Pith. sign in

REVIEW 4 major objections 5 minor 12 cited by

This paper sets out to show that machine-learned interatomic potentials can be scaled to large datasets without hard-coding rotational symmetries or energy conservation, and that such unconstrained models match or beat equivariant, symmetry

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 08:39 UTC pith:3WPVHCCC

load-bearing objection Useful scaling study with a real result—unconstrained 730M-parameter PET matches equivariant SOTA on matbench—but the abstract's 'superior in accuracy and speed' rests on a SPICE comparison that is not matched (3x epochs, borrowed timings), so the strong form of the claim is not yet established. the 4 major comments →

arxiv 2601.16195 v3 pith:3WPVHCCC submitted 2026-01-22 physics.chem-ph stat.ML

Pushing the limits of unconstrained machine-learned interatomic potentials

Filippo Bigi , Paolo Pegolo , Arslan Mazitov , Jonathan Schmidt , Michele Ceriotti This is my paper
classification physics.chem-ph stat.ML
keywords machine-learned interatomic potentialsunconstrained architecturesrotational invarianceequivariant neural networksnon-conservative forcesmaterials discovery benchmarksgeometry optimizationlattice dynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper's central claim is that fully unconstrained machine-learned interatomic potentials — architectures that do not hard-code rotational symmetry and may output forces directly instead of deriving them from an energy — can be trained on very large, diverse datasets and reach the accuracy of state-of-the-art equivariant models, with faster inference. The demonstration is built around a transformer-based graph neural network scaled to hundreds of millions of parameters, trained on large materials and molecular datasets, and tested on discovery benchmarks as well as geometry optimization and phonon calculations. If the claim holds, hard-coding physical symmetries is not a prerequisite for accurate large-scale atomistic simulation; simple inference-time modifications — averaging over rotations, looser symmetry tolerances, symmetrizing force constants — can restore symmetry-consistent observables. The paper also finds that direct-force non-conservative versions are faster but less trustworthy for static property calculations, so they are best used to accelerate or pre-train conservative models.

Core claim

Fully unconstrained architectures — no hard-coded rotation symmetry, and optionally direct-force outputs — can be scaled to large, diverse datasets and match or exceed state-of-the-art equivariant neural networks in accuracy while running faster at inference. The demonstration uses a transformer-based graph neural network scaled to 730M parameters on materials data and 190M parameters on molecular data, reaching competitive results on discovery and molecular benchmarks, with benchmark numbers reported after rotational symmetrization. Conservative unconstrained models are safe for geometry optimization and phonons when symmetry detection is loosened or predictions are rotationally averaged. N

What carries the argument

The central object is PET, a graph neural network that processes each atom's neighborhood as a set of edge tokens through a transformer without equivariant features. For scale, the paper quadruples node features relative to edge features, carries node features across layers, and uses modern transformer components (RMSNorm, SwiGLU, pre-normalization) and a smooth adaptive cutoff, reaching 730M parameters at low inference cost. Rotational invariance is learned from data augmentation during training; at inference it can be restored approximately by averaging over a Lebedev grid of rotations, projecting forces onto a known space group, or loosening symmetry-detection tolerances. A second head em

Load-bearing premise

The load-bearing premise is the informal estimate that a rotationally unconstrained model can learn rotational invariance from roughly 20,000 orientation samples on a sphere of radius about 4 Å at 0.1 Å resolution, and that a low-order Lebedev grid at inference suppresses symmetry breaking enough for geometry optimization and phonons.

What would settle it

Train the same architecture on the same large datasets but limit rotational augmentation to a single axis, then evaluate on test structures rotated around an orthogonal axis. A sharp force-error degradation would confirm the paper's estimate that roughly 20,000 dense orientation samples are needed to learn rotational invariance; little degradation would falsify it, implying the model relies on other inductive biases. A practical counterpart: on a perfectly symmetric BCC titanium cell from a trained conservative model, measure the residual forces that should vanish under the space group without

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Unconstrained models are viable at scale: a 730M-parameter materials model and a 190M-parameter molecular model reach state-of-the-art benchmark accuracy, in several cases exceeding equivariant baselines.
  • Inference is faster: avoiding equivariant operations and using direct-force heads gives a 2–3x speedup, which matters for long molecular dynamics runs; the extra training epochs needed from scratch are offset by cheaper per-epoch evaluation.
  • Fine-tuning transfers well: a model pre-trained on a large open materials dataset can be fine-tuned to a much smaller dataset in fewer than 1/20th of the epochs needed from scratch, roughly halving validation errors.
  • Static workflows can be made reliable: geometry optimization works with unconstrained models, and symmetry breaking can even help an unstable high-symmetry cell escape to a lower-energy structure; phonon calculations are safe with the conservative model when the Hessian is symmetrized and central finite differences are used.
  • Non-conservative forces are not a free lunch: despite comparable test-set accuracy, direct-force models systematically trail on downstream tasks such as phonon-derived properties and elastic constants, so the paper positions them as pretraining engines or partners in multiple-time-stepping dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If rotational invariance is genuinely learned from orientation diversity in data, the accuracy gap between equivariant and unconstrained architectures may close further as datasets grow, making dataset design — not architecture — the dominant factor; the paper leaves this scaling prediction implicit.
  • A direct test of the paper's learnability estimate would be to train the same architecture with rotational augmentation restricted to a single axis and evaluate on rotations around an orthogonal axis; a sharp degradation would confirm the ~20,000-orientation estimate, while little degradation would point to other inductive biases.
  • The hybrid workflow suggested by the results — non-conservative head for pretraining and most force evaluations, conservative head for static and vibrational properties — is a natural next benchmark to quantify energy drift and computational savings on realistic molecular dynamics.
  • The symmetry-breaking that lets an unstable BCC titanium cell relax toward close-packed structures could be turned into a feature for automated structure search, where exactly equivariant models sometimes get trapped in high-symmetry metastable states.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper asks whether machine-learned interatomic potentials that do not enforce rotational equivariance or energy conservation can be scaled to large, diverse datasets and still match or beat physically constrained, equivariant models. The authors introduce a scaled-up version of the PET architecture and train models on MPtrj, subsampled Alexandria, OMat24, SPICE, and OMol-1. They benchmark these models on matbench-discovery, LAMBench, MADBench, and SPICE, and they test geometry optimization and phonon workflows. The central claim is that fully unconstrained models can be trained at scale and reach accuracy on par with state-of-the-art equivariant architectures, while offering competitive inference speed; they also argue that rotational symmetry breaking can be corrected at inference time by SO(3) averaging. The manuscript is candid about cases where non-conservative, direct-force models underperform, particularly for phonons and elastic constants.

