pith. sign in

arxiv: 2606.00794 · v1 · pith:2DFCN4ZUnew · submitted 2026-05-30 · ❄️ cond-mat.mtrl-sci · cs.LG

Benchmark Dataset for Catalysis on 2D MXenes

Pith reviewed 2026-06-28 18:10 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.LG
keywords MXenesmachine learning interatomic potentialsDFTcatalysis2D materialsbenchmark datasetTi2CTyforce prediction
0
0 comments X

The pith

Machine learning interatomic potentials trained on 60,000 DFT calculations predict MXene forces and energies at meV accuracy while delivering 1000- to 4000-fold CPU speedup.

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

The paper generates a dataset of 50,000 DFT calculations for training and 10,000 for testing on Ti2CTy MXene configurations and molecular systems, plus an additional set of 1,000 genuinely new larger systems. It trains several competitive ML interatomic potential models on this data to predict the atomic forces and formation energies that repeated DFT calculations would otherwise supply during structural and catalytic investigations. The resulting DFT-ML workflow reaches the stated accuracy targets of roughly 10 meV per angstrom for forces and 1 meV per atom for energies. This acceleration opens the door to routine study of larger MXene slabs and more realistic surface terminations whose direct DFT treatment remains prohibitive. The authors also supply qualitative model evaluations that go beyond standard numerical benchmarks.

Core claim

A combined DFT-ML framework built on 50,000 training and 10,000 test DFT calculations for Ti2CTy MXenes and molecules, together with 1,000 new larger systems, allows EquiformerV2, MACE, MatRIS, and UPET models to replace repeated first-principles force and energy evaluations. The models maintain approximately 10 meV/Å force accuracy and 1 meV per-atom energy accuracy while providing 1-4·10^3 computational acceleration on CPU, thereby enabling more extensive catalytic simulations of 2D MXenes than direct DFT permits.

What carries the argument

Machine learning interatomic potentials trained on a large DFT dataset of MXene and molecular configurations to replace repeated first-principles force and energy calculations.

If this is right

  • Structural relaxations and molecular-dynamics trajectories of MXene surfaces become feasible at scales previously limited by DFT cost.
  • High-throughput screening of different surface terminations and adsorbates on MXenes can be performed with the reported speedup.
  • The released dataset serves as a public benchmark for future MLIP development targeted at 2D catalytic materials.
  • Qualitative simulation-based checks become a necessary complement to numerical error metrics when validating models for catalysis.
  • The 1,000-system generalization test provides a concrete protocol for assessing transferability to larger MXene models.

Where Pith is reading between the lines

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

  • The same dataset-plus-MLIP strategy could be repeated for other families of 2D materials once equivalent DFT reference data exist.
  • Coupling the fast ML potentials to Monte Carlo or grand-canonical sampling would allow direct prediction of surface coverage under realistic gas pressures.
  • Active-learning loops seeded by the existing 60,000-point set could further reduce the number of new DFT calculations needed for specific reaction pathways.
  • The reported CPU speedup makes it practical to embed the potentials inside larger multiscale models that link atomic catalysis to mesoscale transport.

Load-bearing premise

The trained models will retain the target accuracy when applied to genuinely new and larger MXene systems outside the training distribution.

What would settle it

If force or energy predictions on the 1,000 new larger systems exceed roughly 10 meV/Å or 1 meV per atom relative to fresh DFT reference values, the maintained-accuracy claim is falsified.

Figures

Figures reproduced from arXiv: 2606.00794 by Ania Beatriz Rodr\'iguez-Barrera, Anmar Karmush, Johanna Rosen, Jonas Bj\"ork, M{\aa}rten Wadenb\"ack, Michael Felsberg, Pavlo Melnyk.

