Geometric Deep Learning for Materials Discovery: GNoME, MatterGen, 2026 SOTA

Last Updated: 2026-05-16

Architecture at a glance

In November 2023, Google DeepMind announced it had used graph neural networks to discover 2.2 million new crystalline materials, of which roughly 380,000 were predicted to be thermodynamically stable — a haul that, by the press-release framing, multiplied the entire human catalogue of known inorganic crystals by an order of magnitude overnight. The number sounded fantastical, and within a year materials scientists at Princeton and UC Santa Barbara were publicly disputing how many of those structures were genuinely novel and stable. Eighteen months later, the dust has settled enough to ask the question that actually matters: has geometric deep learning materials discovery shipped useful chemistry, or are we still in the demo-reel phase? This post walks through the math (SE(3)-equivariant message passing on atomic graphs), the two flagship systems of the era (GNoME and MatterGen), the validation loop with density functional theory that makes any of it credible, and an honest 2×2 of what has reached real labs versus what is still aspirational. Expect equal parts excitement and skepticism.

The Materials Discovery Problem: 10^60 Possible Compounds

Picture the search space. The periodic table gives you ~90 stable elements; combine them in stoichiometries up to a dozen atoms per formula unit, then for each composition consider the possible crystal structures (space groups, Wyckoff positions, lattice parameters) and you arrive at a combinatorial explosion that materials scientists typically estimate at around 10^60 candidate compounds — more than atoms in the observable universe by 20 orders of magnitude. Most of these are nonsense (wrong charge balance, atoms forced too close), but even after physically-reasonable filtering you are still looking at perhaps 10^9 plausible candidates, while the human-known catalogue (the Inorganic Crystal Structure Database, ICSD) contains roughly 250,000 experimentally-verified entries as of 2026. We have explored an infinitesimal sliver.

The traditional pipeline is brutal: a materials scientist hypothesises a target, computes properties with density functional theory (DFT) — a quantum-mechanical method that solves an approximate Schrödinger equation on a per-electron basis — and if DFT is encouraging, attempts synthesis. DFT for a single mid-sized unit cell takes minutes to hours on a CPU node; synthesis attempts take weeks. Screening 10^5 candidates means 10^5 DFT runs (a six-figure compute bill) and at most a few dozen synthesis attempts. The cost-per-discovery for a useful material — say a new battery cathode — has historically hovered around 15-20 years and tens of millions of dollars.

Geometric deep learning attacks this funnel by replacing the DFT bottleneck with a graph neural network that, given a candidate crystal structure, predicts formation energy and stability in milliseconds — six to seven orders of magnitude faster than DFT. The trade-off is approximation: the GNN is trained on DFT labels, so it inherits both DFT’s errors and its own generalization gap. The trick that makes this work in practice is iteration: predict cheaply, validate the most promising candidates with DFT, retrain on the new labels, repeat. (See ./assets/arch_01.png for the funnel.)

Why Geometric Deep Learning Wins on Crystals

A crystal is fundamentally a geometric object — atoms with 3D coordinates inside a periodic lattice — and the physics that determines its energy is equivariant under rigid motions. Rotate the whole crystal in space, and the energy is unchanged (invariant); rotate it, and the forces on each atom rotate the same way (equivariant). This is not a soft preference; it is a hard constraint. A neural network that does not respect it will, with enough training data, almost-but-not-quite learn the symmetry and produce embarrassingly wrong predictions on rotated inputs. Geometric deep learning, formalized in the Bronstein-Bruna-Cohen-Veličković monograph, builds the symmetry directly into the architecture so that equivariance holds by construction, not by curve-fitting.

The dominant family for materials is the SE(3)-equivariant graph neural network, where SE(3) is the group of 3D rotations and translations. Atoms become nodes, with features being scalar atomic numbers Z_i and equivariant 3D position vectors r_i. Edges connect every pair of atoms within a cutoff radius (typically 5-6 Å), with edge features being the vector r_ij = r_j − r_i decomposed into a scalar distance |r_ij| and a unit direction. Message passing then proceeds via a tensor product: the scalar distance feeds a radial basis function φ(|r_ij|), the unit direction feeds a spherical harmonic expansion Y_lm(r̂_ij) up to some maximum angular momentum L, and these are combined via Clebsch-Gordan tensor products that respect the rotation group’s algebra. The output is a mixture of scalar features (energy), vector features (forces), and tensor features (stress) that all transform correctly under rotation. (See ./assets/arch_02.png.)