Significance. If the central claim is established, this is a significant result for the MLIP community. It suggests that expensive equivariant constraints may be unnecessary at scale, enabling simpler, faster architectures without sacrificing accuracy. The paper also provides open-source models and reproducible workflows, which is a strength. The material-benchmark results and the honest reporting of non-conservative failure modes are valuable. The main uncertainty is whether the headline 'superior in accuracy and speed' holds under matched training budgets and controlled timing comparisons; the current evidence supports 'on par under favorable evaluation choices' more than it supports a general superiority claim.

major comments (4)
  1. [Sec. IV B a, Table II, Fig. 3] The claim that unconstrained models are 'superior in accuracy and speed' rests heavily on the SPICE comparison, but the comparison is not matched. PET-L was trained for 300 epochs, three times the number reported for eSEN, and the eSEN accuracies are taken from Ref. [31] rather than re-evaluated. Table II reports a single run with no seed variation or error bars. The statement that the two models required 'around the same amount of compute to train' is inferred from inference timings, not measured wall-clock training time. This is load-bearing for the abstract's superiority claim. Please either run eSEN with the same training budget under controlled conditions, report PET-L at the eSEN epoch budget, or explicitly restrict the claim to 'can match' with the unequal budget stated as a caveat.
  2. [Sec. IV B b, App. F, Fig. 3] The accuracy-speed Pareto front is not a controlled measurement. Appendix F states that eSEN timings are taken from Ref. [31], while PET and MACE timings are evaluated by the authors, with PET additionally using torchscript compilation. The manuscript argues that differences are minimal, but a Pareto plot that mixes measurement setups does not establish a speed advantage. Please provide timings for eSEN, MACE, and PET on the same hardware and software stack, or remove eSEN from the timing comparison and restrict the speed claim accordingly.
  3. [Sec. IV A b, Table I, Table VI, App. H] The matbench-discovery headline comparison uses evaluation choices that favor the proposed models. All results in Table I are reported after SO(3) rotational averaging, while baselines from the leaderboard may not use this post-processing. In addition, Table VI and Appendix H show that central finite differences and displacement size materially affect the phonon metric κSRME for non-equivalent models (e.g., 0.157 at 0.01 Å versus 0.110 at 0.05 Å). If leaderboard baselines were evaluated with forward differences and no averaging, Table I is not an apples-to-apples comparison. Please report raw and averaged metrics side by side, specify the evaluation protocol for every baseline, and avoid ranking conclusions that depend on protocol choices.
  4. [Sec. V, Table V, Table VI] The phrase 'unconstrained models can be superior in accuracy and speed' is broader than the paper's own evidence. The non-conservative direct-force heads consistently underperform conservative models on static workflows: κSRME is 0.197–0.216 for non-conservative versus 0.119 for conservative PET-OAM, and elastic moduli are markedly worse (Table IX). The paper's nuanced discussion correctly recommends non-conservative models primarily as pretraining or multiple-time-stepping components. The abstract and introduction should be aligned with that nuance, so that 'unconstrained' clearly refers to rotationally unconstrained conservative models when accuracy on static tasks is claimed.
minor comments (5)
  1. [Sec. II A c] The displayed locality equation appears garbled: the same term V({r_i,a_i}_{i≠n}) is subtracted twice, and the text's mathematical rendering is hard to follow. Please correct the formula so that the near-sightedness condition is stated cleanly.
  2. [Table I] The model listed as 'PET' in Table I is not fully specified in the table caption. Please state which checkpoint (PET-OAM conservative, with or without SO(3) averaging) is used, and whether the other entries are reproduced from the leaderboard or re-evaluated with the same protocol.
  3. [Sec. III A c] The learnability estimate of ~20,000 orientation samples assumes a 0.1 Å resolution and a 4 Å environment radius. This is a heuristic with no sensitivity analysis. It is not the main empirical claim, but the manuscript should label it as an order-of-magnitude argument rather than a quantitative bound.
  4. [Sec. IV A a, Fig. 2] The text says the stable high-temperature phase of Ti is BCC but that it is stabilized by entropic effects and static calculations find HCP preferred. This is physically coherent, but the wording is easy to misread. Please rephrase to distinguish static enthalpy from free energy.
  5. [App. F] The footnote about different GPU power settings and torchscript compilation is appropriate, but the main-text sentence 'the two models required around the same amount of compute' should be flagged as an inference, not a measurement, in the main text as well.

Circularity Check

0 steps flagged

No construction-level circularity; the central claims rest on external benchmark comparisons, with only fairness/protocol caveats (unequal epochs, borrowed timings, post-hoc displacement choice) that are not circularity.

full rationale

The paper's derivation chain is empirical rather than analytical: unconstrained PET models are trained on large datasets and evaluated on externally defined benchmarks (matbench-discovery, SPICE, LAMBench) against externally reported models. No equation reduces to a fitted parameter, no target metric is a renaming of a training loss, and no 'uniqueness theorem' is imported from same-author work. The rotational-learnability estimate in Sec. III A c is a heuristic about data augmentation, not an input to the benchmark accuracies, and Table V explicitly reports raw versus SO(3)-averaged results. Same-group citations (Refs. [9], [19], [32], [50]) supply architecture and methodological priors, but they are not load-bearing in the sense of forcing the conclusion: the accuracy comparisons in Tables I, II, and VII include external baselines, and the self-cited MADBench is only one of several evaluations. The manuscript itself flags the main evaluation caveats: Sec. IV B a says PET-L was trained for 'three times the number of epochs reported by eSEN' and that eSEN training times are not available; App. F says 'the eSEN timings are taken from Ref.[31]' rather than re-measured; App. C b shows the finite-difference displacement was varied and 'is crucial for non-equivariant models', a post-hoc sensitivity choice rather than a fitted prediction; App. D limits LAMBench to 'qualitative model assessment' due to inconsistent DFT settings; App. G concedes models 'would benefit from additional training.' These are correctness/fairness limitations that weaken the specific 'superior in accuracy and speed' headline, but none exhibits the required reduction of a predicted quantity to its own input. Therefore the appropriate finding is no significant circularity, with a small nonzero score reflecting minor self-citation and protocol-selection concerns rather than load-bearing circularity.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