Figure 1
Figure 1. Figure 1: Mean absolute error (MAE) of force predictions across publicly available foundation models given Ti2CTy MXene systems. The results indicate limited transferability of existing founda￾tion models to MXene catalysis data, hence the need for the proposed CATALIUST TI2C-MXENE dataset. Star markers denote models trained from scratch and foundation models fine-tuned on the proposed dataset. However, despite thei… view at source ↗
Figure 2
Figure 2. Figure 2: Types of (a) systems and (b) DFT calculations included in the dataset. It comprises [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distributions for energies, number of atoms, and mean force magnitudes (per atom and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Molecular dynamics simulations of (a-c) CO [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Molecular dynamics simulations of (a,b) CO [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Molecular dynamics simulations of (a,b) CO [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Molecular dynamics simulations of CO2 adsorbed on a fully OH-terminated MXene at 300 K, comparing different MACE foundation models. Panels (a,b) show MACE omat foundation models (MACE PT omat) without and with fine-tuning, respectively, while panels (c,d) show the corresponding models for the MATPES (MACE PT matpes) foundation model. Each simulation consists of 10 000 time steps with a step size of 0.5 fs.… view at source ↗
Figure 8
Figure 8. Figure 8: Molecular dynamics simulations of HCOOH adsorbed on a fully O-terminated MXene [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Differences in radial distribution functions between molecular dynamics simulations using [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
read the original abstract

Merging first-principles calculations with machine learning (ML), we aim to accelerate the exploration of catalytic behaviour in novel materials. We focus on two-dimensional (2D) Ti$_2$CT$_y$ MXenes, whose versatile surface chemistry makes them particularly compelling candidates for catalysis. Resolving their composition and structure under realistic conditions exceeds the reach of standard density functional theory (DFT) due to computational cost. To address this challenge, we generate a comprehensive dataset of 50,000 DFT calculations for training and 10,000 for testing, encompassing both Ti$_2$CT$_y$ MXene configurations and molecular systems, along with an additional test dataset with 1000 genuinely new, larger systems to investigate how well models generalise. We train and validate widely used and competitive machine learning interatomic potential (MLIP) models, including EquiformerV2, MACE, MatRIS, and UPET, that accurately predict atomic forces and formation energies -- quantities that DFT must repeatedly compute for structural and catalytic investigations -- for these 2D materials. This combined DFT-ML framework achieves computational acceleration on the order of approximately $1-4 \cdot 10^3$ (on a CPU) while maintaining desired-level accuracy (approximately +/- $10$ meV/A for forces and approximately +/- $1$ meV for per-atom energies), paving the way for more efficient investigations of MXene catalytic behaviour. Moreover, we perform an extensive qualitative evaluation of the trained models, showcasing the importance of comprehensive simulation-based comparison beyond benchmark metrics. The dataset and the trained models with the code are available at https://huggingface.co/datasets/CatalystAnonymous/catalyst_mxenes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a benchmark dataset comprising 50,000 DFT calculations for training and 10,000 for testing on Ti₂CTy MXene configurations and molecular systems relevant to catalysis, plus a separate 1,000-system hold-out of genuinely larger structures. Several ML interatomic potentials (EquiformerV2, MACE, MatRIS, UPET) are trained to predict forces and formation energies, with the combined DFT-ML approach claimed to deliver 1–4 × 10³ CPU speedup while retaining target accuracy of approximately ±10 meV/Å for forces and ±1 meV/atom for energies. The dataset, trained models, and code are released publicly.

Significance. If the reported accuracy generalizes, the work supplies a substantial, openly available resource that could materially accelerate high-throughput screening of MXene catalytic properties, where repeated DFT evaluations of forces and energies are the dominant cost. The public release of both the 60k+ DFT dataset and the trained MLIP checkpoints constitutes a concrete, reusable contribution beyond the benchmark numbers themselves.