Three architectures dominate as of 2026, each pushing on a different axis. NequIP (Batzner et al., Nature Communications 2022) was the first to demonstrate that high-order spherical harmonics (L up to 3) give dramatic data efficiency — a NequIP model with 1,000 training structures often matches a non-equivariant model trained on 100,000. Allegro (Musaelian et al., 2023) preserved the equivariance but made it strictly local, eliminating long-range message passing in favor of pairwise interactions, which lets it scale to millions of atoms on a GPU without losing accuracy on relevant chemistry. MACE (Batatia et al., NeurIPS 2022) combined high-body-order features (capturing 4- and 5-body atomic interactions) with equivariant messages and has become the practical workhorse for molecular dynamics — by 2026, MACE-MP-0, a single foundation-model variant trained on Materials Project, is used as a drop-in replacement for DFT in production MD codes at several national labs.

For context, the older non-equivariant baselines like SchNet (Schütt et al., 2018) and CGCNN (crystal graph CNN) still appear in papers but are essentially obsolete for energy/force tasks — they require 10-100x more training data for the same accuracy and lose ground continuously on benchmarks. The newer Allegro/MACE-class models hit DFT-level accuracy (~1-5 meV/atom error on relaxed structures) and run at 10^4 to 10^6 times the speed of DFT on the same hardware. That speedup is what made the GNoME-scale search practical in the first place.

The deeper “why this works” is information-theoretic. By baking SE(3) equivariance and translational periodicity into the architecture, you remove the model’s need to learn them from data — you have effectively given it for free the prior that “rotation doesn’t change physics.” Every parameter that would have been spent reproducing symmetry can instead be spent on actual chemistry. This is the same trick that makes convolutional networks dominate vision (translation equivariance is built in) and transformers dominate language (permutation equivariance via attention) — geometric DL is the materials-specific instance of a general principle.

GNoME: Google DeepMind’s Discovery of 2.2 Million Stable Materials

GNoME — Graph Networks for Materials Exploration — is the system Merchant et al. described in their November 2023 Nature paper “Scaling deep learning for materials discovery” (DOI 10.1038/s41586-023-06735-9). The headline claim was that the system had predicted 2.2 million stable crystalline structures, of which 381,000 had been added to the Materials Project’s open-access database, expanding the known stable-materials catalogue by roughly an order of magnitude. The paper became the most-cited AI-for-science result of 2024.

Mechanically, GNoME is an active-learning loop. The proposer side has two pipelines (see ./assets/arch_03.png). The substitution pipeline starts from known stable prototypes in the Materials Project and the ICSD, and substitutes elements at each site using priors from SMACT (a charge-balance heuristic) and from ionic-radius compatibility — roughly the same logic a materials scientist would apply when guessing a Li-replacement in a known cathode. The random structure search pipeline generates candidate structures with the right symmetry constraints but no prior templates, exploring novel prototypes the substitution pipeline cannot reach.

Each candidate gets a stability prediction from an ensemble of graph networks: predict the formation energy, compare it to the convex hull of known compositions in chemical space, and if the candidate’s energy-above-hull is below a threshold (50 meV/atom is typical), promote it to DFT validation. DFT then computes the true relaxed structure and true formation energy using VASP with PBE exchange-correlation — and crucially, every DFT result is added back to the training set. The convex hull itself is updated as new stable phases are found, so structures that were stable today may become unstable next week if a more-stable competitor is discovered.

The compute budget was enormous: tens of millions of DFT calculations over the project lifetime, equivalent to several hundred CPU-millennia of compute, plus the GNN training and inference. DeepMind reported a “hit rate” — fraction of GNN-predicted-stable candidates that DFT confirmed as stable — improving from around 1% in the first iteration to over 80% by late iterations as the model learned what regions of chemical space were trustworthy.

