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A Universal Graph Deep Learning Interatomic Potential for the Periodic Table
Chi Chen, Shyue Ping Ong
TL;DR
Existing interatomic potentials are limited by narrow chemical coverage or insufficient accuracy for general materials applications. This work develops M3GNet, a universal graph-based interatomic potential with three-body interactions trained on Materials Project relaxations. It identifies about 1.8 million potentially stable materials among 31 million hypothetical structures, while the authors note that predictions require further DFT and experimental verification.
Problem
Existing interatomic potentials are not universally applicable across the periodic table and all crystal types, and some lack physical constraints such as continuity of energies.
Method
M3GNet is a materials graph neural-network interatomic potential incorporating three-body interactions and trained using reference energies for chemical elements.
Results
About 1.8 million of 31 million hypothetical materials were predicted potentially stable against Materials Project crystals using M3GNet energies.
Takeaways & Limitations
M3GNet supports universal application to materials without further retraining and can serve as a surrogate for DFT in structural exploration and dynamics.
Takeaways & Limitations
The candidate space includes many chemical systems absent from Materials Project training data, so predictions likely include extrapolations and require further DFT and experimental verification.
Abstract
from arXiv · showhide
Interatomic potentials (IAPs), which describe the potential energy surface of atoms, are a fundamental input for atomistic simulations. However, existing IAPs are either fitted to narrow chemistries or too inaccurate for general applications. Here, we report a universal IAP for materials based on graph neural networks with three-body interactions (M3GNet). The M3GNet IAP was trained on the massive database of structural relaxations performed by the Materials Project over the past 10 years and has broad applications in structural relaxation, dynamic simulations and property prediction of materials across diverse chemical spaces. About 1.8 million materials were identified from a screening of 31 million hypothetical crystal structures to be potentially stable against existing Materials Project crystals based on M3GNet energies. Of the top 2000 materials with the lowest energies above hull, 1578 were verified to be stable using DFT calculations. These results demonstrate a machine learning-accelerated pathway to the discovery of synthesizable materials with exceptional properties.
Materials Graphs with Many-Body Interactions
M3GNet introduces a three-body materials graph architecture for a broadly applicable interatomic potential, achieving accurate energy, force, and stress predictions and enabling rapid relaxation and materials discovery across diverse chemistries.
- Materials Graphs with Many-Body Interactions: M3GNet explicitly incorporates many-body interactions and focuses on three-body interactions to construct a materials graph potential.The architecture was developed as a new materials graph architecture with explicit many-body interactions.
- Model accuracy: The final M3GNet-EFS model achieved test MAEs of 0.035 eV atom−1 for energy, 0.072 eV Å−1 for force, and 0.41 GPa for stress.Including energy, force, and stress during training was reported as critical for obtaining a practical IAP.
- Model accuracy: 50% of test data had energy, force, and stress errors below 0.01 eV atom−1, 0.033 eV Å−1, and 0.042 GPa, respectively.Model predictions and DFT ground truth showed high linearity in parity plots.
- Structural relaxation: M3GNet relaxation reduced volume errors from 2.4% and 22.2% at the 50th and 5th percentiles to 0.6% and 6.6%, respectively.Energy predictions on M3GNet-relaxed structures had a 0.035 eV atom−1 MAE, compared with 0.169 eV atom−1 using initial structures.
- Structural relaxation: M3GNet relaxation took about 22 seconds on one CPU core, whereas the corresponding DFT relaxation took 15 hours on 32 cores.The model was reported to produce structures and energies close to DFT-relaxed results.
Ethics Declaration
The model uses graph-based neural-network components, smooth basis functions, and property-specific readouts. Training incorporates energy, force, and stress losses with validation-based convergence monitoring.
- Ethics Declaration: The authors declare that they have no competing financial interests.
- Model architecture: Continuous, smooth basis functions ensure that the first and second derivatives vanish at the cutoff radius.
- Model architecture: M3GNet uses three three-body information-exchange and graph-convolution blocks.
- Property prediction: Extensive-property prediction applies a three-layer gated MLP to atom attributes and sums the outputs into the final prediction.
- Training: Validation metrics monitor convergence, and training stops when the validation metric fails to improve for 200 epochs.
- Training: The universal IAP training loss includes energy, force, and, for inorganic compounds, stress terms.
Potential for the Periodic Table
The paper is authored by Chi Chen and Shyue Ping Ong, who are affiliated with the Materials Virtual Lab at the University of California San Diego.
- Chi Chen and Shyue Ping Ong are listed as the paper’s authors.
- The authors are affiliated with the Materials Virtual Lab, Department of NanoEngineering, University of California San Diego.
- The listed institutional address is 9500 Gilman Dr, Mail Code 0448, La Jolla, California 92093-0448, United States.
Long-range interactions
M3GNet is designed to capture long-range interactions through stacked graph-convolution layers without increasing the cutoff radius. In MgO tests, it outperforms MTP in extrapolation and exhibits nonlocal behavior beyond the set cutoff.
- Architecture: M3GNet can simulate long-range interactions by stacking graph-convolution layers without increasing the cutoff radius.