major comments (2)
  1. [Abstract] Abstract: The 1,000 genuinely new, larger systems are explicitly introduced “to investigate how well models generalise,” yet the manuscript supplies no quantitative error metrics (MAE, RMSE, or force/energy histograms) on this hold-out set. Because catalytic investigations routinely involve structures larger than the 50k/10k training distribution, the absence of these numbers leaves the central claim that the framework “maintains desired-level accuracy” on realistic systems unverified.
  2. [Abstract] Abstract and methods: The stated accuracy targets (±10 meV/Å forces, ±1 meV/atom energies) and the 1–4 × 10³ speedup are presented without accompanying details on DFT convergence criteria, k-point sampling, or error-bar methodology for the reference calculations. Without these controls it is impossible to judge whether the ML models are being benchmarked against sufficiently converged targets or whether the reported errors already incorporate DFT uncertainty.
minor comments (2)
  1. [Abstract] Abstract: The force accuracy is written as “+/- 10 meV/A”; the conventional unit is meV/Å.
  2. The manuscript states that an “extensive qualitative evaluation” of the models is performed, but the corresponding figures or supplementary material are not referenced in the provided text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will incorporate the requested information into the revised version.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The 1,000 genuinely new, larger systems are explicitly introduced “to investigate how well models generalise,” yet the manuscript supplies no quantitative error metrics (MAE, RMSE, or force/energy histograms) on this hold-out set. Because catalytic investigations routinely involve structures larger than the 50k/10k training distribution, the absence of these numbers leaves the central claim that the framework “maintains desired-level accuracy” on realistic systems unverified.

    Authors: We agree that quantitative metrics on the 1,000 larger hold-out systems are necessary to support the generalization claims. The revised manuscript will add MAE, RMSE, and force/energy error histograms specifically for this hold-out set, enabling direct evaluation of model performance on structures outside the original training distribution. revision: yes

  2. Referee: [Abstract] Abstract and methods: The stated accuracy targets (±10 meV/Å forces, ±1 meV/atom energies) and the 1–4 × 10³ speedup are presented without accompanying details on DFT convergence criteria, k-point sampling, or error-bar methodology for the reference calculations. Without these controls it is impossible to judge whether the ML models are being benchmarked against sufficiently converged targets or whether the reported errors already incorporate DFT uncertainty.

    Authors: We acknowledge this omission. The revised manuscript will include a new subsection in the Methods detailing the DFT convergence criteria (energy and force thresholds), k-point sampling settings, and any error estimation procedures used for the reference calculations. This will confirm that the reported ML accuracies are measured against sufficiently converged DFT targets. revision: yes

Circularity Check

0 steps flagged

No circularity; accuracy and speedup are direct held-out comparisons.

full rationale

The paper generates a 50k/10k DFT dataset split, trains standard MLIPs (EquiformerV2, MACE, etc.), and reports force/energy errors as direct MAE/RMSE against the held-out 10k DFT labels. Speedup (1-4·10³ on CPU) is a timing ratio between DFT and ML inference. The 1000 larger systems are introduced only to probe generalization and carry no reported metrics that feed back into the accuracy claim. No equations, fitted parameters, or self-citations reduce any reported number to a tautology or to the training inputs by construction. The derivation chain is therefore self-contained against external DFT benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that DFT supplies reliable reference data for forces and formation energies and that standard MLIP training procedures transfer to this materials class; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption DFT calculations with the chosen functional and settings provide sufficiently accurate reference forces and energies for training MLIPs intended for catalysis studies.
    The entire training and accuracy claim is predicated on DFT being the ground truth; invoked implicitly throughout the abstract.

pith-pipeline@v0.9.1-grok · 5874 in / 1347 out tokens · 26642 ms · 2026-06-28T18:10:07.194879+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

53 extracted references · 17 canonical work pages

  1. [1]

    Anderson, T

    B. Anderson, T. S. Hy, and R. Kondor. Cormorant: Covariant molecular neural networks. Advances in Neural Information Processing Systems, pages 14510–14519, 2019

  2. [2]

    Aykent and T

    S. Aykent and T. Xia. Gotennet: Rethinking efficient 3d equivariant graph neural networks.The Thirteenth International Conference on Learning Representations, 2025

  3. [3]

    Barroso-Luque, S

    L. Barroso-Luque, S. Muhammed, X. Fu, B. M. Wood, M. Dzamba, M. Gao, A. Rizvi, C. L. Zitnick, and Z. W. Ulissi. Open materials 2024 (omat24) inorganic materials dataset and models. arXiv, 2024