No genuinely new physical entity is postulated. The central result rests on standard ML/DFT assumptions and on a set of hand-chosen hyperparameters; the most significant epistemic load is carried by the heuristics for learnable symmetries and by benchmark evaluation choices, not by a formal derivation.

free parameters (6)
  • Architecture hyperparameters (edge features, GNN layers, attention layers) = OAM: 640/5/3; SPICE-L: 512/3/2; OMat-XS..XL: 128/2/1 .. 640/5/3
    Chosen by hand/scaling studies (Table III, Table A5); not derived from theory, and directly control expressivity and speed.
  • Adaptive cutoff target neighbor number n̄ = 40 for OAM; 8–40 for OMat size series
    App. A2 introduces B(r)=n̄(r/r_max)^3 and δr=Δr/4 as design heuristics; the target n̄ sets the computational/accuracy tradeoff.
  • Loss weights and Huber thresholds = E/F/SV weights 0.01/1/0.01 for OAM-NC and 1/1/1 for conservative; Huber thresholds 0.003–0.05
    Table III; hand-tuned training objectives that affect the balance between energy, force, and stress accuracy.
  • Learning-rate schedule and batch parameters = warmup 10%; max LR 2e-4/1e-4/5e-6; batch 128–2048; max 350 atoms/batch
    Hand-chosen standard choices; convergence and training-time comparisons depend on these settings.
  • Training durations = OAM: 10+5+1 epochs; SPICE: 300 epochs; eSEN baseline used ~100 (PET used 3x)
    Sec. IV B a; the SPICE accuracy comparison is not strictly training-compute matched, since PET was trained for 3x the epochs reported for eSEN.
  • Evaluation hyperparameters: SO(3) averaging, finite-difference displacement, symprec = Lebedev L=3; displacement 0.05 Å; symprec 0.01/0.1 Å
    App. C b and Sec. IV A 0 a; 0.05 Å was chosen after observing Table VI improvements over the 0.03 Å default, and symprec thresholds change detected symmetry and thus phonon BZ paths.
axioms (6)
  • domain assumption DFT labels in MPtrj, sAlexandria, OMat24, and SPICE are sufficiently accurate and consistent to serve as ground truth for training and evaluation
    All benchmark conclusions treat these reference data as ground truth; App. D and E acknowledge cross-dataset DFT inconsistency, and MADBench is designed to control for it.
  • domain assumption Locality/nearsightedness permits finite-cutoff message passing with cutoffs 4.5–10 Å
    GNN edges and the adaptive cutoff (App. A2) assume distant atoms do not interact; the paper cites Prodan-Kohn locality, Ref. [12].
  • domain assumption Rotational symmetry can be learned from roughly 2×10^4 rotation samples at 0.1 Å resolution
    Sec. III A c; this heuristic underpins the claim that large datasets can teach rotation invariance. If the required resolution is finer, unconstrained models would need substantially more data.
  • domain assumption Benchmark metrics (DAF, κ_SRME, MAE, LAMBench scores) are valid proxies for practical MLIP utility
    Used to conclude that unconstrained models can be applied with confidence; the authors themselves caution that public benchmarks should not be the sole metric (Sec. IV A b).
  • domain assumption Inference-time O(3)/SO(3) averaging and force/Hessian symmetrization recover physical observables
    Central to the conclusion that symmetry breaking is benign; Sec. III C and Sec. IV A 0 a rely on this for geometry optimization and phonon calculations.
  • standard math Standard ML training assumptions: automatic differentiation, neural network expressivity, and stochastic optimization convergence
    No formal proofs are offered; the paper relies on standard ML practice for training and inference.

pith-pipeline@v1.3.0-alltime-deepseek · 24164 in / 13422 out tokens · 270500 ms · 2026-08-03T08:39:13.389271+00:00 · methodology

0 comments
read the original abstract

Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to fulfill a number of physical laws exactly, from geometric symmetries to energy conservation. Evidence is mounting that relaxing some of these constraints can be beneficial to the efficiency and (somewhat surprisingly) accuracy of MLIPs, even though care should be taken to avoid qualitative failures associated with the breaking of physical symmetries. Given the recent trend of scaling up models to larger numbers of parameters and training samples, a very important question is how unconstrained MLIPs behave in this limit. Here we investigate this issue, showing that -- when trained on large datasets -- unconstrained models can be superior in accuracy and speed when compared to physically constrained models. We assess these models both in terms of benchmark accuracy and in terms of usability in practical scenarios, focusing on static simulation workflows such as geometry optimization and lattice dynamics. We conclude that accurate unconstrained models can be applied with confidence, especially since simple inference-time modifications can be used to recover observables that are consistent with the relevant physical symmetries.

Figures

Figures reproduced from arXiv: 2601.16195 by Arslan Mazitov, Filippo Bigi, Jonathan Schmidt, Michele Ceriotti, Paolo Pegolo.

Figure 2
Figure 2. Figure 2: FIG. 2. Geometry optimization and phonon calculations with PET-OAM. (a,b) Deviation of unit-cell lengths as a function of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Accuracy-speed Pareto front for models trained on the SPICE dataset, at varying structure sizes. The energy error [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. JanusPipe: Efficient Pipeline Parallel Training for Machine Learning Interatomic Potentials

    cs.DC 2026-05 unverdicted novelty 7.0

    JanusPipe introduces SymFold and WaveK to enable efficient 3D-parallel training for conservative MLIPs, reporting 1.51x and 1.45x average throughput gains over 1F1B and Hanayo baselines on 32 GPUs.

