Net Study Material For Paper 1

[Michael Rosiles]

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Novel functional materials enable fundamental breakthroughs across technological applications from clean energy to information processing1,2,3,4,5,6,7,8,9,10,11. From microchips to batteries and photovoltaics, discovery of inorganic crystals has been bottlenecked by expensive trial-and-error approaches. Concurrently, deep-learning models for language, vision and biology have showcased emergent predictive capabilities with increasing data and computation12,13,14. Here we show that graph networks trained at scale can reach unprecedented levels of generalization, improving the efficiency of materials discovery by an order of magnitude. Building on 48,000 stable crystals identified in continuing studies15,16,17, improved efficiency enables the discovery of 2.2 million structures below the current convex hull, many of which escaped previous human chemical intuition. Our work represents an order-of-magnitude expansion in stable materials known to humanity. Stable discoveries that are on the final convex hull will be made available to screen for technological applications, as we demonstrate for layered materials and solid-electrolyte candidates. Of the stable structures, 736 have already been independently experimentally realized. The scale and diversity of hundreds of millions of first-principles calculations also unlock modelling capabilities for downstream applications, leading in particular to highly accurate and robust learned interatomic potentials that can be used in condensed-phase molecular-dynamics simulations and high-fidelity zero-shot prediction of ionic conductivity.

The discovery of energetically favourable inorganic crystals is of fundamental scientific and technological interest in solid-state chemistry. Experimental approaches over the decades have catalogued 20,000 computationally stable structures (out of a total of 200,000 entries) in the Inorganic Crystal Structure Database (ICSD)15,18. However, this strategy is impractical to scale owing to costs, throughput and synthesis complications19. Instead, computational approaches championed by the Materials Project (MP)16, the Open Quantum Materials Database (OQMD)17, AFLOWLIB20 and NOMAD21 have used first-principles calculations based on density functional theory (DFT) as approximations of physical energies. Combining ab initio calculations with simple substitutions has allowed researchers to improve to 48,000 computationally stable materials according to our own recalculations22,23,24 (see Methods). Although data-driven methods that aid in further materials discovery have been pursued, thus far, machine-learning techniques have been ineffective in estimating stability (decomposition energy) with respect to the convex hull of energies from competing phases25.

In this paper, we scale up machine learning for materials exploration through large-scale active learning, yielding the first models that accurately predict stability and, therefore, can guide materials discovery. Our approach relies on two pillars: first, we establish methods for generating diverse candidate structures, including new symmetry-aware partial substitutions (SAPS) and random structure search26. Second, we use state-of-the art graph neural networks (GNNs) that improve modelling of material properties given structure or composition. In a series of rounds, these graph networks for materials exploration (GNoME) are trained on available data and used to filter candidate structures. The energy of the filtered candidates is computed using DFT, both verifying model predictions and serving as a data flywheel to train more robust models on larger datasets in the next round of active learning.

Finally, we demonstrate that the dataset produced in GNoME discovery unlocks new modelling capabilities for downstream applications. The structures and relaxation trajectories present a large and diverse dataset to enable training of learned, equivariant interatomic potentials30,31 with unprecedented accuracy and zero-shot generalization. We demonstrate the promise of these potentials for materials property prediction through the estimation of ionic conductivity from molecular-dynamics simulations.

The space of possible materials is far too large to sample in an unbiased manner. Without a reliable model to cheaply approximate the energy of candidates, researchers guided searches by restricting generation with chemical intuition, accomplished by substituting similar ions or enumerating prototypes22. Although improving search efficiency17,27, this strategy fundamentally limited how diverse candidates could be. By guiding searches with neural networks, we are able to use diversified methods for generating candidates and perform a broader exploration of crystal space without sacrificing efficiency.

To generate and filter candidates, we use two frameworks, which are visualized in Fig. 1a. First, structural candidates are generated by modifications of available crystals. However, we strongly augment the set of substitutions by adjusting ionic substitution probabilities to give priority to discovery and use newly proposed symmetry aware partial substitutions (SAPS) to efficiently enable incomplete replacements32. This expansion results in more than 109 candidates over the course of active learning; the resulting structures are filtered by means of GNoME using volume-based test-time augmentation and uncertainty quantification through deep ensembles33. Finally, structures are clustered and polymorphs are ranked for evaluation with DFT (see Methods). In the second framework, compositional models predict stability without structural information. Inputs are reduced chemical formulas. Generation by means of oxidation-state balancing is often too strict (for example, neglecting Li15Si4). Using relaxed constraints (see Methods), we filter compositions using GNoME and initialize 100 random structures for evaluation through ab initio random structure searching (AIRSS)26. In both frameworks, models provide a prediction of energy and a threshold is chosen on the basis of the relative stability (decomposition energy) with respect to competing phases. Evaluation is performed through DFT computations in the Vienna Ab initio Simulation Package (VASP)34 and we measure both the number of stable materials discovered as well as the precision of predicted stable materials (hit rate) in comparison with the Materials Project16.

a, A summary of the GNoME-based discovery shows how model-based filtration and DFT serve as a data flywheel to improve predictions. b, Exploration enabled by GNoME has led to 381,000 new stable materials, almost an order of magnitude larger than previous work. c, 736 structures have been independently experimentally verified, with six examples shown50,51,52,53,54,55. d, Improvements from graph network predictions enable efficient discovery in combinatorial regions of materials, for example, with six unique elements, even though the training set stopped at four unique elements. e, GNoME showcases emergent generalization when tested on out-of-domain inputs from random structure search, indicating progress towards a universal energy model.

The test loss performance of GNoME models exhibit improvement as a power law with further data. These results are in line with neural scaling laws in deep learning28,38 and suggest that further discovery efforts could continue to improve generalization. Emphatically, unlike the case of language or vision, in materials science, we can continue to generate data and discover stable crystals, which can be reused to continue scaling up the model. We also demonstrate emergent generalization to out-of-distribution tasks by testing structural models trained on data originating from substitutions on crystals arising from random search26 in Fig. 1e. These examples are often high-energy local minima and out of distribution compared with data generated by our structural pipeline (which, by virtue of substitutions, contains structures near their minima). Nonetheless, we observe clear improvement with scale. These results indicate that final GNoME models are a substantial step towards providing the community with a universal energy predictor, capable of handling diverse materials structures through deep learning.

Using the described process of scaling deep learning for materials exploration, we increase the number of known stable crystals by almost an order of magnitude. In particular, GNoME models found 2.2 million crystal structures stable with respect to the Materials Project. Of these, 381,000 entries live on the updated convex hull as newly discovered materials.

We highlight the benefits of a catalogue of stable materials an order of magnitude larger than previous work. When searching for a material with certain desirable properties, researchers often filter such catalogues, as computational stability is often linked with experimental realizability. We perform similar analyses for three applications. First, layered materials are promising systems for electronics and energy storage44. Methods from previous studies45 suggest that approximately 1,000 layered materials are stable compared with the Materials Project, whereas this number increases to about 52,000 with GNoME-based discoveries. Similarly, following a holistic screening approach with filters such as exclusion of transition metals or by lithium fraction, we find 528 promising Li-ion conductors among GNoME discoveries, a 25 times increase compared with the original study46. Finally, Li/Mn transition-metal oxides are a promising family to replace LiCoO2 in rechargeable batteries25 and GNoME has discovered an extra 15 candidates stable relative to the Materials Project compared with the original nine.

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