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Generative Adversarial Networks for Crystal Structure Prediction
Sungwon Kim, Juhwan Noh, Geun Ho Gu, Alán Aspuru-Guzik, Yousung Jung
TL;DR
Discovering functional materials beyond known crystal families remains difficult with substitution-based searches. This work develops a GAN-based crystal generator and high-throughput screening workflow, predicting 23 new Mg-Mn-O structures with reasonable stability and bandgaps.
Problem
Crystal-structure discovery needs representations that can construct real 3D structures while extending searches beyond conventional substitution of known crystals.
Method
The study builds a crystal-structure GAN using an inversion-free, low-memory representation based on unit-cell information and fractional atomic coordinates.
Results
The generative-HTVS workflow predicted 23 new Mg-Mn-O crystal structures with reasonable stability and bandgaps, including MgMn4O8 and Mg2MnO4 near convex-hull minima.
Takeaways & Limitations
The proposed generative model provides an approach for exploring portions of chemical space that conventional substitution-based discovery does not reach.
Takeaways & Limitations
The representation lacks translational, rotational, and supercell invariances.
Abstract
from arXiv · showhide
The constant demand for new functional materials calls for efficient strategies to accelerate the materials design and discovery. In addressing this challenge, machine learning generative models can offer promising opportunities since they allow for the continuous navigation of chemical space via low dimensional latent spaces. In this work, we employ a crystal representation that is inversion-free with a low memory requirement based on unit cell information and fractional atomic coordinates, and build the generative adversarial network (GAN) for crystal structures. The proposed model is then applied to the Mg-Mn-O ternary inorganic materials system to generate novel structures with application as potential water-splitting photoanodes, and combined with the evaluation of their photoanode properties for high-throughput virtual screening (HTVS). The generative-HTVS system that we built predicts 23 new crystal structures with a reasonable predicted stability and bandgap. These findings suggest that the proposed generative model can be an effective way to explore hidden portions of the chemical space, an area that is usually unreachable when conventional substitution-based discovery is employed.
Introduction
The paper addresses the limited coverage of substitution-based HTVS by combining an inversion-free, low-memory crystal representation with a GAN for generating structures beyond known crystal motifs. Applied to Mg-Mn-O photoanode discovery, the generative-HTVS workflow predicts 23 novel structures inaccessible to conventional database enumeration.
- Motivation and Limitation: Substitution-based HTVS expands known crystal databases through combinatorial elemental replacement but cannot search beyond existing crystal-structure templates.This limitation motivates generative approaches that can produce structures and compositions differing from known materials.
- Generative Materials Design: Generative models encode materials in continuous latent spaces that can support new-material generation, inverse design, and less structured HTVS sampling.Generated materials can serve as feeder structures for chemical-space exploration beyond conventional HTVS.
- Representation Challenge: Crystal generative models require representations that can be inverted to real three-dimensional structures, but many existing descriptors have not demonstrated this capability.Invertibility is needed to confirm generated materials as actual crystal structures.
- Method: The work constructs a GAN using an inversion-free crystal representation with low memory requirements to generate new structures for a desired chemical composition.The representation uses unit-cell information and fractional atomic coordinates and requires 400 times less memory than the cited 3D voxel representation.
- Contribution and Results: 23 novel Mg-Mn-O structures were predicted as potential photoanodes and could not have been found through conventional substitution-based database enumeration.The structures were obtained using the generative-HTVS workflow.
RESULT AND DISCUSSION
The generative-HTVS workflow discovered stable Mg-Mn-O structures beyond conventional substitution-based searches and identified 23 new photoanode candidates. Comparison on V-O showed performance comparable to iMatGen while enabling composition-controlled sampling with crystal-unit-cell invariances.
- V-O comparison: About 40% of iMatGen’s metastable V-O polymorphs were rediscovered, and the coordinate-based GAN generated more stable polymorphs for V3O4 and V6O7.The authors interpret the remaining 60% difference as arising from differences in latent-space structure or sampling method and conclude that GAN performance is comparable to iMatGen.
- Mg-Mn-O generative-HTVS: 753 of 6,000 structures from compositions absent in the Materials Project were predicted metastable, including 113 potentially synthesizable structures.For Mg2MnO4, the model found a structure at the convex-hull minimum, indicating a new ground state within DFT accuracy.
- Mg-Mn-O generative-HTVS: 28 Mg-Mn-O materials passed the final photoanode screening, including 14 entirely new compositions and 14 materials in existing compositions.Five of the materials in existing compositions matched previous substitutional-HTVS findings.
- Mg-Mn-O generative-HTVS: 23 newly found Mg-Mn-O photoanode candidates included 14 materials in new compositions and 9 in existing compositions.These candidates were identified among materials showing promising photoanode properties; their Pourbaix stabilities and HSE band gaps are shown in Figure 5.