  4. [4]

    Batatia, D

    I. Batatia, D. P. Kovacs, G. Simm, C. Ortner, and G. Cs´anyi. MACE: Higher order equivari- ant message passing neural networks for fast and accurate force fields.Advances in neural information processing systems, 35:11423–11436, 2022

  5. [5]

    Batatia, P

    I. Batatia, P. Benner, Y . Chiang, A. M. Elena, D. P. Kov ´acs, J. Riebesell, X. R. Advincula, M. Asta, W. J. Baldwin, N. Bernstein, A. Bhowmik, S. M. Blau, V . C˘arare, J. P. Darby, S. De, F. D. Pia, V . L. Deringer, R. Elijoˇsius, Z. El-Machachi, E. Fako, A. C. Ferrari, A. Genreith- Schriever, J. George, R. E. A. Goodall, C. P. Grey, S. Han, W. Handley,...

  6. [6]

    Batzner, A

    S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt, and B. Kozinsky. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nat. Commun., 13(1):2453, 2022

  7. [7]

    F. Bigi, P. Pegolo, A. Mazitov, and M. Ceriotti. Pushing the limits of unconstrained machine- learned interatomic potentials, 2026. URLhttps://arxiv.org/abs/2601.16195

  8. [8]

    P. E. Bl¨ochl. Projector augmented-wave method.Phys. Rev. B, 50(24):17953–17979, Dec. 1994. ISSN 0163-1829, 1095-3795. doi: 10.1103/PhysRevB.50.17953. URL https://link.aps. org/doi/10.1103/PhysRevB.50.17953

  9. [9]

    M. M. Bronstein, J. Bruna, Y . LeCun, A. Szlam, and P. Vandergheynst. Geometric deep learning: going beyond euclidean data.IEEE Signal Processing Magazine, 34(4):18–42, 2017

  10. [10]

    M. M. Bronstein, J. Bruna, T. Cohen, and P. Veliˇckovi´c. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges.arXiv preprint arXiv:2104.13478, 2021. 10

  11. [11]

    Chanussot, A

    L. Chanussot, A. Das, S. Goyal, T. Lavril, M. Shuaibi, M. Riviere, K. Tran, J. Heras-Domingo, C. Ho, W. Hu, A. Palizhati, A. Sriram, B. Wood, J. Yoon, D. Parikh, C. L. Zitnick, and Z. Ulissi. Open catalyst 2020 (OC20) dataset and community challenges.ACS Catal., 11(10): 6059–6072, May 2021. ISSN 2155-5435, 2155-5435. doi: 10.1021/acscatal.0c04525. URL htt...

  12. [12]

    Chen and S

    C. Chen and S. P. Ong. A universal graph deep learning interatomic potential for the periodic table.Nat. Comput. Sci., 2(11):718–728, 2022

  13. [13]

    L. Chen, J. Rosen, and J. Bj ¨ork. A density functional benchmark for dehydrogenation and dehalogenation reactions on coinage metal surfaces.ChemPhysChem, 26(1):e202400865, Jan. 2025. ISSN 1439-4235, 1439-7641. doi: 10.1002/cphc.202400865. URL https:// chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cphc.202400865

  14. [14]

    V . L. Deringer, M. A. Caro, and G. Cs´anyi. Machine learning interatomic potentials as emerging tools for materials science.Adv. Mater ., 31(46):1902765, 2019

  15. [15]

    M. Dion, H. Rydberg, E. Schr¨oder, D. C. Langreth, and B. I. Lundqvist. Van der waals density functional for general geometries.Phys. Rev. Lett., 92(24):246401, June 2004. ISSN 0031-9007, 1079-7114. doi: 10.1103/PhysRevLett.92.246401. URL https://link.aps.org/doi/10. 1103/PhysRevLett.92.246401

  16. [16]

    Esteves, C

    C. Esteves, C. Allen-Blanchette, A. Makadia, and K. Daniilidis. Learning SO(3) Equivariant Representations With Spherical CNNs.CoRR, 2017. URL http://arxiv.org/abs/1711. 06721

