Scaling deep learning for materials discovery

Scaling deep learning for materials discovery Amil Merchant Simon Batzner Samuel S. Schoenholz Muratahan Aykol Gowoon Cheon Ekin D. Cubuk

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Scaling deep learning for materials discovery 2023 Nature 10.1038/s41586-023-06735-9 merchant2023-scaling-deep-learning-for-material merchant2023-scaling-deep-learning-for-material.txt, the project's staged copy e406ead7f08e8bb9543f1d540668f0df52bc0f80 cc-by materials-science

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them inorganic crystal structures and whether a graph neural network can predict which are thermodynamically stable Quotation withheld because this record is not cleared for redistribution. whether machine learning can estimate stability against the convex hull accurately enough to guide discovery, which prior methods could not Quotation withheld because this record is not cleared for redistribution. 2.2 million structures stable with respect to the Materials Project, of which 381,000 sit on the updated convex hull, plus learned interatomic potentials from the resulting dataset Quotation withheld because this record is not cleared for redistribution. existence Quotation withheld because this record is not cleared for redistribution. emergent out-of-distribution generalisation in a graph network trained at scale Quotation withheld because this record is not cleared for redistribution. system-or-tool-building system-or-tool-building Quotation withheld because this record is not cleared for redistribution. DFT verifies the model's filtered candidates and the verified results become the next round's training data, so the same computation both audits the model and improves it the data flywheel Quotation withheld because this record is not cleared for redistribution. prediction quality improves as a power law in the amount of data, matching what has been observed in language and vision rather than being specific to materials power-law scaling of prediction error Quotation withheld because this record is not cleared for redistribution. the discovered materials can themselves be bumped off the convex hull by future work - stability is a claim about a catalogue at a moment Quotation withheld because this record is not cleared for redistribution. the experimental-match count is a lower bound, because the compositional match is enforced strictly Quotation withheld because this record is not cleared for redistribution. the matching answer moves by about 100 structures depending on parser and matcher tolerance settings Quotation withheld because this record is not cleared for redistribution. the discovery functional was chosen for a speed-accuracy trade-off rather than accuracy, and 84% rather than 100% survive the more accurate one Quotation withheld because this record is not cleared for redistribution. neural scaling laws, carried from language and vision into materials-stability prediction Quotation withheld because this record is not cleared for redistribution. recomputation under the more accurate r2SCAN functional, to test whether discovery overfitted the cheaper PBE one eliminates: a discovery set that exists only under the cheap functional it was searched with · outcome: partial Quotation withheld because this record is not cleared for redistribution. an explicit check that model-based exploration did not overfit the simulation parameters eliminates: model-based exploration finding materials that are artefacts of the simulation parameters it was trained against · outcome: held Quotation withheld because this record is not cleared for redistribution. matching against crystals experimentally realised by other groups after the training snapshot eliminates: a match rate inflated by structures the model could have seen, since these were realised experimentally after the training snapshot · outcome: held Quotation withheld because this record is not cleared for redistribution. comparison against compositions added to the Materials Project after the March 2021 snapshot eliminates: a match rate computed only against the database the model was trained on · outcome: held Quotation withheld because this record is not cleared for redistribution. a sensitivity check on the parser and matcher tolerances used to count experimental matches eliminates: an experimental match count that exists only at one parser and matcher tolerance setting · outcome: partial Quotation withheld because this record is not cleared for redistribution. convex hull convex hull Quotation withheld because this record is not cleared for redistribution. decomposition energy decomposition energy Quotation withheld because this record is not cleared for redistribution. hit rate hit rate Quotation withheld because this record is not cleared for redistribution. active learning active learning Quotation withheld because this record is not cleared for redistribution. GNoME GNoME Quotation withheld because this record is not cleared for redistribution. Materials Project Materials Project Quotation withheld because this record is not cleared for redistribution. r2SCAN r2SCAN Quotation withheld because this record is not cleared for redistribution. experimental match experimental match Quotation withheld because this record is not cleared for redistribution. prototypes prototypes Quotation withheld because this record is not cleared for redistribution. graph networks trained at scale graph networks trained at scale Quotation withheld because this record is not cleared for redistribution. efficiency of materials discovery efficiency of materials discovery Quotation