The controversy. Within months of publication, materials chemists raised serious objections to the discovery claims. Anthony Cheetham and Ram Seshadri published a widely-circulated critique (initially as a preprint and later in expanded form in Chemistry of Materials / JACS-adjacent venues in 2024) arguing that a substantial fraction of GNoME’s “novel” structures were either (a) compositional duplicates of known materials with trivial differences, (b) members of well-known structural families that any materials chemist would have considered routine, or (c) DFT-stable but unlikely to be synthesizable due to kinetic or chemical-environment issues that DFT does not capture. Their sampling suggested only a single-digit percentage of GNoME entries were genuinely useful new chemistry. DeepMind’s published response acknowledged the methodological points about novelty thresholds while defending the underlying ML pipeline as a useful screening tool — broadly the right framing.

Where does that leave us in 2026? GNoME’s biggest legacy is not the headline number but the active-learning recipe — a pattern that has been replicated by Microsoft (the MatterGen team), Meta (Open Catalyst project), and academic groups, all of whom have shifted from pure-supervised GNN training to iterative GNN-DFT loops. The 380,000-structures release also seeded the training data for nearly every subsequent materials foundation model, which is a real, durable contribution regardless of how many of those structures end up in a lab notebook. Skepticism about “discovery” claims should not be confused with skepticism about the methodology.

MatterGen: From Property-Conditioned Generation to Synthesizability

GNoME proposes structures by enumeration (substitute, randomize, score). The alternative paradigm is generative modeling: train a model to sample directly from the distribution of stable crystals, optionally conditioned on a target property. MatterGen (Zeni et al., “MatterGen: a generative model for inorganic materials design,” Nature, January 2025, from Microsoft Research AI4Science) is the most credible exemplar of this approach.

MatterGen is a diffusion model over crystal structures. The forward process adds noise to three things simultaneously: the lattice parameters (the 3×3 matrix defining the unit cell), the fractional atomic coordinates inside the cell (continuous, with periodic boundary conditions), and the atomic types (discrete categorical variable per site). Gaussian noise for the continuous variables, a discrete diffusion kernel for the types. The reverse (denoising) process is parameterised by an equivariant graph neural network — the same SE(3)-equivariant tensor-product machinery as NequIP/MACE — that, given a noisy crystal and a timestep, predicts the noise to remove. (See ./assets/arch_04.png.)

The trick that makes this useful for inverse design is classifier-free conditioning on properties. At training time, the model is given (structure, property) pairs and learns to predict noise conditioned on the property; at inference time, you specify a target property — desired bandgap of 1.5 eV, magnetic moment above some threshold, bulk modulus above 200 GPa — and the reverse process produces structures that hit the target. The published results showed MatterGen could generate structures conditioned on combinations of properties (e.g., “magnetic AND wide bandgap”), an unconditioned-stable rate around 13% of samples, and modest but real improvements over heuristic search on multi-objective tasks.

What sets MatterGen apart from earlier generative models for crystals (CDVAE 2022, DiffCSP 2023, FlowMM 2024) is scale and a more rigorous post-generation pipeline. Microsoft trained on the full Alex-MP-20 dataset (~600,000 structures from Alexandria and Materials Project), used DFT to validate every reported result, and crucially partnered with collaborators at PNNL and the Pacific Northwest National Lab who attempted experimental synthesis of a hand-selected subset. The follow-up paper reported successful synthesis of a previously-unreported tantalum-chromium oxide (‘TaCr2O6’) with the predicted bulk modulus within experimental uncertainty — the first MatterGen-conditioned compound actually made.

The bigger picture: generative models address a different bottleneck than GNoME. GNoME-style enumeration is good at finding stable structures, but the user has no direct lever for “I want bandgap X and conductivity Y.” MatterGen-style diffusion lets you condition. The two approaches are complementary, and in practice the 2026 state of the art is to use generation to propose property-targeted candidates and an active-learning GNN+DFT loop to triage and validate them. Microsoft has open-sourced MatterGen at github.com/microsoft/mattergen, which has accelerated adoption considerably.

The honest caveat: “conditioned on bandgap” sounds tidy, but bandgap from DFT-PBE is systematically off by 30-50% versus experiment due to the well-known DFT bandgap problem. So generating a “1.5 eV” structure means generating something whose PBE bandgap is 1.5 eV — the experimental bandgap could easily be 2.2 eV. For many applications (catalysis, mechanical properties, formation energies) the DFT labels are reliable enough; for optoelectronic properties, the model is only as good as the underlying labels, and that ceiling is real.