Discussion
The generative framework learns the distribution of crystal structures in a continuous latent space, making it comparable and complementary to global-optimization methods. Its current composition-conditioned design requires property screening, while broader inverse design will require property-guided generation and improved novelty, validity, and synthesizability assessment.
- Comparison with global optimization: The framework generates materials from a continuous latent space encoding the training chemical space, whereas global-optimization methods explore local minima using prior configurational trajectories.Its efficiency and accuracy depend strongly on the structural diversity of the training dataset.
- Comparison with global optimization: Generative-HTVS and global-optimization methods are comparable and complementary: the former samples the learned distribution of training structures, while the latter searches global minima using geometric information and generation rules.Both approaches also face computational burdens from dataset preparation, generated-structure optimization, or global optimization.
- Limitations and future directions: The current model conditions generation only on composition, so high-throughput property screening remains necessary for final functional discovery.Direct inverse design would instead condition generation on properties such as bandgap energy or dielectric constant, or combine generation with reinforcement learning.
- Limitations and future directions: The ternary model could be extended to quaternary and higher-order compounds by adding input rows or channels, but training data become more challenging because of combinatorial complexity beyond four elements.A separate segmentation network could also classify elemental information.
- Limitations and future directions: Future development should quantify generated-sample novelty, uncertainty or validity, and synthesizability to support experimental verification of materials found through inverse design.The paper identifies these measures as important unresolved aspects for practical crystal inverse design.
Conclusions
The study uses a composition-conditioned GAN with an inversion-free, coordinate-based crystal representation to generate materials with desired compositions. Applied to Mg-Mn-O compounds, it identified 23 new crystal structures with reasonable stability and bandgaps, including two near stable-phase conditions.
- The proposed GAN generates crystal structures using a coordinate-based, inversion-free representation inspired by point clouds.
- Conditioning the network with crystal composition enables generation of materials with a desired chemical composition.
- 23 new Mg-Mn-O crystal compounds were discovered with reasonable stability in an aqueous environment and bandgap.
- MgMn4O8 and Mg2MnO4 corresponded to the convex hull minimum, a stable new phase, or were very close within DFT accuracy.
- The model could be extended toward general-purpose inverse design by incorporating materials properties in future work.
Supporting Information
The Supporting Information details the crystal representation, WGAN training, and computational evaluation procedures, and reports that most newly identified structures differ substantially from database structures. It also shows that training converges toward realistic atomic coordinates and composition.
- GAN training: The model uses a Wasserstein GAN whose Wasserstein-distance loss addresses unstable training and mode collapse, with a gradient-penalty regularizer for more stable training.The gradient-penalty coefficient λ is set to 10.
- GAN training: As training progresses, the Wasserstein distance converges to zero and generated atomic and zero-padding coordinates become reasonable with the correct composition.Early outputs contain atoms bound together in erroneous coordinates, while later outputs increasingly resemble the real data.
- Computational evaluation: Generated structures are evaluated using spin-polarized GGA+U calculations, structural relaxation, phase diagrams, formation energies, and energy-above-hull screening.Structures with energy stability Ehull≤0.2 eV/atom receive refined formation-energy calculations using a denser reciprocal-lattice grid.
- Structural comparison: 5 of 14 newly identified Mg-Mn-O structures match structures in the database, whereas the other 9 have different structural motifs and large structural dissimilarity values.Figure S8 compares the 14 newly identified structures with their most similar database structures.
S6. V.O system S6.1 V.O dataset
The V-O dataset comprised 86 compositions and 86,000 augmented training structures, while the model generated stable, novel polymorphs and rediscovered known materials. Data augmentation of at least 1,000 structures per composition enabled the critic network to learn symmetry invariance.
- S6.1 V.O dataset: The initial V-O dataset contained 1,396 unique structures spanning 86 compositions and was augmented to 86,000 training structures.The initial structures were obtained by elemental substitution for binary compounds in the Material Project database, followed by duplicate removal.
- S6.1 V.O dataset: 562 unique new structures were predicted, including 91 potentially synthesizable structures under the stated stability criterion.The criterion corresponds to the range containing 80% of experimentally known sulfides and oxides.
- S6.1 V.O dataset: 13 of 33 iMatGen structures with E_hull less than 200 meV/atom were also generated by the Composition-conditioned Crystal GAN.The comparison is reported in Table S4.
- Data augmentation experiment: Aug1000, Aug2000, and Aug3000 produced critic-output distributions centered at zero, unlike No Aug, indicating learned invariance under symmetric operations.The authors estimate that augmenting 1,000 data points per composition is sufficient in this work.