withheld because this record is not cleared for redistribution. human chemical intuition human chemical intuition Quotation withheld because this record is not cleared for redistribution. learned interatomic potentials learned interatomic potentials Quotation withheld because this record is not cleared for redistribution. condensed-phase molecular-dynamics simulations condensed-phase molecular-dynamics simulations Quotation withheld because this record is not cleared for redistribution. zero-shot prediction of ionic conductivity zero-shot prediction of ionic conductivity Quotation withheld because this record is not cleared for redistribution. large-scale active learning large-scale active learning Quotation withheld because this record is not cleared for redistribution. first models that accurately predict stability first models that accurately predict stability Quotation withheld because this record is not cleared for redistribution. diverse candidate structures diverse candidate structures Quotation withheld because this record is not cleared for redistribution. symmetry-aware partial substitutions (SAPS) symmetry-aware partial substitutions (SAPS) Quotation withheld because this record is not cleared for redistribution. random structure search random structure search Quotation withheld because this record is not cleared for redistribution. graph neural networks (GNNs) graph neural networks (GNNs) Quotation withheld because this record is not cleared for redistribution. material properties material properties Quotation withheld because this record is not cleared for redistribution. candidate structures candidate structures Quotation withheld because this record is not cleared for redistribution. filtered candidates filtered candidates Quotation withheld because this record is not cleared for redistribution. DFT DFT Quotation withheld because this record is not cleared for redistribution. data flywheel data flywheel Quotation withheld because this record is not cleared for redistribution. more robust models more robust models Quotation withheld because this record is not cleared for redistribution. larger datasets larger datasets Quotation withheld because this record is not cleared for redistribution. model-based filtration and DFT model-based filtration and DFT Quotation withheld because this record is not cleared for redistribution. predictions predictions Quotation withheld because this record is not cleared for redistribution. structural candidates structural candidates Quotation withheld because this record is not cleared for redistribution. ionic substitution probabilities ionic substitution probabilities Quotation withheld because this record is not cleared for redistribution. incomplete replacements incomplete replacements Quotation withheld because this record is not cleared for redistribution. volume-based test-time augmentation volume-based test-time augmentation Quotation withheld because this record is not cleared for redistribution. uncertainty quantification through deep ensembles uncertainty quantification through deep ensembles Quotation withheld because this record is not cleared for redistribution. polymorphs polymorphs Quotation withheld because this record is not cleared for redistribution. compositional models compositional models Quotation withheld because this record is not cleared for redistribution. reduced chemical formulas reduced chemical formulas Quotation withheld because this record is not cleared for redistribution. oxidation-state balancing oxidation-state balancing Quotation withheld because this record is not cleared for redistribution. relaxed constraints relaxed constraints Quotation withheld because this record is not cleared for redistribution. ab initio random structure searching (AIRSS) ab initio random structure searching (AIRSS) Quotation withheld because this record is not cleared for redistribution. relative stability (decomposition energy) relative stability (decomposition energy) Quotation withheld because this record is not cleared for redistribution. Vienna Ab initio Simulation Package (VASP) Vienna Ab initio Simulation Package (VASP) Quotation withheld because this record is not cleared for redistribution. number of stable materials discovered number of stable materials discovered Quotation withheld because this record is not cleared for redistribution. total energy of a crystal total energy of a crystal Quotation withheld because this record is not cleared for redistribution. one-hot embedding of the elements one-hot embedding of the elements Quotation withheld because this record is not cleared for redistribution. message-passing formulation message-passing formulation Quotation withheld because this record is not cleared for redistribution. shallow multilayer perceptrons (MLPs) shallow multilayer perceptrons (MLPs) Quotation withheld because this record is not cleared for redistribution. swish nonlinearities swish nonlinearities Quotation withheld because this record is not cleared for redistribution. average adjacency of atoms average adjacency of atoms Quotation withheld because this record is not cleared for redistribution. mean absolute error (MAE) mean absolute error (MAE) Quotation withheld because this record is not cleared for redistribution. test loss performance test loss performance Quotation withheld because this record is not cleared for redistribution. power law with further data power law with further data Quotation withheld because this record is not cleared for redistribution. neural scaling laws neural scaling laws Quotation withheld because this record is not cleared for redistribution. out-of-distribution