The DFT-ML Validation Loop That Actually Works

Both GNoME and MatterGen depend critically on a feedback loop that pairs ML predictions with DFT validation. Without DFT, you have unfalsifiable ML predictions; without ML, you cannot afford to screen at scale. The loop’s effectiveness depends on three numbers worth being explicit about.

Hit rate. Of structures the GNN predicts stable, what fraction does DFT confirm as stable (energy-above-hull below threshold)? In published GNoME iterations, this rose from ~1% early to ~80% late. For MatterGen, unconditioned hit rate is around 13% of generated samples. These numbers are in the same ballpark as the rough “30-70% true stable” figure circulated in informal materials-ML circles — close to the upper bound when the model is well-trained on the chemistry, near the lower bound when it is asked to extrapolate.

Synthesizability rate. Of DFT-confirmed-stable structures, what fraction can actually be made? This is a much harder question because synthesis depends on kinetics (whether the target phase is accessible from achievable precursors and conditions), defects, and side reactions that DFT does not model. Empirically, the rate from “DFT-stable” to “successfully synthesized in lab” has been on the order of 30-50% in well-designed studies — and often much lower in autonomous-synthesis settings.

Usefulness rate. Of synthesized materials, how many are better than the incumbent for any application? Honestly, this drops to single-digit percentages in even the most optimistic accountings. The 10^60 → 10 funnel from earlier captures this: across the entire pipeline, you lose orders of magnitude at every stage, and “discovered” is a long way from “shipped.”

The most publicized integration of this loop with downstream synthesis was A-Lab, the autonomous lab at Lawrence Berkeley described in Szymanski et al., Nature 2023 (“An autonomous laboratory for the accelerated synthesis of novel materials”). A-Lab paired GNoME-style predictions with robotic synthesis attempts and claimed 41 successful syntheses out of 58 attempts (a 71% success rate) over 17 days. This number became a centerpiece of the “AI is discovering materials autonomously” narrative.

Subsequent independent analysis by external materials chemists (most notably the Robert Palgrave and Leslie Schoop groups, with a detailed reanalysis published in 2024) raised significant validation concerns about A-Lab’s results: several of the “novel” syntheses appeared to be mixtures of known phases mis-identified by the automated XRD analysis, the novelty claims relied on database lookups that missed close matches in the ICSD, and the human-in-the-loop oversight was less independent than the original paper implied. The methodological objections were substantive, and the case has become a cautionary tale about the difficulty of doing rigorous synthesis validation at robotic speeds. A-Lab is still operating, the team has acknowledged the critique and refined methodology, but the takeaway is unambiguous: the autonomous-discovery story is more like “AI proposes, humans validate slowly” than “AI discovers.”

What’s Shipped vs What’s Hype

After all the caveats, the honest 2026 picture has four quadrants (see ./assets/arch_05.png).

High impact, shipped today. Universal machine-learning interatomic potentials (MLIPs) like MACE-MP-0, CHGNet, and SevenNet have become routine in materials modeling — they drop into LAMMPS and ASE as straightforward DFT replacements for molecular dynamics, giving 1000-10000x speedup with controlled error. Battery research uses GNN screening at scale for cathode and electrolyte exploration, with at least one Toyota-CATL collaboration and the QuesTek-AlphaCathode pipeline having moved candidates through to cell-level testing. MOF (metal-organic framework) screening for CO2 capture and gas storage has produced real, made-and-measured candidates, with several entering pilot deployment at carbon-capture companies (Climeworks-adjacent vendors). Solid-state electrolyte screening for Li-ion alternatives is mature enough that the top-3 commercial solid-state battery startups all employ ML-screening teams.

High impact, not yet. Room-temperature superconductors remain elusive; despite intermittent hype cycles (LK-99 in 2023, several follow-ups), no ML-predicted superconductor has been experimentally verified above 200 K. High-Tc magnets at affordable rare-earth content, photovoltaic absorbers above 30% single-junction efficiency, programmable metamaterials with arbitrary mechanical response, and cheap precious-metal-free hydrogen-evolution catalysts are all active targets where GNN prediction exists but experimental confirmation has not materialized. These are the targets that justify continued investment but should not be over-promised.

