Cluster expansions¶

class icet.ClusterExpansion(cluster_space: icet.core.cluster_space.ClusterSpace, parameters: numpy.array, metadata: dict = None)[source]

Cluster expansions are obtained by combining a cluster space with a set of parameters, where the latter is commonly obtained by optimization. Instances of this class allow one to predict the property of interest for a given structure.

Note: Each element of the parameter vector corresponds to an effective cluster interaction (ECI) multiplied by the multiplicity of the underlying orbit.

cluster_space

cluster space that was used for constructing the cluster expansion

Type

icet.ClusterSpace

parameters

parameter vector

Type

np.ndarray

Example

The following snippet illustrates the initialization and usage of a ClusterExpansion object. Here, the parameters are taken to be a list of ones. Usually, they would be obtained by training with respect to a set of reference data:

>>> from ase.build import bulk
>>> from icet import ClusterSpace, ClusterExpansion

>>> # create cluster expansion with fake parameters
>>> prim = bulk('Au')
>>> cs = ClusterSpace(prim, cutoffs=[7.0, 5.0],
...                   chemical_symbols=[['Au', 'Pd']])
>>> parameters = len(cs) * [1.0]
>>> ce = ClusterExpansion(cs, parameters)

>>> # make prediction for supercell
>>> sc = prim.repeat(3)
>>> for k in [1, 4, 7]:
>>>     sc[k].symbol = 'Pd'
>>> print(ce.predict(sc))

property fractional_position_tolerance

tolerance applied when comparing positions in fractional coordinates (inherited from the underlying cluster space)

get_cluster_space_copy() → icet.core.cluster_space.ClusterSpace[source]

Gets copy of cluster space on which cluster expansion is based

property metadata

property orders

orders included in cluster expansion

property parameters

parameter vector; each element of the parameter vector corresponds to an effective cluster interaction (ECI) multiplied by the multiplicity of the respective orbit

plot_ecis(orders=None)[source]

Plot ECIs for given orders, default plots for all orders

property position_tolerance

tolerance applied when comparing positions in Cartesian coordinates (inherited from the underlying cluster space)

predict(structure: Union[ase.atoms.Atoms, _icet.Structure]) → float[source]

Predicts the property of interest (e.g., the energy) for the input structure using the cluster expansion.

Parameters

structure – atomic configuration

Returns

property value of predicted by the cluster expansion

Return type

float

property primitive_structure

primitive structure on which cluster expansion is based

print_overview(print_threshold: int = None, print_minimum: int = 10) → None[source]

Print an overview of the cluster expansion in terms of the orbits (order, radius, multiplicity, corresponding ECI etc).

Parameters
• print_threshold – if the number of orbits exceeds this number print dots

• print_minimum – number of lines printed from the top and the bottom of the orbit list if print_threshold is exceeded

prune(indices: List[int] = None, tol: float = 0) → None[source]

Removes orbits from the cluster expansion (CE), for which the absolute values of the corresponding parameters are zero or close to zero. This commonly reduces the computational cost for evaluating the CE and is therefore recommended prior to using it in production. If the method is called without arguments orbits will be pruned, for which the ECIs are strictly zero. Less restrictive pruning can be achieved by setting the tol keyword.

Parameters
• indices – indices of parameters to remove from the cluster expansion.

• tol – all orbits will be pruned for which the absolute parameter value(s) is/are within this tolerance

static read(filename: str)[source]

Parameters

filename – file from which to read

property symprec

tolerance imposed when analyzing the symmetry using spglib (inherited from the underlying cluster space)

to_dataframe() → pandas.core.frame.DataFrame[source]

Returns representation of the cluster expansion in the form of a DataFrame containing orbit information and effective cluster interactions (ECIs).

write(filename: str) → None[source]

Writes ClusterExpansion object to file.

Parameters

filename – name of file to which to write