  17. [17]

    X. Fu, B. M. Wood, L. Barroso-Luque, D. S. Levine, M. Gao, M. Dzamba, and C. L. Zitnick. Learning smooth and expressive interatomic potentials for physical property prediction. In International Conference on Machine Learning, pages 17875–17893. PMLR, 2025

  18. [18]

    Fuchs, D

    F. Fuchs, D. Worrall, V . Fischer, and M. Welling. Se(3)-transformers: 3d roto-translation equivariant attention networks.Advances in Neural Information Processing Systems, 33:1970– 1981, 2020

  19. [19]

    Guo and S

    H. Guo and S. G. Lee. Machine learning-guided discovery of thermodynamically stable single-atom catalysts on functionalized MXenes for enhanced oxygen reduction and evolution reactions.J. Mater . Chem. A, 13(28):22730–22744, 2025. ISSN 2050-7488, 2050-7496. doi: 10.1039/D5TA02929E. URLhttps://xlink.rsc.org/?DOI=D5TA02929E

  20. [20]

    I. Hamada. van der waals density functional made accurate.Phys. Rev. B, 89(12):121103,

  21. [21]

    doi: 10.1103/PhysRevB.89.121103

    ISSN 1098-0121, 1550-235X. doi: 10.1103/PhysRevB.89.121103. URL https: //link.aps.org/doi/10.1103/PhysRevB.89.121103

  22. [22]

    Hohenberg and W

    P. Hohenberg and W. Kohn. Inhomogeneous electron gas.Phys. Rev., 136(3B):B864–B871,

  23. [23]

    Inhomogeneous electron gas,

    ISSN 0031-899X. doi: 10.1103/PhysRev.136.B864. URL https://link.aps.org/ doi/10.1103/PhysRev.136.B864

  24. [24]

    A. D. Kaplan, R. Liu, J. Qi, T. W. Ko, B. Deng, J. Riebesell, G. Ceder, K. A. Persson, and S. P. Ong. A foundational potential energy surface dataset for materials, 2025

  25. [25]

    Self-consistent equations including exchange and correlation effects,

    W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation effects. Phys. Rev., 140(4A):A1133–A1138, 1965. ISSN 0031-899X. doi: 10.1103/PhysRev.140.A1133. URLhttps://link.aps.org/doi/10.1103/PhysRev.140.A1133

  26. [26]

    Kresse and J

    G. Kresse and J. Furthm¨uller. Efficient iterative schemes forab initiototal-energy calculations using a plane-wave basis set.Phys. Rev. B, 54(16):11169–11186, Oct. 1996. ISSN 0163- 1829, 1095-3795. doi: 10.1103/PhysRevB.54.11169. URL https://link.aps.org/doi/ 10.1103/PhysRevB.54.11169

  27. [27]

    Kresse and D

    G. Kresse and D. Joubert. From ultrasoft pseudopotentials to the projector augmented-wave method.Phys. Rev. B, 59(3):1758–1775, Jan. 1999. ISSN 0163-1829, 1095-3795. doi: 10.1103/ PhysRevB.59.1758. URLhttps://link.aps.org/doi/10.1103/PhysRevB.59.1758

  28. [28]

    A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, T. Maxson, T. Olsen, L. Pastewka, A. Peterson, C. Rostgaard, J. Schiøtz, O. Sch ¨u...

  29. [29]

    D. S. Levine, M. Shuaibi, E. W. C. Spotte-Smith, M. G. Taylor, M. R. Hasyim, K. Michel, I. Batatia, G. Cs ´anyi, M. Dzamba, P. Eastman, N. C. Frey, X. Fu, V . Gharakhanyan, A. S. Krishnapriyan, J. A. Rackers, S. Raja, A. Rizvi, A. S. Rosen, Z. Ulissi, S. Vargas, C. L. Zitnick, S. M. Blau, and B. M. Wood. The open molecules 2025 (omol25) dataset, evaluatio...