  2. Dyna-Mat: End-to-end benchmarking of foundation machine learning interatomic potentials in finite-temperature ensembles

    cond-mat.mtrl-sci 2026-07 conditional novelty 6.5

    Dyna-Mat-v1.0 benchmarks 15 foundation MLIPs on finite-T MD observables, finding average force-error correlation with RDF/VDOS but systematic pressure failures and near-Pareto optimality of latest cross-trained models.

  3. Finite-temperature bulk moduli from an EOS-based Gr\"uneisen function

    cond-mat.mtrl-sci 2026-07 conditional novelty 6.0

    An EOS-anchored, elasticity-constrained Grüneisen function predicts finite-temperature bulk-modulus softening in four solids without fitting to thermal data.

  4. Correcting DFT formation energies towards experimental accuracy using foundational MLIPs and latent-feature delta-learning

    cond-mat.mtrl-sci 2026-07 conditional novelty 6.0

    Zero-shot r2SCAN energies from the PET-OMATPES MLIP cut GGA formation-energy errors by >40%, and delta-learning on the MLIP's latent features pushes the MAE below 50 meV/atom.

  5. Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

    stat.ML 2026-07 conditional novelty 6.0

    Edge Cluster Expansion plus Radial Rotary Complex Attention yield TECE-OAM-RRA-1.0, a Matbench Discovery SOTA SO(2) MLIP trained on OMat24, sAlex, and MPTrj.

  6. Non-covalent Interactions at cm$^{-1}$ Accuracy: Data Efficient Physics-Informed Distillation for Machine Learning Interatomic Potentials

    physics.chem-ph 2026-06 unverdicted novelty 6.0

    Physics-informed distillation from a universal MLIP plus limited CCSD(T) fine-tuning yields cm^{-1} accurate potentials for non-covalent interactions, with teacher choice strongly affecting accuracy on some systems.

  7. JanusPipe: Efficient Pipeline Parallel Training for Machine Learning Interatomic Potentials

    cs.DC 2026-05 unverdicted novelty 6.0

    JanusPipe is a new 3D-parallel training system for conservative MLIPs that uses SymFold and WaveK to achieve 1.51x and 1.45x average throughput gains over 1F1B and Hanayo on 32 GPUs.

  8. Errors that matter: Uncertainty-aware universal machine-learning potentials calibrated on experiments

    physics.chem-ph 2026-04 conditional novelty 6.0

    PET-UAFD ensemble of ML potentials, calibrated on experimental cohesive energies and moduli, matches experimental accuracy on liquid properties and supplies uncertainty estimates via the PET-EXP protocol.

  9. Fast and Accurate Foundation Models for Equivariant Machine-Learned Interatomic Potentials

    physics.comp-ph 2026-07 accept novelty 5.0

    Fast NequIP/Allegro foundation MLIPs reach leading MD inference speeds and strong benchmark accuracy; materials-discovery gains need better chemical diversity and consistent transition-metal energy surfaces.

  10. Universal Interatomic Potentials as Configuration-Space Generators for One-Shot and Iterative Fine-Tuning of Ab Initio-Accurate Material-Specific Models

    cond-mat.mtrl-sci 2026-06 unverdicted novelty 5.0

    Universal MLIPs serve as configuration generators whose DFT-relabeled subsamples enable one-shot or iterative training of material-specific MLIPs that recover accurate reactive energy profiles with 600-2000 DFT calculations.

  11. Melt-Quench Failures and Practical Solutions for Universal Machine-Learning Interatomic Potentials in Amorphous Structure Generation

    cond-mat.mtrl-sci 2026-06 conditional novelty 5.0

    Universal machine-learning interatomic potentials fail standard melt-quench amorphous-structure generation, expanding IrO2 to gas-like densities; a fixed-volume quench plus low-temperature NPT equilibration restores A...

  12. Benchmark Dataset for Catalysis on 2D MXenes

    cond-mat.mtrl-sci 2026-05 unverdicted novelty 5.0

    A benchmark dataset of 60,000 DFT calculations on 2D MXenes is created and used to train MLIPs achieving ~1000-4000x CPU speedup with ~10 meV/A force and ~1 meV/atom energy accuracy.

Reference graph

Works this paper leans on

69 extracted references · 12 linked inside Pith · cited by 11 Pith papers

  1. [1]

    Equa- tion of State Calculations by Fast Computing Machines

    Nicholas Metropolis, Arianna W Rosenbluth, Marshall N Rosenbluth, Augusta H Teller, and Edward Teller. Equa- tion of State Calculations by Fast Computing Machines. 9 Journal of Chemical Physics, 21(6):1087–1092, 1953

    1953

  2. [2]

    B. J. Alder and T. E. Wainwright. Studies in molecular dynamics. I. General method.The Journal of Chemical Physics, 31(2):459–466, August 1959

    1959

  3. [3]

    Generalized Neural- Network Representation of High-Dimensional Potential- Energy Surfaces.Physical Review Letters, 98(14):146401, April 2007

    J¨ org Behler and Michele Parrinello. Generalized Neural- Network Representation of High-Dimensional Potential- Energy Surfaces.Physical Review Letters, 98(14):146401, April 2007

    2007

  4. [4]

    Chgnet as a pretrained universal neural network potential for charge-informed atomistic mod- elling.Nature Machine Intelligence, 5(9):1031–1041, 2023

    Bowen Deng, Peichen Zhong, KyuJung Jun, Janosh Riebesell, Kevin Han, Christopher J Bartel, and Ger- brand Ceder. Chgnet as a pretrained universal neural network potential for charge-informed atomistic mod- elling.Nature Machine Intelligence, 5(9):1031–1041, 2023

    2023

  5. [5]

    A universal graph deep learning interatomic potential for the periodic table.Na- ture Computational Science, 2(11):718–728, 2022

    Chi Chen and Shyue Ping Ong. A universal graph deep learning interatomic potential for the periodic table.Na- ture Computational Science, 2(11):718–728, 2022

    2022

  6. [6]

    A hitchhiker’s guide to geometric gnns for 3d atomic systems.arXiv preprint arXiv:2312.07511, 2023

