(pycalphad.tests.databases)
dbf = Database(test_database_directory / "COST507.tdb")
phases = list(dbf.phases.keys())
wks = Workspace(dbf, components, phases)

data_rows = []
print(f"Evaluating {len(composition_rows)} simplex points × {len(temperatures)} temperatures = {n_points} total")
for temperature in temperatures:
    for comp_conds in composition_conditions:
        conditions = {v.T: temperature, v.P: pressure, v.N: 1, **comp_conds}
        wks.conditions = conditions
        out = {
            str(key): value[()]
            for key, value in wks.get_dict("T", "X(*)", "NP(*)", "X(*,*)").items()
        }
        data_rows.append(out)

/Users/bocklund1/src/calphad-workspace/packages/pycalphad/pycalphad/io/tdb.py:293: UserWarning: The type definition character `C` in `TYPE_DEFINITION C GES AMEND_PHASE_DESCRIPTION CBCC_A12 MAGNETIC -3 0.280, ` is not used by any phase.
  warnings.warn(f"The type definition character `{typechar}` in `TYPE_DEFINITION {typechar} {line}` is not used by any phase.")
/Users/bocklund1/src/calphad-workspace/packages/pycalphad/pycalphad/io/tdb.py:1017: UserWarning: The type definition character `R` was defined in the following phases: ['LIQUID'], but no corresponding TYPE_DEFINITION line was found in the TDB.
  warnings.warn(f"The type definition character `{typechar}` was defined in the following phases: "

Evaluating 30 simplex points × 3 temperatures = 90 total

[7]:

# Build a pandas DataFrame from the results
workspace_df = drop_empty_columns(pd.DataFrame(data_rows))
workspace_df

[7]:

	T	X_AL	X_CU	X_MG	X_SI	NP_BCC_B2	NP_CUMGSI_TAU	NP_DIAMOND_A4	NP_FCC_A1	NP_GAMMA_D83	...	X_LAVES_C15_MG	X_LAVES_C15_SI	X_LIQUID_AL	X_LIQUID_CU	X_LIQUID_MG	X_LIQUID_SI	X_MG2SI_AL	X_MG2SI_CU	X_MG2SI_MG	X_MG2SI_SI
0	1000.0	0.294784	0.143096	0.172437	0.389683	NaN	NaN	0.187663	NaN	NaN	...	NaN	NaN	0.372407	0.180777	0.200347	0.246469	0.0	0.0	0.666667	0.333333
1	1000.0	0.389918	0.238316	0.309003	0.062763	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.403179	0.246421	0.296839	0.053561	0.0	0.0	0.666667	0.333333
2	1000.0	0.053801	0.363918	0.281288	0.300992	NaN	NaN	0.090452	NaN	NaN	...	0.332141	0.235545	0.232509	0.417196	0.147563	0.202732	NaN	NaN	NaN	NaN
3	1000.0	0.726518	0.053857	0.041151	0.178473	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.726518	0.053857	0.041151	0.178473	NaN	NaN	NaN	NaN
4	1000.0	0.113442	0.135071	0.141870	0.609618	NaN	NaN	0.474927	NaN	NaN	...	NaN	NaN	0.236623	0.281740	0.232434	0.249203	0.0	0.0	0.666667	0.333333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
85	1500.0	0.333667	0.163897	0.228379	0.274057	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.333667	0.163897	0.228379	0.274057	NaN	NaN	NaN	NaN
86	1500.0	0.032311	0.225124	0.703895	0.038670	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.032311	0.225124	0.703895	0.038670	NaN	NaN	NaN	NaN
87	1500.0	0.275258	0.380345	0.066848	0.277549	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.275258	0.380345	0.066848	0.277549	NaN	NaN	NaN	NaN
88	1500.0	0.163474	0.088235	0.508454	0.239838	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.163474	0.088235	0.508454	0.239838	NaN	NaN	NaN	NaN
89	1500.0	0.148688	0.116956	0.274485	0.459871	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.148688	0.116956	0.274485	0.459871	NaN	NaN	NaN	NaN

90 rows × 45 columns