tasks out-of-distribution tasks Quotation withheld because this record is not cleared for redistribution. high-energy local minima high-energy local minima Quotation withheld because this record is not cleared for redistribution. universal energy predictor universal energy predictor Quotation withheld because this record is not cleared for redistribution. ionic relaxations ionic relaxations Quotation withheld because this record is not cleared for redistribution. first-principles energies and forces first-principles energies and forces Quotation withheld because this record is not cleared for redistribution. general-purpose machine-learning interatomic potential (MLIP) general-purpose machine-learning interatomic potential (MLIP) Quotation withheld because this record is not cleared for redistribution. bulk solids bulk solids Quotation withheld because this record is not cleared for redistribution. ab initio molecular dynamics (AIMD) ab initio molecular dynamics (AIMD) Quotation withheld because this record is not cleared for redistribution. general applicability and adoption general applicability and adoption Quotation withheld because this record is not cleared for redistribution. large-scale pretraining of MLIPs large-scale pretraining of MLIPs Quotation withheld because this record is not cleared for redistribution. unprecedented zero-shot accuracy unprecedented zero-shot accuracy Quotation withheld because this record is not cleared for redistribution. superionic conductors superionic conductors Quotation withheld because this record is not cleared for redistribution. material-specific data material-specific data Quotation withheld because this record is not cleared for redistribution. increasing the pretraining dataset increasing the pretraining dataset Quotation withheld because this record is not cleared for redistribution. power-law improvements in accuracy power-law improvements in accuracy Quotation withheld because this record is not cleared for redistribution. pretrained GNoME potential pretrained GNoME potential Quotation withheld because this record is not cleared for redistribution. unseen compositions unseen compositions Quotation withheld because this record is not cleared for redistribution. melted structures melted structures Quotation withheld because this record is not cleared for redistribution. structures including vacancies structures including vacancies Quotation withheld because this record is not cleared for redistribution. transferability of MLIPs transferability of MLIPs Quotation withheld because this record is not cleared for redistribution. potential pretrained on GNoME data potential pretrained on GNoME data Quotation withheld because this record is not cleared for redistribution. potential trained from scratch potential trained from scratch Quotation withheld because this record is not cleared for redistribution. GNoME-pretrained GNoME-pretrained Quotation withheld because this record is not cleared for redistribution. randomly initialized potential randomly initialized potential Quotation withheld because this record is not cleared for redistribution. distribution shift distribution shift Quotation withheld because this record is not cleared for redistribution. stable crystals stable crystals Quotation withheld because this record is not cleared for redistribution. identically distributed data at train and test times identically distributed data at train and test times Quotation withheld because this record is not cleared for redistribution. out-of-distribution effort out-of-distribution effort Quotation withheld because this record is not cleared for redistribution. emergent out-of-distribution capabilities emergent out-of-distribution capabilities Quotation withheld because this record is not cleared for redistribution. unseen chemical spaces unseen chemical spaces Quotation withheld because this record is not cleared for redistribution. kinetic properties kinetic properties Quotation withheld because this record is not cleared for redistribution. graph neural networks (GNNs) → candidate structures GNoME graph networks are used to filter candidate structures. Used-to-filter is absent from the eight types. Quotation withheld because this record is not cleared for redistribution. DFT → model predictions DFT verifies the model predictions. Verifies is absent from the eight types. Quotation withheld because this record is not cleared for redistribution. GNoME dataset → general-purpose machine-learning interatomic potential (MLIP) The GNoME dataset enables pretraining a general-purpose MLIP. Enablement is absent from the eight types. Quotation withheld because this record is not cleared for redistribution. final GNoME models → universal energy predictor Final GNoME models are a substantial step toward a universal energy predictor. Progress-toward is absent from the eight types. Quotation withheld because this record is not cleared for redistribution. 'stable' sense 1 = below the convex hull OF A PRIOR CATALOGUE - 2.2 million structures Quotation withheld because this record is not cleared for redistribution. 'stable' sense 2 = ON the UPDATED convex hull after this work - 381,000 entries, six times fewer Quotation withheld because this record is not cleared for redistribution. stability is REVOCABLE: these materials can be bumped off the hull by future discoveries, exactly as this work bumps off 5,000 others Quotation withheld because this record is not cleared for redistribution. 'meaningfully stable' = distributed like known stable phases, not merely filling gaps in the hull Quotation withheld because this record is not cleared for redistribution. 