M3GNet

M3GNet is a new materials graph neural network architecture that incorporates 3-body interactions. A key difference with prior materials graph implementations such as MEGNet is the addition of the coordinates for atoms and the 3×3 lattice matrix in crystals, which are necessary for obtaining tensorial quantities such as forces and stresses via auto-differentiation.

As a framework, M3GNet has diverse applications, including:

• Interatomic potential development. With the same training data, M3GNet performs similarly to state-of-the-art machine learning interatomic potentials (ML-IAPs). However, a key feature of a graph representation is its flexibility to scale to diverse chemical spaces. One of the key accomplishments of M3GNet is the development of a universal IAP that can work across the entire periodic table of the elements by training on relaxations performed in the Materials Project.
• Surrogate models for property predictions. Like the previous MEGNet architecture, M3GNet can be used to develop surrogate models for property predictions, achieving in many cases accuracies that better or similar to other state-of-the-art ML models.

For detailed performance benchmarks, please refer to the publication in the References section. The API documentation is available via the Github Page.

Table of Contents

• System requirements
• Installation
• Change Log
• Usage
• Model training
• Matterverse
• API docs
• Datasets
• References

System requirements

Inferences using the pre-trained models can be ran on any standard computer. For model training, the GPU memory needs to be > 18 Gb for a batch size of 32 using the crystal training data. In our work, we used a single RTX 3090 GPU for model training.

Installation

M3GNet can be installed via pip:

pip install m3gnet

You can also directly download the source from Github and install from source.

Apple Silicon Installation

Apple Silicon (M1, M1 Pro, M1 Max, M1 Ultra) has extremely powerful ML capabilities, but special steps are needed for the installation of tensorflow and other dependencies. Here are the recommended installation steps.

1. Ensure that you already have XCode and CLI installed.

2. Install Miniconda or Anaconda.

3. Create a Python 3.9 environment.

   conda create --name m3gnet python=3.9
   conda activate m3gnet

4. First install tensorflow and its dependencies for Apple Silicon.

   conda install -c apple tensorflow-deps
   pip install tensorflow-macos

5. If you wish, you can install tensorflow-metal, which helps speed up training. If you encounter strange tensorflow errors, you should uninstall tensorflow-metal and see if it fixes the errors first.

   pip install tensorflow-metal

6. Install m3gnet but ignore dependencies (otherwise, pip will look for tensorflow).

   pip install --no-deps m3gnet

7. Install other dependencies like pymatgen, etc. manually.

   pip install protobuf==3.20.0 pymatgen ase cython

8. Once you are done, you can try running pytest m3gnet to see if all tests pass.

Change Log

See change log

Usage

Structure relaxation

A M3Gnet universal potential for the periodic table has been developed using data from Materials Project relaxations since 2012. This universal potential can be used to perform structural relaxation of any arbitrary crystal as follows.

import warnings

from m3gnet.models import Relaxer
from pymatgen.core import Lattice, Structure

for category in (UserWarning, DeprecationWarning):
    warnings.filterwarnings("ignore", category=category, module="tensorflow")

# Init a Mo structure with stretched lattice (DFT lattice constant ~ 3.168)
mo = Structure(Lattice.cubic(3.3), ["Mo", "Mo"], [[0., 0., 0.], [0.5, 0.5, 0.5]])

relaxer = Relaxer()  # This loads the default pre-trained model

relax_results = relaxer.relax(mo, verbose=True)

final_structure = relax_results['final_structure']
final_energy_per_atom = float(relax_results['trajectory'].energies[-1] / len(mo))

print(f"Relaxed lattice parameter is {final_structure.lattice.abc[0]:.3f} Å")
print(f"Final energy is {final_energy_per_atom:.3f} eV/atom")

The output is as follows:

Relaxed lattice parameter is  3.169 Å
Final energy is -10.859 eV/atom

The initial lattice parameter of 3.3 Å was successfully relaxed to 3.169 Å, close to the DFT value of 3.168 Å. The final energy -10.859 eV/atom is also close to Materials Project DFT value of -10.8456 eV/atom.

The relaxation takes less than 20 seconds on a single laptop.

The table below provides more comprehensive benchmarks for cubic crystals based on exp data on Wikipedia and MP DFT data. The Jupyter notebook is in the examples folder. This benchmark is limited to cubic crystals for ease of comparison since there is only one lattice parameter. Of course, M3GNet is not limited to cubic systems (see LiFePO4 example).