Low impact, shipped. Property prediction benchmarks (MatBench, JARVIS, Matbench Discovery) have driven a steady accuracy march. Phonon spectra prediction, elastic constants, and reaction-pathway proposals from neural network potentials are now routine. These are useful — they are the boring substrate that makes the higher-impact applications possible — but no single result justifies a press release.

Low impact, hype. Headline numbers like “2.2 million new materials” without adequate novelty filtering belong here, as do “autonomous lab” demonstrations with weak validation, and any “AI discovered X” press release where “X” is a well-known compound a chemist would have suggested in 30 seconds. Synthesizability scores from current models are largely unvalidated and should not be trusted as gating criteria for synthesis attempts.

The pattern across the four quadrants: MLIPs and screening pipelines are quietly winning, while flashy discovery claims continue to wobble. The infrastructure side of ML-for-materials is in good shape; the headline-result side is uneven.

Open Problems: Synthesizability, Multi-property, Transferability

Three problems define the 2026-2028 research agenda.

Synthesizability. DFT tells you whether a structure is thermodynamically stable; it does not tell you whether you can make it. Kinetic accessibility depends on which precursor phases exist, what temperatures and pressures are achievable, what side reactions dominate, and whether the target phase is even reachable from any reasonable starting material. ML synthesizability scores exist (DiSCoVeR, SynthNN, several published in 2024-25) but their predictive validity on out-of-distribution chemistry is weak — they essentially memorize which compositions have been made before and extrapolate poorly. The cleanest current approach is retrosynthesis-via-template plus DFT phase-diagram analysis, which is interpretable but slow.

Multi-property optimization. Real-world materials selection is multi-objective: a battery cathode needs high capacity AND high voltage AND structural stability AND low cost AND acceptable conductivity AND no toxic elements. Single-objective models are common; multi-objective models that respect the genuine Pareto frontier are rare and brittle. Conditional generative models like MatterGen point at the right approach, but conditioning on five-plus correlated properties remains an open optimization problem with no clear winning architecture.

Transferability. A model trained on Materials Project (heavily oxide-biased, PBE-DFT-labelled) is reliable for oxides at room temperature but degrades on intermetallics, on hybrid organic-inorganic perovskites, on conditions like high pressure or strong magnetism, and on the gradient-corrected/hybrid-functional regime that experiments actually probe for optoelectronic properties. Foundation models (MACE-MP-0, ORB-v2 in 2025) are starting to address this by training on broader datasets, but the “ImageNet moment” of a universal materials model that just works everywhere has not arrived.

Why This Matters Beyond Academia

For industrial PLM and supply-chain practitioners, the case for paying attention to geometric deep learning materials discovery is not the next press-release breakthrough — it is the steady infrastructure shift. ML-accelerated DFT replacements mean that R&D groups in batteries, catalysts, structural alloys, and polymers can run 100x more candidate evaluations per quarter than three years ago, which compresses formulation cycles and shortens the gap between concept and pilot production. That changes how IP is captured (more, faster, narrower claims), how supplier qualification works (digital pre-screening before physical samples), and where competitive advantage accrues (proprietary training data on your own product chemistry beats public-database models).

The PLM tie-in is direct: materials-property predictions become data inputs to digital twins of products and processes, the same way that simulation results feed digital twins today. A battery digital twin that ingests GNN-predicted electrolyte degradation kinetics is more accurate than one that ignores it. (For sibling research-explainer reads, see our coverage of AlphaFold 3’s diffusion architecture for protein structure, AlphaProteo for de novo protein binder design, CRISPR epigenetic editing, the quantum threat to elliptic curve cryptography, and cell-free biomanufacturing in 2026 — the AI-for-science wave is broader than any one domain.) The single most underrated commercial angle is that the same equivariant-GNN machinery transfers cleanly from inorganic crystals to molecular catalysts, polymers, and even certain biomaterials — companies that build their materials-ML capability for one product line acquire a moat for adjacent product lines almost for free.

FAQ

Q1. Is “AI-discovered materials” a real category or marketing?
Both. Real in that GNN-screened candidates are now routinely synthesized and tested at industrial R&D scale, with at least dozens of compounds traceable to ML proposal and now in commercial pilots (battery electrolytes, MOFs for capture, solid-state electrolytes). Marketing in that “2.2 million discovered” headlines conflate ML-prediction-of-stability with practical novelty. The honest framing is “AI-accelerated screening” — the human pipeline is still essential, but the funnel is wider and cheaper.