    Alexandre Duval, Simon V Mathis, Chaitanya K Joshi, Victor Schmidt, Santiago Miret, Fragkiskos D Malliaros, Taco Cohen, Pietro Lio, Yoshua Bengio, and Michael Bronstein. A hitchhiker’s guide to geometric gnns for 3d atomic systems.arXiv preprint arXiv:2312.07511, 2023

    Pith/arXiv arXiv 2023

  7. [7]

    Resolving the body-order paradox of ma- chine learning interatomic potentials.arXiv preprint arXiv:2509.14146, 2025

    Sanggyu Chong, Tong Jiang, Michelangelo Domina, Fil- ippo Bigi, Federico Grasselli, Joonho Lee, and Michele Ceriotti. Resolving the body-order paradox of ma- chine learning interatomic potentials.arXiv preprint arXiv:2509.14146, 2025

    arXiv 2025

  8. [8]

    Gemnet: Universal directional graph neural networks for molecules.Advances in Neural Information Processing Systems, 34:6790–6802, 2021

    Johannes Gasteiger, Florian Becker, and Stephan G¨ unnemann. Gemnet: Universal directional graph neural networks for molecules.Advances in Neural Information Processing Systems, 34:6790–6802, 2021

    2021

  9. [9]

    Smooth, ex- act rotational symmetrization for deep learning on point clouds

    Sergey Pozdnyakov and Michele Ceriotti. Smooth, ex- act rotational symmetrization for deep learning on point clouds. InAdvances in Neural Information Processing Systems, volume 36, pages 79469–79501. Curran Asso- ciates, Inc., 2023

    2023

  10. [10]

    Unke, Klaus-Robert M¨ uller, and Stefan Gugler

    Max Eissler, Tim Korjakow, Stefan Ganscha, Oliver T. Unke, Klaus-Robert M¨ uller, and Stefan Gugler. How simple can you go? an off-the-shelf transformer approach to molecular dynamics, 2026

    2026

  11. [11]

    Matbench discovery–a framework to evaluate machine learning crystal stability predictions

    Janosh Riebesell, Rhys EA Goodall, Philipp Benner, Yuan Chiang, Bowen Deng, Alpha A Lee, Anubhav Jain, and Kristin A Persson. Matbench discovery–a framework to evaluate machine learning crystal stability predictions. arXiv preprint arXiv:2308.14920, 2023

    Pith/arXiv arXiv 2023

  12. [12]

    Nearsightedness of electronic matter.Proceedings of the National Academy of Sciences, 102(33):11635–11638, August 2005

    E Prodan and W Kohn. Nearsightedness of electronic matter.Proceedings of the National Academy of Sciences, 102(33):11635–11638, August 2005

    2005

  13. [13]

    Unke, Stefan Chmiela, Huziel E

    Oliver T. Unke, Stefan Chmiela, Huziel E. Sauceda, Michael Gastegger, Igor Poltavsky, Kristof T. Sch¨ utt, Alexandre Tkatchenko, and Klaus-Robert M¨ uller. Ma- chine Learning Force Fields.Chem. Rev., 121(16):10142– 10186, August 2021

    2021

  14. [14]

    Deringer, Albert P

    Volker L. Deringer, Albert P. Bart´ ok, Noam Bern- stein, David M. Wilkins, Michele Ceriotti, and G´ abor Cs´ anyi. Gaussian Process Regression for Materials and Molecules.Chem. Rev., 121(16):10073–10141, August 2021

    2021

  15. [15]

    Four Generations of High-Dimensional Neu- ral Network Potentials.Chem

    J¨ org Behler. Four Generations of High-Dimensional Neu- ral Network Potentials.Chem. Rev., 121(16):10037– 10072, August 2021

    2021

  16. [16]

    A foundation model for atomistic materials chemistry.arXiv preprint arXiv:2401.00096, 2023

    Ilyes Batatia, Philipp Benner, Yuan Chiang, Alin M Elena, D´ avid P Kov´ acs, Janosh Riebesell, Xavier R Ad- vincula, Mark Asta, Matthew Avaylon, William J Bald- win, et al. A foundation model for atomistic materials chemistry.arXiv preprint arXiv:2401.00096, 2023

    Pith/arXiv arXiv 2023

  17. [17]

    Graph atomic cluster expansion for semilocal interactions beyond equivariant message passing.Physical Review X, 14(2):021036, 2024

    Anton Bochkarev, Yury Lysogorskiy, and Ralf Drautz. Graph atomic cluster expansion for semilocal interactions beyond equivariant message passing.Physical Review X, 14(2):021036, 2024

    2024

  18. [18]

    Orb-v3: atomistic simulation at scale.arXiv preprint arXiv:2504.06231, 2025

    Benjamin Rhodes, Sander Vandenhaute, Vaidotas ˇSimkus, James Gin, Jonathan Godwin, Tim Duignan, and Mark Neumann. Orb-v3: atomistic simulation at scale.arXiv preprint arXiv:2504.06231, 2025

    Pith/arXiv arXiv 2025

  19. [19]

    Pet-mad as a lightweight universal interatomic potential for ad- vanced materials modeling.Nature Communications, 16(1), November 2025

    Arslan Mazitov, Filippo Bigi, Matthias Kellner, Paolo Pegolo, Davide Tisi, Guillaume Fraux, Sergey Pozd- nyakov, Philip Loche, and Michele Ceriotti. Pet-mad as a lightweight universal interatomic potential for ad- vanced materials modeling.Nature Communications, 16(1), November 2025

    2025

  20. [20]

    Scalable parallel algorithm for graph neu- ral network interatomic potentials in molecular dynamics simulations.Journal of chemical theory and computation, 20(11):4857–4868, 2024

    Yutack Park, Jaesun Kim, Seungwoo Hwang, and Se- ungwu Han. Scalable parallel algorithm for graph neu- ral network interatomic potentials in molecular dynamics simulations.Journal of chemical theory and computation, 20(11):4857–4868, 2024

    2024

  21. [21]

    Uma: A family of universal models for atoms.arXiv preprint arXiv:2506.23971, 2025