- Equation-of-state test: M3GNet outperforms MTP in equation-of-state extrapolation outside the training-data regimes in the MgO dataset.
- Locality test: The locality test perturbs atoms outside rlocal and measures the center atom’s force standard deviation σ(f).
- Locality test: At rlocal = 10 Å, Buckingham with long-range electrostatics has large σ(f), while M3GNet retains non-zero σ(f).
- Locality test: MTP interactions are localized, with σ(f) vanishing at 2rc = 10 Å.
- Conclusion: The authors conclude that M3GNet captures long-range interactions well beyond its set cutoff radius.
Potential smoothness
M3GNet is evaluated for smoothness under structural changes. In strained Ni cells, energy, forces, and stresses change smoothly even when cutoff-defined bond counts change non-smoothly.
- Motivation: Prediction smoothness across structural changes is identified as a critical requirement for an interatomic potential.
- Strain test: Under applied strain to a Ni cell, energy, forces, and stresses change smoothly despite non-smooth changes in the number of bonds.
- Strain test: All bonds break near 150% strain, while energy, force, and stress changes remain continuous.
MPF.2021.2.8 distribution and M3GNet fitting using
The MPF.2021.2.8 dataset’s distribution is documented, and supplementary tables report its statistics and M3GNet fitting errors across progressively richer training targets.
- The MPF.2021.2.8 dataset’s formation-energy distribution is shown in Figure S3.
- Table S1 reports the dataset’s mean, standard deviation, minimum, maximum, and quantiles.
- Table S2 compares MAEs for models trained on energy; energy and force; or energy, force, and stress.
M3GNet dynamic properties calculations
M3GNet reproduces several DFT-derived dynamic and mechanical properties while requiring substantially less computation for phonon calculations, though shear moduli are harder to match than bulk moduli.
- M3GNet phonon results for SiO2 polymorphs agree quantitatively with DFT calculations.The model uses a frozen-phonon approach, whereas the original calculations used DFPT.
- M3GNet phonon calculations took seconds, at least four orders of magnitude faster than DFT calculations.
- The frozen-phonon approach requires larger supercells for long-wavelength behavior, producing differences in the number of bands.
- The phonon DOS center versus average atomic mass also agrees with prior results.
- M3GNet bulk moduli matched DFT well, whereas shear moduli were more challenging to match.
M3GNet relaxation for materials discovery
M3GNet relaxations approach DFT-equilibrium structures efficiently and can reduce subsequent DFT relaxation cost, while energy changes and stability thresholds help characterize discovery-pool candidates.
- MAE dropped to 0.047 eV atom−1 after about 10 M3GNet relaxation steps.This MAE was one order of magnitude smaller than the M3GNet energy changes, indicating relaxation close to equilibrium.
- An example relaxation converged energy, force, and stress within less than 200 steps.Lattice constants, angles, mean atom distances, and XRD patterns converged close to the DFT-relaxed structures.
- M3GNet and DFT relaxation energy-change distributions were compared for all-chemistry and oxide categories.The supplied passages indicate that DFT energy changes were at least one order of magnitude smaller than M3GNet energy changes.
- 0.31: the DFT stable ratio at an Ehull−m threshold of 0.001 eV atom−1.The stable ratio decreased monotonically as the Ehull−m threshold decreased across the sampled discovery pool.
- 2.971 times: DFT relaxation without M3GNet pre-relaxation cost that much more CPU time on average.M3GNet pre-relaxation therefore accelerated the subsequent DFT relaxation procedure.
M3GNet for molecular dynamics simulations
M3GNet supports molecular-dynamics screening, conductivity analysis, and materials-property prediction across diverse datasets, identifying known trends while exposing limitations for defect-dependent transport.
- M3GNet molecular dynamics reproduced Li3YCl6 conductivity and activation-energy behavior in agreement with AIMD simulations.The calculated Li conductivity and Arrhenius-fitted activation energy matched the cited AIMD results.
- 837 potential lithium superionic conductors were selected for short molecular-dynamics simulations.The screening used 25 ps simulations at 800 K and 1200 K, recording mean-squared displacements of diffusive species.
- Very few screened materials combined high MSDs with diffusion energy barriers below 0.4 eV.The distribution therefore suggested difficulty in finding new superionic conductors.
- M3GNet rediscovered known lithium superionic conductors with high MSDs at both temperatures.Halide conductors also performed well, but generally had slightly smaller MSDs than the first group.
- The cubic Li7La3Zr2O12 phase had much larger MSD at 800 K than the tetragonal phase, suggesting better low-temperature ionic conduction.
- Anion and polyanion trends matched experimental findings and distilled chemical knowledge for guiding lithium superionic-conductor design.Examples include strong conduction associated with sulfur, iodides, PS6, PS4, and BH4 groups, while oxides were usually poor conductors.
- M3GNet achieved consistently high accuracy across nine structural MatBench tasks and exceeded previous MEGNet models in all nine.Reported improvements over the previous best graph model included 20.5% for perovskite formation energy, 22.1% for MP band gap, and 41.3% for MP metallicity classification.
- M3GNet achieved excellent MD17 accuracies across molecules, with state-of-the-art results on selected energies and forces.The models also achieved consistently lower errors than the less complex EANN model.