ElementEmbeddings

The Element Embeddings package provides high-level tools for analysing elemental and ionic species embeddings data. This primarily involves visualising the correlation between embedding schemes using different statistical measures.

• Documentation: https://wmd-group.github.io/ElementEmbeddings/
• Examples: https://github.com/WMD-group/ElementEmbeddings/tree/main/examples

Motivation

Machine learning approaches for materials informatics have become increasingly widespread. Some of these involve the use of deep learning techniques where the representation of the elements is learned rather than specified by the user of the model. While an important goal of machine learning training is to minimise the chosen error function to make more accurate predictions, it is also important for us material scientists to be able to interpret these models. As such, we aim to evaluate and compare different atomic embedding schemes in a consistent framework.

Getting started

ElementEmbeddings's main feature, the Embedding class is accessible by importing the class.

Installation

The latest stable release can be installed via pip using:

bash pip install ElementEmbeddings

Alternatively, ElementEmbeddings is available via conda through the conda-forge channel on Anaconda Cloud:

bash conda install -c conda-forge elementembeddings

For installing the development or documentation dependencies via pip:

bash pip install "ElementEmbeddings[dev]" pip install "ElementEmbeddings[docs]"

For development, you can clone the repository and install the package in editable mode. To clone the repository and make a local installation, run the following commands:

bash git clone https://github.com/WMD-group/ElementEmbeddings.git cd ElementEmbeddings pip install -e ".[docs,dev]"

With -e pip will create links to the source folder so that changes to the code will be immediately reflected on the PATH.

Usage

For simple usage, you can instantiate an Embedding object using one of the embeddings in the data directory. For this example, let's use the magpie elemental representation.

```pycon

Import the class

from elementembeddings.core import Embedding

Load the magpie data

magpie = Embedding.load_data("magpie") ```

We can access some of the properties of the Embedding class. For example, we can find the dimensions of the elemental representation and the list of elements for which an embedding exists.

```pycon

Print out some of the properties of the ElementEmbeddings class

print(f"The magpie representation has embeddings of dimension {magpie.dim}") print( ... f"The magpie representation contains these elements: \n {magpie.elementlist}" ... ) # prints out all the elements considered for this representation print( ... f"The magpie representation contains these features: \n {magpie.featurelabels}" ... ) # Prints out the feature labels of the chosen representation

The magpie representation has embeddings of dimension 22 The magpie representation contains these elements: ['H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'Ar', 'K', 'Ca', 'Sc', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'Ga', 'Ge', 'As', 'Se', 'Br', 'Kr', 'Rb', 'Sr', 'Y', 'Zr', 'Nb', 'Mo', 'Tc', 'Ru', 'Rh', 'Pd', 'Ag', 'Cd', 'In', 'Sn', 'Sb', 'Te', 'I', 'Xe', 'Cs', 'Ba', 'La', 'Ce', 'Pr', 'Nd', 'Pm', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu', 'Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au', 'Hg', 'Tl', 'Pb', 'Bi', 'Po', 'At', 'Rn', 'Fr', 'Ra', 'Ac', 'Th', 'Pa', 'U', 'Np', 'Pu', 'Am', 'Cm', 'Bk'] The magpie representation contains these features: ['Number', 'MendeleevNumber', 'AtomicWeight', 'MeltingT', 'Column', 'Row', 'CovalentRadius', 'Electronegativity', 'NsValence', 'NpValence', 'NdValence', 'NfValence', 'NValence', 'NsUnfilled', 'NpUnfilled', 'NdUnfilled', 'NfUnfilled', 'NUnfilled', 'GSvolume_pa', 'GSbandgap', 'GSmagmom', 'SpaceGroupNumber'] ```

Plotting

We can quickly generate heatmaps of distance/similarity measures between the element vectors using heatmap_plotter and plot the representations in two dimensions using the dimension_plotter from the plotter module. Before we do that, we will standardise the embedding using the standardise method available to the Embedding class

```python from elementembeddings.plotter import heatmapplotter, dimensionplotter import matplotlib.pyplot as plt

magpie.standardise(inplace=True) # Standardises the representation

fig, ax = plt.subplots(1, 1, figsize=(6, 6)) heatmapparams = {"vmin": -1, "vmax": 1} heatmapplotter( embedding=magpie, metric="cosinesimilarity", showaxislabels=False, cmap="Bluesr", ax=ax, **heatmapparams ) ax.settitle("Magpie cosine similarities") fig.tightlayout() fig.show() ```

```python fig, ax = plt.subplots(1, 1, figsize=(6, 6))

reducerparams = {"nneighbors": 30, "randomstate": 42} scatterparams = {"s": 100}

dimensionplotter( embedding=magpie, reducer="umap", ncomponents=2, ax=ax, adjusttext=True, reducerparams=reducerparams, scatterparams=scatterparams, ) ax.settitle("Magpie UMAP (nneighbours=30)") ax.legend().remove() handles, labels = ax1.getlegendhandleslabels() fig.legend(handles, labels, bboxto_anchor=(1.25, 0.5), loc="center right", ncol=1)

fig.tight_layout() fig.show() ```

Compositions

The package can also be used to featurise compositions. Your data could be a list of formula strings or a pandas dataframe of the following format:

| formula | | ------- | | CsPbI3 | | Fe2O3 | | NaCl | | ZnS |

The composition_featuriser function can be used to featurise the data. The compositions can be featurised using different representation schemes and different types of pooling through the embedding and stats arguments respectively.

```python from elementembeddings.composition import composition_featuriser

dffeaturised = compositionfeaturiser(df, embedding="magpie", stats=["mean", "sum"])

df_featurised ```

| formula | meanNumber | meanMendeleevNumber | meanAtomicWeight | meanMeltingT | meanColumn | meanRow | meanCovalentRadius | meanElectronegativity | meanNsValence | meanNpValence | meanNdValence | meanNfValence | meanNValence | meanNsUnfilled | meanNpUnfilled | meanNdUnfilled | meanNfUnfilled | meanNUnfilled | meanGSvolumepa | meanGSbandgap | meanGSmagmom | meanSpaceGroupNumber | sumNumber | sumMendeleevNumber | sumAtomicWeight | sumMeltingT | sumColumn | sumRow | sumCovalentRadius | sumElectronegativity | sumNsValence | sumNpValence | sumNdValence | sumNfValence | sumNValence | sumNsUnfilled | sumNpUnfilled | sumNdUnfilled | sumNfUnfilled | sumNUnfilled | sumGSvolumepa | sumGSbandgap | sumGSmagmom | sumSpaceGroupNumber | | ------- | ----------- | -------------------- | ------------------ | ----------------- | ----------- | -------- | ------------------- | ---------------------- | -------------- | -------------- | ------------------ | ------------------ | ------------- | --------------- | --------------- | --------------- | --------------- | -------------- | ---------------- | -------------- | ------------------ | --------------------- | ---------- | ------------------- | ----------------- | ------------ | ---------- | ------- | ------------------ | --------------------- | ------------- | ------------- | ------------- | ------------- | ------------ | -------------- | -------------- | -------------- | -------------- | ------------- | ------------------ | ------------- | ------------ | -------------------- | | CsPbI3 | 59.2 | 74.8 | 144.16377238 | 412.55 | 13.2 | 5.4 | 161.39999999999998 | 2.22 | 1.8 | 3.4 | 8.0 | 2.8000000000000003 | 16.0 | 0.2 | 1.4 | 0.0 | 0.0 | 1.6 | 54.584 | 0.6372 | 0.0 | 129.20000000000002 | 296.0 | 374.0 | 720.8188619 | 2062.75 | 66.0 | 27.0 | 807.0 | 11.100000000000001 | 9.0 | 17.0 | 40.0 | 14.0 | 80.0 | 1.0 | 7.0 | 0.0 | 0.0 | 8.0 | 272.92 | 3.186 | 0.0 | 646.0 | | Fe2O3 | 15.2 | 74.19999999999999 | 31.937640000000002 | 757.2800000000001 | 12.8 | 2.8 | 92.4 | 2.7960000000000003 | 2.0 | 2.4 | 2.4000000000000004 | 0.0 | 6.8 | 0.0 | 1.2 | 1.6 | 0.0 | 2.8 | 9.755 | 0.0 | 0.8442651200000001 | 98.80000000000001 | 76.0 | 371.0 | 159.6882 | 3786.4 | 64.0 | 14.0 | 462.0 | 13.98 | 10.0 | 12.0 | 12.0 | 0.0 | 34.0 | 0.0 | 6.0 | 8.0 | 0.0 | 14.0 | 48.775000000000006 | 0.0 | 4.2213256 | 494.0 | | NaCl | 14.0 | 48.0 | 29.221384640000004 | 271.235 | 9.0 | 3.0 | 134.0 | 2.045 | 1.5 | 2.5 | 0.0 | 0.0 | 4.0 | 0.5 | 0.5 | 0.0 | 0.0 | 1.0 | 26.87041666665 | 1.2465 | 0.0 | 146.5 | 28.0 | 96.0 | 58.44276928000001 | 542.47 | 18.0 | 6.0 | 268.0 | 4.09 | 3.0 | 5.0 | 0.0 | 0.0 | 8.0 | 1.0 | 1.0 | 0.0 | 0.0 | 2.0 | 53.7408333333 | 2.493 | 0.0 | 293.0 | | ZnS | 23.0 | 78.5 | 48.7225 | 540.52 | 14.0 | 3.5 | 113.5 | 2.115 | 2.0 | 2.0 | 5.0 | 0.0 | 9.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | 19.8734375 | 1.101 | 0.0 | 132.0 | 46.0 | 157.0 | 97.445 | 1081.04 | 28.0 | 7.0 | 227.0 | 4.23 | 4.0 | 4.0 | 10.0 | 0.0 | 18.0 | 0.0 | 2.0 | 0.0 | 0.0 | 2.0 | 39.746875 | 2.202 | 0.0 | 264.0 |

The returned dataframe contains the mean-pooled and sum-pooled features of the magpie representation for the four formulas.

Development notes

Bugs, features and questions

Please use the issue tracker to report bugs and any feature requests. Hopefully, most questions should be solvable through the docs. For any other queries related to the project, please contact Anthony Onwuli by e-mail: anthony.onwuli16@imperial.ac.uk.

Code contributions

We welcome new contributions to this project. See the contributing guide for detailed instructions on how to contribute to our project.

Add an embedding scheme

The steps required to add a new representation scheme are:

1. Add data file to data/element_representations.
2. Edit docstring table in core.py.
3. Edit utils/config.py to include the representation in DEFAULT_ELEMENT_EMBEDDINGS and CITATIONS.
4. Update the documentation reference.md and README.md.

Developer

• Anthony Onwuli (Department of Materials, Imperial College London)

References

A. Onwuli et al, "Ionic species representations for materials informatics"

H. Park et al, "Mapping inorganic crystal chemical space" Faraday Discuss. (2024)

A. Onwuli et al, "Element similarity in high-dimensional materials representations" Digital Discovery 2, 1558 (2023)