Material	Crystal structure	a (Å)	MP a (Å)	M3GNet a (Å)	% error vs Expt	% error vs MP
Ac	FCC	5.31	5.66226	5.6646	6.68%	0.04%
Ag	FCC	4.079	4.16055	4.16702	2.16%	0.16%
Al	FCC	4.046	4.03893	4.04108	-0.12%	0.05%
AlAs	Zinc blende (FCC)	5.6605	5.73376	5.73027	1.23%	-0.06%
AlP	Zinc blende (FCC)	5.451	5.50711	5.50346	0.96%	-0.07%
AlSb	Zinc blende (FCC)	6.1355	6.23376	6.22817	1.51%	-0.09%
Ar	FCC	5.26	5.64077	5.62745	6.99%	-0.24%
Au	FCC	4.065	4.17129	4.17431	2.69%	0.07%
BN	Zinc blende (FCC)	3.615	3.626	3.62485	0.27%	-0.03%
BP	Zinc blende (FCC)	4.538	4.54682	4.54711	0.20%	0.01%
Ba	BCC	5.02	5.0303	5.03454	0.29%	0.08%
C (diamond)	Diamond (FCC)	3.567	3.57371	3.5718	0.13%	-0.05%
Ca	FCC	5.58	5.50737	5.52597	-0.97%	0.34%
CaVO3	Cubic perovskite	3.767	3.83041	3.83451	1.79%	0.11%
CdS	Zinc blende (FCC)	5.832	5.94083	5.9419	1.88%	0.02%
CdSe	Zinc blende (FCC)	6.05	6.21283	6.20987	2.64%	-0.05%
CdTe	Zinc blende (FCC)	6.482	6.62905	6.62619	2.22%	-0.04%
Ce	FCC	5.16	4.72044	4.71921	-8.54%	-0.03%
Cr	BCC	2.88	2.87403	2.84993	-1.04%	-0.84%
CrN	Halite	4.149	-	4.16068	0.28%	-
Cs	BCC	6.05	6.11004	5.27123	-12.87%	-13.73%
CsCl	Caesium chloride	4.123	4.20906	4.20308	1.94%	-0.14%
CsF	Halite	6.02	6.11801	6.1265	1.77%	0.14%
CsI	Caesium chloride	4.567	4.66521	4.90767	7.46%	5.20%
Cu	FCC	3.597	3.62126	3.61199	0.42%	-0.26%
Eu	BCC	4.61	4.63903	4.34783	-5.69%	-6.28%
EuTiO3	Cubic perovskite	7.81	3.96119	3.92943	-49.69%	-0.80%
Fe	BCC	2.856	2.84005	2.85237	-0.13%	0.43%
GaAs	Zinc blende (FCC)	5.653	5.75018	5.75055	1.73%	0.01%
GaP	Zinc blende (FCC)	5.4505	5.5063	5.5054	1.01%	-0.02%
GaSb	Zinc blende (FCC)	6.0959	6.21906	6.21939	2.03%	0.01%
Ge	Diamond (FCC)	5.658	5.76286	5.7698	1.98%	0.12%
HfC0.99	Halite	4.64	4.65131	4.65023	0.22%	-0.02%
HfN	Halite	4.392	4.53774	4.53838	3.33%	0.01%
InAs	Zinc blende (FCC)	6.0583	6.18148	6.25374	3.23%	1.17%
InP	Zinc blende (FCC)	5.869	5.95673	5.9679	1.69%	0.19%
InSb	Zinc blende (FCC)	6.479	6.63322	6.63863	2.46%	0.08%
Ir	FCC	3.84	3.87573	3.87716	0.97%	0.04%
K	BCC	5.23	5.26212	5.4993	5.15%	4.51%
KBr	Halite	6.6	6.70308	6.70797	1.64%	0.07%
KCl	Halite	6.29	6.38359	6.39634	1.69%	0.20%
KF	Halite	5.34	5.42398	5.41971	1.49%	-0.08%
KI	Halite	7.07	7.18534	7.18309	1.60%	-0.03%