Q2. What’s the difference between an equivariant GNN and a regular GNN?
A regular GNN treats positions as input features and may approximately learn rotational symmetry given enough data. An equivariant GNN builds rotational symmetry into the architecture using spherical harmonics and tensor products, so the symmetry holds by construction at every layer. The practical consequence is 10-100x better data efficiency on tasks involving 3D structure (energies, forces, dipoles), which is everything in materials and most of chemistry.

Q3. Will ML replace DFT in the next five years?
No, but it will replace 90% of DFT calculations. Universal MLIPs are already used as DFT-replacements for molecular dynamics, defect calculations, and structure searches where DFT cost is prohibitive. DFT remains the validation step for high-stakes predictions and for chemistry outside the training distribution. The combined ML+DFT workflow is the durable pattern, not full replacement.

Q4. What’s the catch with GNoME’s 2.2 million number?
Several. (a) Novelty was defined liberally — many “new” structures are minor compositional variants of known prototypes. (b) “Stable” means DFT-stable on the convex hull, which is necessary but not sufficient for synthesizability. (c) Only a small fraction have been attempted in a lab; success rates there are not yet validated at scale. The number is real as an ML prediction count; it is not 2.2 million new useful materials.

Q5. Where should an engineer start learning equivariant GNNs?
Read the original NequIP paper (Batzner et al., 2022) for intuition, then the MACE paper (Batatia et al., 2022) for the modern body-order-aware variant. Install MACE or NequIP from GitHub and train on a Materials Project subset. The Bronstein-Bruna-Cohen-Veličković “Geometric Deep Learning” monograph (proto-book, 2021) is the theory backbone. Microsoft’s MatterGen repo (github.com/microsoft/mattergen) is the most accessible production-grade generative materials code as of 2026.

Further Reading

• Bronstein, Bruna, Cohen, Veličković (2021): “Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges” — the canonical monograph, arXiv:2104.13478
• Merchant et al. (2023): “Scaling deep learning for materials discovery,” Nature 624, 80-85 (the GNoME paper)
• Zeni et al. (2025): “MatterGen: a generative model for inorganic materials design,” Nature (Microsoft Research)
• Batzner et al. (2022): “E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials,” Nature Communications 13, 2453 (NequIP)
• Batatia et al. (2022): “MACE: Higher Order Equivariant Message Passing Neural Networks,” NeurIPS 2022
• Szymanski et al. (2023): “An autonomous laboratory for the accelerated synthesis of novel materials,” Nature 624, 86-91 (A-Lab) — read alongside the 2024 critiques
• Cheetham & Seshadri (2024): critique of GNoME’s discovery claims (multiple venues, Chemistry of Materials and arXiv preprints)

References

1. Merchant, A. et al. “Scaling deep learning for materials discovery.” Nature 624, 80-85 (2023). DOI: 10.1038/s41586-023-06735-9
2. Zeni, C. et al. “MatterGen: a generative model for inorganic materials design.” Nature (2025). Microsoft Research AI4Science. Code: https://github.com/microsoft/mattergen
3. Batzner, S. et al. “E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.” Nature Communications 13, 2453 (2022). (NequIP)
4. Musaelian, A. et al. “Learning local equivariant representations for large-scale atomistic dynamics.” Nature Communications 14, 579 (2023). (Allegro)
5. Batatia, I. et al. “MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields.” NeurIPS (2022).
6. Schütt, K. T. et al. “SchNet — A deep learning architecture for molecules and materials.” J. Chem. Phys. 148, 241722 (2018).
7. Szymanski, N. J. et al. “An autonomous laboratory for the accelerated synthesis of novel materials.” Nature 624, 86-91 (2023). (A-Lab)
8. Cheetham, A. K. & Seshadri, R. “Artificial intelligence driving materials discovery? Perspective on the article: Scaling deep learning for materials discovery.” Chemistry of Materials 36, 3490-3495 (2024).
9. Bronstein, M. M., Bruna, J., Cohen, T., Veličković, P. “Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.” arXiv:2104.13478 (2021).
10. Leeman, J. et al. “Challenges in High-Throughput Inorganic Materials Prediction and Autonomous Synthesis.” PRX Energy 3, 011002 (2024). (A-Lab critique)