'experimental match' = integer-rounded composition match AND a pymatgen structure match, declared a lower bound Quotation withheld because this record is not cleared for redistribution. GNoME discovery flywheel - generate candidates, filter with GNNs, verify energies with DFT, and reuse results as next-round training data Quotation withheld because this record is not cleared for redistribution. Structural framework - modify known crystals, expand substitutions with SAPS, quantify uncertainty, cluster polymorphs, and rank for DFT Quotation withheld because this record is not cleared for redistribution. Compositional framework - predict from reduced formulas, relax oxidation constraints, filter compositions, and initialize AIRSS structures Quotation withheld because this record is not cleared for redistribution. GNoME graph model - element embeddings and message passing predict total crystal energy Quotation withheld because this record is not cleared for redistribution. Scaling law - GNoME test loss improves by a power law as training data increase Quotation withheld because this record is not cleared for redistribution. Universal energy predictor - model handling diverse material structures including random-search inputs outside the training distribution Quotation withheld because this record is not cleared for redistribution. General-purpose MLIP - potential pretrained on diverse ionic-relaxation energies and forces for zero-shot bulk-solid use Quotation withheld because this record is not cleared for redistribution. Zero-shot evaluation - pretrained potential applied to unseen compositions, melted structures, vacancies, and AIMD data without AIMD training Quotation withheld because this record is not cleared for redistribution. claim_type: method a second reading DIFFERING from the recorded value. Recorded: existence — note: A BLIND second reading by the project on 2026-08-25: the record's own claim type/method/phenomenon were not looked at until every value here was written and substring-verified. Not applied - a person decides. Sampling frame: the 504 staged records carrying no alternatives block, so this never re-measures the 202. All 11 records with 130+ tags were taken as a census and 19 more spread one per discipline across 22 disciplines - the dense non-neuroscience cell is the one the 202 do not contain (inside them, 94-100% of the densest bands are neuroscience; among these 11, one is)., Quotation withheld because this record is not cleared for redistribution. method: system-or-tool-building a second reading DIFFERING from the recorded value. Recorded: system-or-tool-building — note: A BLIND second reading by the project on 2026-08-25: the record's own claim type/method/phenomenon were not looked at until every value here was written and substring-verified. Not applied - a person decides. Sampling frame: the 504 staged records carrying no alternatives block, so this never re-measures the 202. All 11 records with 130+ tags were taken as a census and 19 more spread one per discipline across 22 disciplines - the dense non-neuroscience cell is the one the 202 do not contain (inside them, 94-100% of the densest bands are neuroscience; among these 11, one is)., Quotation withheld because this record is not cleared for redistribution. phenomenon: discovery of energetically stable inorganic crystal structures at a scale experiment cannot reach a second reading DIFFERING from the recorded value. Recorded: emergent out-of-distribution generalisation in a graph network trained at scale — note: A BLIND second reading by the project on 2026-08-25: the record's own claim type/method/phenomenon were not looked at until every value here was written and substring-verified. Not applied - a person decides. Sampling frame: the 504 staged records carrying no alternatives block, so this never re-measures the 202. All 11 records with 130+ tags were taken as a census and 19 more spread one per discipline across 22 disciplines - the dense non-neuroscience cell is the one the 202 do not contain (inside them, 94-100% of the densest bands are neuroscience; among these 11, one is)., Quotation withheld because this record is not cleared for redistribution. contradicts → the prior position that machine learning cannot estimate stability against the convex hull note: the paper states that position as the state of the art it overturns, and the hit-rate figures are what it offers against it Quotation withheld because this record is not cleared for redistribution. extends → the Materials Project, OQMD, AFLOWLIB and NOMAD catalogues of computationally stable structures note: extends by an order of magnitude AND revises downward - at least 5,000 of their entries are displaced Quotation withheld because this record is not cleared for redistribution. GNoME —contrasted-with→ Materials Project GNoME Materials Project differs in: scale, and the direction of revision - GNoME removes at least 5,000 entries the Materials Project called stable · strength of the relation: 0.95 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says GNoME displaces some 'stable' materials from the Materials Project; contrasted-with is loose. Quotation withheld because this record is not cleared for redistribution. active learning —causes→ hit rate active learning hit rate direction on the measure: increases · strength of the relation: 0.85 · direction on the measure (stated by the tagger, no quotation): increases Quotation withheld because this record is not cleared for redistribution. graph networks trained at scale —causes→ efficiency of materials discovery graph networks trained at scale efficiency