    Brandon M Wood, Misko Dzamba, Xiang Fu, Meng Gao, Muhammed Shuaibi, Luis Barroso-Luque, Kareem Abdelmaqsoud, Vahe Gharakhanyan, John R Kitchin, Daniel S Levine, et al. Uma: A family of universal models for atoms.arXiv preprint arXiv:2506.23971, 2025

    arXiv 2025

  22. [22]

    Improving machine- learning models in materials science through large datasets.Materials Today Physics, 48:101560, 2024

    Jonathan Schmidt, Tiago FT Cerqueira, Aldo H Romero, Antoine Loew, Fabian J¨ ager, Hai-Chen Wang, Silvana Botti, and Miguel AL Marques. Improving machine- learning models in materials science through large datasets.Materials Today Physics, 48:101560, 2024

    2024

  23. [23]

    Open materials 2024 (omat24) inorganic materials dataset and models.arXiv preprint arXiv:2410.12771, 2024

    Luis Barroso-Luque, Muhammed Shuaibi, Xiang Fu, Brandon M Wood, Misko Dzamba, Meng Gao, Ammar Rizvi, C Lawrence Zitnick, and Zachary W Ulissi. Open materials 2024 (omat24) inorganic materials dataset and models.arXiv preprint arXiv:2410.12771, 2024

    Pith/arXiv arXiv 2024

  24. [24]

    The open molecules 2025 (omol25) dataset, evaluations, and models.arXiv preprint arXiv:2505.08762, 2025

    Daniel S Levine, Muhammed Shuaibi, Evan Wal- ter Clark Spotte-Smith, Michael G Taylor, Muhammad R Hasyim, Kyle Michel, Ilyes Batatia, G´ abor Cs´ anyi, Misko Dzamba, Peter Eastman, et al. The open molecules 2025 (omol25) dataset, evaluations, and models.arXiv preprint arXiv:2505.08762, 2025

    arXiv 2025

  25. [25]

    Open catalyst 2020 (oc20) dataset and commu- nity challenges.Acs Catalysis, 11(10):6059–6072, 2021

    Lowik Chanussot, Abhishek Das, Siddharth Goyal, Thibaut Lavril, Muhammed Shuaibi, Morgane Riviere, Kevin Tran, Javier Heras-Domingo, Caleb Ho, Weihua Hu, et al. Open catalyst 2020 (oc20) dataset and commu- nity challenges.Acs Catalysis, 11(10):6059–6072, 2021

    2020

  26. [26]

    The open catalyst 2022 (oc22) dataset and challenges for oxide electrocatalysts.ACS Catalysis, 13(5):3066–3084, 2023

    Richard Tran, Janice Lan, Muhammed Shuaibi, Bran- don M Wood, Siddharth Goyal, Abhishek Das, Javier Heras-Domingo, Adeesh Kolluru, Ammar Rizvi, Nima Shoghi, et al. The open catalyst 2022 (oc22) dataset and challenges for oxide electrocatalysts.ACS Catalysis, 13(5):3066–3084, 2023

    2022

  27. [27]

    Spice, a dataset of drug-like molecules and peptides for training machine learning potentials.Scien- tific Data, 10(1):11, 2023

    Peter Eastman, Pavan Kumar Behara, David L Dotson, Raimondas Galvelis, John E Herr, Josh T Horton, Yuezhi Mao, John D Chodera, Benjamin P Pritchard, Yuanqing Wang, et al. Spice, a dataset of drug-like molecules and peptides for training machine learning potentials.Scien- tific Data, 10(1):11, 2023

    2023

  28. [28]

    Massive atomic diversity: a compact universal dataset for atomistic machine learning.Scientific Data, 12(1), November 2025

    Arslan Mazitov, Sofiia Chorna, Guillaume Fraux, Marnik Bercx, Giovanni Pizzi, Sandip De, and Michele Ceriotti. Massive atomic diversity: a compact universal dataset for atomistic machine learning.Scientific Data, 12(1), November 2025. 10

    2025

  29. [29]

    Orb: A fast, scalable neural network potential.arXiv preprint arXiv:2410.22570, 2024

    Mark Neumann, James Gin, Benjamin Rhodes, Steven Bennett, Zhiyi Li, Hitarth Choubisa, Arthur Hussey, and Jonathan Godwin. Orb: A fast, scalable neural network potential.arXiv preprint arXiv:2410.22570, 2024

    Pith/arXiv arXiv 2024

  30. [30]

    Eric Qu and Aditi Krishnapriyan. The importance of be- ing scalable: Improving the speed and accuracy of neu- ral network interatomic potentials acrosfs chemical do- mains.Advances in Neural Information Processing Sys- tems, 37:139030–139053, 2024

    2024

  31. [31]

    Learning smooth and expressive interatomic potentials for physical property prediction

    Xiang Fu, Brandon M Wood, Luis Barroso-Luque, Daniel S Levine, Meng Gao, Misko Dzamba, and C Lawrence Zitnick. Learning smooth and expressive interatomic potentials for physical property prediction. arXiv preprint arXiv:2502.12147, 2025

    Pith/arXiv arXiv 2025

  32. [32]

    The dark side of the forces: assessing non-conservative force models for atomistic machine learning.arXiv preprint arXiv:2412.11569, 2024

    Filippo Bigi, Marcel Langer, and Michele Ceriotti. The dark side of the forces: assessing non-conservative force models for atomistic machine learning.arXiv preprint arXiv:2412.11569, 2024

    arXiv 2024

  33. [33]

    R. Peierls. Zur kinetischen theorie der w¨ armeleitung in kristallen.Annalen der Physik, 395(8):1055–1101, 1929

    1929

  34. [34]

    Frank H Stillinger and Aneesur Rahman. Improved sim- ulation of liquid water by molecular dynamics Compar- ison of simple potential functions for simulating liquid water Improved simulation of liquid water by molecular dynamics*.The Journal of Chemical Physics The Jour- nal of Chemical Physics The Journal of Chemical Physics I. General Method The Journal ...