KTaO3	Cubic perovskite	3.9885	4.03084	4.03265	1.11%	0.05%
Kr	FCC	5.72	6.49646	6.25924	9.43%	-3.65%
Li	BCC	3.49	3.42682	3.41891	-2.04%	-0.23%
LiBr	Halite	5.5	5.51343	5.51076	0.20%	-0.05%
LiCl	Halite	5.14	5.15275	5.14745	0.15%	-0.10%
LiF	Halite	4.03	4.08343	4.08531	1.37%	0.05%
LiI	Halite	6.01	6.0257	6.02709	0.28%	0.02%
MgO	Halite (FCC)	4.212	4.25648	4.2567	1.06%	0.01%
Mo	BCC	3.142	3.16762	3.16937	0.87%	0.06%
Na	BCC	4.23	4.17262	4.19684	-0.78%	0.58%
NaBr	Halite	5.97	6.0276	6.01922	0.82%	-0.14%
NaCl	Halite	5.64	5.69169	5.69497	0.97%	0.06%
NaF	Halite	4.63	4.69625	4.69553	1.42%	-0.02%
NaI	Halite	6.47	6.532	6.52739	0.89%	-0.07%
Nb	BCC	3.3008	3.32052	3.32221	0.65%	0.05%
NbN	Halite	4.392	4.45247	4.45474	1.43%	0.05%
Ne	FCC	4.43	4.30383	6.95744	57.05%	61.66%
Ni	FCC	3.499	3.5058	3.5086	0.27%	0.08%
Pb	FCC	4.92	5.05053	5.02849	2.21%	-0.44%
PbS	Halite (FCC)	5.9362	6.00645	6.01752	1.37%	0.18%
PbTe	Halite (FCC)	6.462	6.56567	6.56111	1.53%	-0.07%
Pd	FCC	3.859	3.95707	3.95466	2.48%	-0.06%
Pt	FCC	3.912	3.97677	3.97714	1.67%	0.01%
Rb	BCC	5.59	5.64416	5.63235	0.76%	-0.21%
RbBr	Halite	6.89	7.02793	6.98219	1.34%	-0.65%
RbCl	Halite	6.59	6.69873	6.67994	1.36%	-0.28%
RbF	Halite	5.65	5.73892	5.76843	2.10%	0.51%
RbI	Halite	7.35	7.48785	7.61756	3.64%	1.73%
Rh	FCC	3.8	3.8439	3.84935	1.30%	0.14%
ScN	Halite	4.52	4.51831	4.51797	-0.04%	-0.01%
Si	Diamond (FCC)	5.43102	5.46873	5.45002	0.35%	-0.34%
Sr	FCC	6.08	6.02253	6.04449	-0.58%	0.36%
SrTiO3	Cubic perovskite	3.98805	3.94513	3.94481	-1.08%	-0.01%
SrVO3	Cubic perovskite	3.838	3.90089	3.90604	1.77%	0.13%
Ta	BCC	3.3058	3.32229	3.31741	0.35%	-0.15%
TaC0.99	Halite	4.456	4.48208	4.48225	0.59%	0.00%
Th	FCC	5.08	5.04122	5.04483	-0.69%	0.07%
TiC	Halite	4.328	4.33565	4.33493	0.16%	-0.02%
TiN	Halite	4.249	4.25353	4.25254	0.08%	-0.02%
V	BCC	3.0399	2.99254	2.99346	-1.53%	0.03%
VC0.97	Halite	4.166	4.16195	4.16476	-0.03%	0.07%
VN	Halite	4.136	4.12493	4.1281	-0.19%	0.08%
W	BCC	3.155	3.18741	3.18826	1.05%	0.03%
Xe	FCC	6.2	6.66148	7.06991	14.03%	6.13%
Yb	FCC	5.49	5.44925	5.45807	-0.58%	0.16%
ZnO	Halite (FCC)	4.58	4.33888	4.33424	-5.37%	-0.11%
ZnS	Zinc blende (FCC)	5.42	5.45027	5.45297	0.61%	0.05%
ZrC0.97	Halite	4.698	4.72434	4.72451	0.56%	0.00%
ZrN	Halite	4.577	4.61762	4.61602	0.85%	-0.03%