of materials discovery direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: Scaled graph networks improve discovery efficiency by an order of magnitude. Quotation withheld because this record is not cleared for redistribution. large-scale active learning —causes→ first models that accurately predict stability large-scale active learning first models that accurately predict stability direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: The paper says large-scale active learning yields the first accurate stability models. Quotation withheld because this record is not cleared for redistribution. model-based filtration and DFT —causes→ predictions model-based filtration and DFT predictions direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: The combined filtration/DFT flywheel is stated to improve predictions. Audit 2026-09-28: DOUBTFUL - read against its span and kept, but filtration and DFT generate candidates; causes 'predictions' is loose. Quotation withheld because this record is not cleared for redistribution. increasing the pretraining dataset —causes→ power-law improvements in accuracy increasing the pretraining dataset power-law improvements in accuracy direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: Increasing pretraining scale produces consistent power-law accuracy improvements. Quotation withheld because this record is not cleared for redistribution. GNoME-pretrained —contrasted-with→ randomly initialized potential GNoME-pretrained randomly initialized potential the relation itself is separately evidenced · strength of the relation: 1 · note: The figure compares pretrained and randomly initialized potentials under distribution shift. Quotation withheld because this record is not cleared for redistribution. potential pretrained on GNoME data —causes→ transferability of MLIPs potential pretrained on GNoME data transferability of MLIPs direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: The pretrained potential shows systematic, strong transferability improvements over training from scratch. Quotation withheld because this record is not cleared for redistribution. graph neural networks (GNNs) —causes→ stable crystals graph neural networks (GNNs) stable crystals direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 1 · note: Large, diverse first-principles training increases stable-crystal discovery by more than an order of magnitude. Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'GNNs'; endpoint abbreviated. Quotation withheld because this record is not cleared for redistribution. GNoME found 2.2 million structures stable relative to the Materials Project, of which 381,000 lie on the updated convex hull. Quotation withheld because this record is not cleared for redistribution. this work removes at least 5,000 entries that two prior catalogues had called stable Quotation withheld because this record is not cleared for redistribution. the networks generalise to structures with 5+ unique elements although such structures were omitted from training Quotation withheld because this record is not cleared for redistribution. the discovered materials are distributed like known stable phases rather than merely filling gaps in the hull Quotation withheld because this record is not cleared for redistribution. convex hull convex hull Quotation withheld because this record is not cleared for redistribution. hit rate hit rate Quotation withheld because this record is not cleared for redistribution. experimental match experimental match Quotation withheld because this record is not cleared for redistribution. 2.2 million structures stable with respect to the Materials Project; 381,000 on the updated hull — None Quotation withheld because this record is not cleared for redistribution. at least 5,000 previously 'stable' materials displaced from the Materials Project and OQMD — None Quotation withheld because this record is not cleared for redistribution. energies predicted to 11 meV per atom; hit rate above 80% with structure, 33% per 100 trials with composition, against 1% before — None Quotation withheld because this record is not cleared for redistribution. 736 of the ICSD's experimental structures match GNoME discoveries; 184 are novel since the project began — None Quotation withheld because this record is not cleared for redistribution. 4,235 composition matches narrowed to 4,180 parsed and then to 736 — None Quotation withheld because this record is not cleared for redistribution. 84% of binaries and ternaries and 86.8% of quaternaries survive r2SCAN — None Quotation withheld because this record is not cleared for redistribution. 45,500 novel prototypes, a 5.6 times increase on the Materials Project's 8,000 — None Quotation withheld because this record is not cleared for redistribution. layered materials rise from about 1,000 to about 52,000 — None Quotation withheld because this record is not cleared for redistribution. the ICSD holds 20,000 computationally stable structures out of 200,000 entries — None Quotation withheld because this record is not cleared for redistribution. power-law improvement of test loss with data power-law improvement of test loss with data Quotation withheld because this record is not cleared for redistribution. precision of stable predictions, reported as a hit rate precision of stable predictions, reported as a hit rate Quotation withheld because this record is not cleared for redistribution. decomposition energy decomposition energy Quotation withheld because this record is not cleared for redistribution. hit rate hit rate Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1038/s41586-023-06735-9.