    1974

  35. [35]

    Andersen

    Hans C. Andersen. Molecular dynamics simulations at constant pressure and/or temperature.The Journal of Chemical Physics, 72(4):2384–2393, 1980

    1980

  36. [36]

    Allen and Dominic J

    Michael P. Allen and Dominic J. Tildesley.Computer Simulation of Liquids, volume 1. Oxford University Press, November 2017

    2017

  37. [37]

    Lambench: A benchmark for large atomic models.arXiv preprint arXiv:2504.19578, 2025

    Anyang Peng, Chun Cai, Mingyu Guo, Duo Zhang, Chengqian Zhang, Antoine Loew, Linfeng Zhang, and Han Wang. Lambench: A benchmark for large atomic models.arXiv preprint arXiv:2504.19578, 2025

    Pith/arXiv arXiv 2025

  38. [38]

    Mlip arena: advancing fairness and transparency in machine learning interatomic potentials through an open and accessible benchmark platform

    Yuan Chiang, Tobias Kreiman, Elizabeth Weaver, Ishan Amin, Matthew Kuner, Christine Zhang, Aaron Kaplan, Daryl Chrzan, Samuel M Blau, Aditi S Krishnapriyan, et al. Mlip arena: advancing fairness and transparency in machine learning interatomic potentials through an open and accessible benchmark platform. InAI for Accelerated Materials Design-ICLR 2025, 2025

    2025

  39. [39]

    Mace-off: Short-range transferable machine learning force fields for organic molecules.Journal of the American Chemical Society, 147(21):17598–17611, 2025

    D´ avid P´ eter Kov´ acs, J Harry Moore, Nicholas J Brown- ing, Ilyes Batatia, Joshua T Horton, Yixuan Pu, Venkat Kapil, William C Witt, Ioan-Bogdan Magdau, Daniel J Cole, et al. Mace-off: Short-range transferable machine learning force fields for organic molecules.Journal of the American Chemical Society, 147(21):17598–17611, 2025

    2025

  40. [40]

    Lilienfeld, and Klaus- Robert M¨ uller

    Gr´ egoire Montavon, Katja Hansen, Siamac Fazli, Matthias Rupp, Franziska Biegler, Andreas Ziehe, Alexandre Tkatchenko, Anatole V. Lilienfeld, and Klaus- Robert M¨ uller. Learning invariant representations of molecules for atomization energy prediction. In F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Wein- berger, editors,Advances in Neural Informati...

    2012

  41. [41]

    E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nature communica- tions, 13(1):2453, 2022

    Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E Smidt, and Boris Kozinsky. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nature communica- tions, 13(1):2453, 2022

    2022

  42. [42]

    Ilyes Batatia, David Peter Kovacs, Gregor N. C. Simm, Christoph Ortner, and Gabor Csanyi. MACE: Higher or- der equivariant message passing neural networks for fast and accurate force fields. In Alice H. Oh, Alekh Agar- wal, Danielle Belgrave, and Kyunghyun Cho, editors,Ad- vances in Neural Information Processing Systems, 2022

    2022

  43. [43]

    Learning local equivariant representa- tions for large-scale atomistic dynamics.Nature Com- munications, 14(1):579, 2023

    Albert Musaelian, Simon Batzner, Anders Johansson, Lixin Sun, Cameron J Owen, Mordechai Kornbluth, and Boris Kozinsky. Learning local equivariant representa- tions for large-scale atomistic dynamics.Nature Com- munications, 14(1):579, 2023

    2023

  44. [44]

    Equiformerv2: Improved equivariant trans- former for scaling to higher-degree representations.arXiv preprint arXiv:2306.12059, 2023

    Yi-Lun Liao, Brandon Wood, Abhishek Das, and Tess Smidt. Equiformerv2: Improved equivariant trans- former for scaling to higher-degree representations.arXiv preprint arXiv:2306.12059, 2023

    Pith/arXiv arXiv 2023

  45. [45]

    So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems.arXiv preprint arXiv:2205.14276, 2022

    J Thorben Frank, Oliver T Unke, and Klaus-Robert M¨ uller. So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems.arXiv preprint arXiv:2205.14276, 2022

    Pith/arXiv arXiv 2022

  46. [46]

    Root mean square layer normalization.Advances in neural information process- ing systems, 32, 2019

    Biao Zhang and Rico Sennrich. Root mean square layer normalization.Advances in neural information process- ing systems, 32, 2019

    2019

  47. [47]

    Glu variants improve transformer.arXiv preprint arXiv:2002.05202, 2020

    Noam Shazeer. Glu variants improve transformer.arXiv preprint arXiv:2002.05202, 2020

    Pith/arXiv arXiv 2002

  48. [48]

    On layer normalization in the transformer architecture

    Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. InInternational conference on machine learning, pages 10524–10533. PMLR, 2020

    2020

  49. [49]

    Beat- ing the egg-box effect in plane-wave DFT simulations

    Ben Durham, Matt I J Probert, and Phil J Hasnip. Beat- ing the egg-box effect in plane-wave DFT simulations. Electron. Struct., 7(2):025004, June 2025

    2025

  50. [50]

    Probing the effects of broken symmetries in machine learning.Mach

    Marcel F Langer, Sergey N Pozdnyakov, and Michele Ceriotti. Probing the effects of broken symmetries in machine learning.Mach. Learn.: Sci. Technol., 5(4):04LT01, December 2024

    2024

  51. [51]

    Gerken and Pan Kessel

    Jan E. Gerken and Pan Kessel. Emergent equivariance in deep ensembles, 2024

    2024

  52. [52]

    Tuckerman, B

    M. Tuckerman, B. J. Berne, and G. J. Martyna. Re- versible multiple time scale molecular dynamics.The Journal of Chemical Physics, 97(3):1990, 1992

    1990

  53. [53]

    Massive atomic diversity: a compact universal dataset for atomistic machine learning, 2025

    Arslan Mazitov, Sofiia Chorna, Guillaume Fraux, Marnik Bercx, Giovanni Pizzi, Sandip De, and Michele Ceriotti. Massive atomic diversity: a compact universal dataset for atomistic machine learning, 2025

    2025

  54. [54]

    Predicting stable crystalline compounds using chemical similarity.npj Computational Materials, 7(1):12, 2021