From the table, it can be observed that almost all M3GNet-relaxed cubic lattice constants are within 1% of the DFT values. The only major errors are with EuTiO3, iodides (RbI and CsI) and the noble gases. It is quite likely the Wikipedia value for EuTiO3 is wrong by a factor of 2 and the lower than expected accuracy on iodides and noble gases may be due to the paucity of data in these chemical systems. It should be noted that M3GNet is expected to reproduce the MP DFT value and not the experimental values, which are only provided as an additional point of reference.

All relaxations take less than 1s on a M1 Max Mac.

CLI tool

A simple CLI tool has been written. Right now, it supports just doing structure relaxations with M3GNet, which is immediately useful for quick testing of the capabilities of M3GNet itself. More features will be developed in future if there is user interest. Examples below.

m3g relax --infile Li2O.cif  # Outputs to stdout the relaxed structure.
m3g relax --infile Li2O.cif --outfile Li2O_relaxed.cif  # Outputs to a file the relaxed structure.

Molecular dynamics

Similarly, the universal IAP can be used to perform molecular dynamics (MD) simulations as well.

from pymatgen.core import Structure, Lattice
from m3gnet.models import MolecularDynamics

# Init a Mo structure with stretched lattice (DFT lattice constant ~ 3.168)
mo = Structure(Lattice.cubic(3.3),
               ["Mo", "Mo"], [[0., 0., 0.], [0.5, 0.5, 0.5]])

md = MolecularDynamics(
    atoms=mo,
    temperature=1000,  # 1000 K
    ensemble='nvt',  # NVT ensemble
    timestep=1, # 1fs,
    trajectory="mo.traj",  # save trajectory to mo.traj
    logfile="mo.log",  # log file for MD
    loginterval=100,  # interval for record the log
)

md.run(steps=1000)

After the run, mo.log contains thermodynamic information similar to the following:

Time[ps]      Etot[eV]     Epot[eV]     Ekin[eV]    T[K]
0.0000         -21.3307     -21.3307       0.0000     0.0
0.1000         -21.3307     -21.3307       0.0000     0.0
0.2000         -21.2441     -21.3087       0.0645   249.7
0.3000         -21.0466     -21.2358       0.1891   731.6
0.4000         -20.9702     -21.1149       0.1447   559.6
0.5000         -20.9380     -21.1093       0.1713   662.6
0.6000         -20.9176     -21.1376       0.2200   850.9
0.7000         -20.9016     -21.1789       0.2773  1072.8
0.8000         -20.8804     -21.1638       0.2835  1096.4
0.9000         -20.8770     -21.0695       0.1925   744.5
1.0000         -20.8908     -21.0772       0.1864   721.2

The MD run takes less than 1 minute.

Model training

You can also train your own IAP using the PotentialTrainer in m3gnet.trainers. The training dataset can include:

• structures, a list of pymatgen Structures
• energies, a list of energy floats with unit eV.
• forces, a list of nx3 force matrix with unit eV/Å, where n is the number of atom in each structure. n does not need to be the same for all structures.
• stresses, a list of 3x3 stress matrices with unit GPa (optional)

For stresses, we use the convention that compressive stress gives negative values. Stresses obtained from VASP calculations (default unit is kBar) should be multiplied by -0.1 to work directly with the model.

We use validation dataset to select the stopping epoch number. The dataset has similar format as the training dataset.

A minimal example of model training is shown below.

from m3gnet.models import M3GNet, Potential
from m3gnet.trainers import PotentialTrainer

import tensorflow as tf

m3gnet = M3GNet(is_intensive=False)
potential = Potential(model=m3gnet)

trainer = PotentialTrainer(
    potential=potential, optimizer=tf.keras.optimizers.Adam(1e-3)
)

trainer.train(
    structures,
    energies,
    forces,
    stresses,
    validation_graphs_or_structures=val_structures,
    val_energies=val_energies,
    val_forces=val_forces,
    val_stresses=val_stresses,
    epochs=100,
    fit_per_element_offset=True,
    save_checkpoint=False,
)

Matterverse

As an example of the power of M3GNet for materials discovery, we have created a database of yet-to-be-synthesized materials called matterverse.ai. At the time of writing, matterverse.ai has 31 million structures, of which more than 1 million are predicted to be potentially stable. The initial candidate list was generated via combinatorial isovalent ionic substitutions based on the common oxidation states of non-noble-gas elements on 5,283 binary, ternary and quaternary structural prototypes in the 2019 version of the ICSD database.

API docs

The API docs are available here.

Datasets

The training data used to develop the universal M3GNet IAP is MPF.2021.2.8 and is hosted on figshare with DOI 10.6084/m9.figshare.19470599.

Reference

Please cite the following work:

Chen, C., Ong, S.P. A universal graph deep learning interatomic potential for the periodic table. Nat Comput Sci 2, 718–728 (2022). https://doi.org/10.1038/s43588-022-00349-3.

Acknowledgements

This work was primarily supported by the Materials Project, funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231: Materials Project program KC23MP. This work used the Expanse supercomputing cluster at the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562.