    Hai-Chen Wang, Silvana Botti, and Miguel AL Marques. Predicting stable crystalline compounds using chemical similarity.npj Computational Materials, 7(1):12, 2021

    2021

  55. [55]

    Matris: Official pytorch implementation, 2025

    HPC+AI Research Group, Institute of Computing Tech- nology, Chinese Academy of Sciences. Matris: Official pytorch implementation, 2025

    2025

  56. [56]

    Thermal conductivity predictions with foundation atomistic models.arXiv preprint arXiv:2408.00755, 2024

    Bal´ azs P´ ota, Paramvir Ahlawat, G´ abor Cs´ anyi, and Michele Simoncelli. Thermal conductivity predictions with foundation atomistic models.arXiv preprint arXiv:2408.00755, 2024

    Pith/arXiv arXiv 2024

  57. [57]

    Abbott, Philip Loche, Ar- slan Mazitov, Davide Tisi, Marcel F

    Filippo Bigi, Joseph W. Abbott, Philip Loche, Ar- slan Mazitov, Davide Tisi, Marcel F. Langer, Alexan- der Goscinski, Paolo Pegolo, Sanggyu Chong, Rohit Goswami, Sofiia Chorna, Matthias Kellner, Michele Ce- riotti, and Guillaume Fraux. Metatensor and metatomic: foundational libraries for interoperable atomistic ma- 11 chine learning, 2025

    2025

  58. [58]

    The atomic simulation environ- ment—a python library for working with atoms.Journal of Physics: Condensed Matter, 29(27):273002, 2017

    Ask Hjorth Larsen, Jens Jørgen Mortensen, Jakob Blomqvist, Ivano E Castelli, Rune Christensen, Marcin Du lak, Jesper Friis, Michael N Groves, Bjørk Ham- mer, Cory Hargus, Eric D Hermes, Paul C Jen- nings, Peter Bjerre Jensen, James Kermode, John R Kitchin, Esben Leonhard Kolsbjerg, Joseph Kubal, Kris- ten Kaasbjerg, Steen Lysgaard, J´ on Bergmann Maron- s...

    2017

  59. [59]

    Thermal conductivity predictions with foundation atomistic models, 2025

    Bal´ azs P´ ota, Paramvir Ahlawat, G´ abor Cs´ anyi, and Michele Simoncelli. Thermal conductivity predictions with foundation atomistic models, 2025

    2025

  60. [60]

    Dpa-2: a large atomic model as a multi-task learner.npj Computational Materials, 10(1):293, 2024

    Duo Zhang, Xinzijian Liu, Xiangyu Zhang, Chengqian Zhang, Chun Cai, Hangrui Bi, Yiming Du, Xuejian Qin, Anyang Peng, Jiameng Huang, et al. Dpa-2: a large atomic model as a multi-task learner.npj Computational Materials, 10(1):293, 2024

    2024

  61. [61]

    Accurate global machine learning force fields for molecules with hundreds of atoms.Science Advances, 9(2):eadf0873, 2023

    Stefan Chmiela, Valentin Vassilev-Galindo, Oliver T Unke, Adil Kabylda, Huziel E Sauceda, Alexandre Tkatchenko, and Klaus-Robert M¨ uller. Accurate global machine learning force fields for molecules with hundreds of atoms.Science Advances, 9(2):eadf0873, 2023

    2023

  62. [62]

    Pytorch: An imperative style, high-performance deep learning li- brary.Advances in neural information processing sys- tems, 32, 2019

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zem- ing Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning li- brary.Advances in neural information processing sys- tems, 32, 2019

    2019

  63. [63]

    Atsuto Seko, Atsushi Togo, Hiroyuki Hayashi, Koji Tsuda, Laurent Chaput, and Isao Tanaka. Predic- tion of low-thermal-conductivity compounds with first- principles anharmonic lattice-dynamics calculations and bayesian optimization.Physical Review Letters, 115(20), November 2015

    2015

  64. [64]

    Spglib: a software library for crystal symmetry search.Sci- ence and Technology of Advanced Materials: Methods, 4(1):2384822, 2024

    Atsushi Togo, Kohei Shinohara, and Isao Tanaka. Spglib: a software library for crystal symmetry search.Sci- ence and Technology of Advanced Materials: Methods, 4(1):2384822, 2024. 12 Appendices Appendix A: Model and training details

    2024

  65. [65]

    [9], and it is implemented in the metatrain library [57]

    Architecture The proposed architecture is based on a modified version of the original PET from Ref. [9], and it is implemented in the metatrain library [57]. Besides the changes to the architecture described in the main text, a number of further smaller modifications were made, namely: •the use of skip connections instead of summing layer-wise predictions...

  66. [66]

    baseline

    Adaptive cutoff Diverse datasets that span the full periodic table include materials with wildly varying densities. This is problematic because the number of edges included within a fixed cutoff varies wildly. To ensure that the computational and parameter budget is allocated more uniformly across different structures, and that data can be packed more tig...

  67. [67]

    All training runs were executed in single-precision, without using TensorFloat-32 operations

    T raining All training and fine-tuning runs were executed with a standard cosine learning rate scheduler, with a linear warm-up stage corresponding to 10% of the total number of training steps. All training runs were executed in single-precision, without using TensorFloat-32 operations. A chemical-composition-based linear model was fitted for the energies...

  68. [68]

    Hyperparameters The hyperparameters employed to train the models presented in this work are shown in Tab. III. See Sec. G for model and training hyperparameters relative to the OMol models. TABLE III. Model and training hyperparameters for the models evaluated in this work. A linear learning-rate warm-up of 10% of the total number of epochs was performed ...

    2048

  69. [69]

    OMat-XL” model we present here is what we call

    Pareto frontier for PET-OMat models TABLE IV. Model hyperparameters for the PET-OMat models. The “OMat-XL” model we present here is what we call ”OMat” elsewhere. Model OMat-XS OMat-S OMat-M OMat-L OMat-XL Parameter count 4.5M 25.9M 109M 255M 730M Edge features 128 256 384 512 640 GNN layers 2 3 3 4 5 Attention layers 1 1 2 2 3 Graph cutoff radius ( ˚A) 7...

    arXiv 2020