  30. [30]

    Liao and T

    Y .-L. Liao and T. Smidt. Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs.The Eleventh International Conference on Learning Representations, 2023

  31. [31]

    Y .-L. Liao, B. Wood, A. Das, and T. Smidt. EquiformerV2: Improved Equivariant Trans- former for Scaling to Higher-Degree Representations.The Twelfth International Conference on Learning Representations, 2024

  32. [32]

    G. Lin, T. Guo, W. Lin, H. Fan, L. Guo, Z. Zhang, B. Li, J. Wang, H. Ji, W. Song, and J. Fu. Machine learning accelerated screening advanced single-atom anchored MXenes electrocat- alyst for nitrogen fixation.ACS Catal., 15(15):13534–13548, Aug. 2025. ISSN 2155-5435, 2155-5435. doi: 10.1021/acscatal.4c06914. URL https://pubs.acs.org/doi/10.1021/ acscatal.4c06914

  33. [33]

    Malosso, F

    C. Malosso, F. Bigi, P. Pegolo, J. W. Abbott, P. Loche, M. Rossi, M. Ceriotti, and A. Mazitov. High-quality, high-information datasets for universal atomistic machine learning, 2026. URL https://arxiv.org/abs/2603.02089

  34. [34]

    Melnyk, M

    P. Melnyk, M. Felsberg, M. Wadenb¨ack, A. Robinson, and C. Le. O n Learning Deep O(n)- Equivariant Hyperspheres.Proceedings of the 41st International Conference on Machine Learning, 235:35324–35339, 7 2024. URL https://proceedings.mlr.press/v235/ melnyk24a.html

  35. [35]

    Melnyk, A

    P. Melnyk, A. Robinson, M. Felsberg, and M. Wadenb¨ack. TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis.Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5620–5630, 6 2024

  36. [36]

    K. Niu, L. Chi, J. Rosen, and J. Bj¨ork. C–h activation of light alkanes on mxenes predicted by hy- drogen affinity.Phys. Chem. Chem. Phys., 22(33):18622–18630, 2020. ISSN 1463-9076, 1463-

  37. [37]

    URLhttps://xlink.rsc.org/?DOI=D0CP02471F

    doi: 10.1039/D0CP02471F. URLhttps://xlink.rsc.org/?DOI=D0CP02471F

  38. [38]

    K. Niu, L. Chi, J. Rosen, and J. Bj ¨ork. Structure-activity correlation of Ti 2CT2 mxenes for c–h activation.J. Phys. Condens. Matter, 33(23):235201, June 2021. ISSN 0953-8984, 1361- 648X. doi: 10.1088/1361-648X/abe8a1. URL https://iopscience.iop.org/article/ 10.1088/1361-648X/abe8a1

  39. [39]

    K. Niu, J. Bj ¨ork, and J. Rosen. First-principles exploration of Sc- and Y-based MX- enes with halogen terminations.npj 2D Mater . Appl., 9(1):69, 2025. ISSN 2397-

  40. [40]

    URL https://www.nature.com/articles/ s41699-025-00589-7

    doi: 10.1038/s41699-025-00589-7. URL https://www.nature.com/articles/ s41699-025-00589-7

  41. [41]

    Parui, P

    A. Parui, P. Srivastava, and A. K. Singh. Selective reduction of CO 2 on Ti2C(OH)2 MXene through spontaneous crossing of transition states.ACS Appl. Mater . Interfaces, 14(36):40913– 40920, 2022. ISSN 1944-8244, 1944-8252. doi: 10.1021/acsami.2c10213. URL https: //pubs.acs.org/doi/10.1021/acsami.2c10213

  42. [42]

    Passaro and C

    S. Passaro and C. L. Zitnick. Reducing SO(3) convolutions to SO(2) for efficient equivariant GNNs.Proceedings of the 40th International Conference on Machine Learning, 202:27420– 27438, 7 2023. URLhttps://proceedings.mlr.press/v202/passaro23a.html

  43. [43]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al. Pytorch: An imperative style, high-performance deep learning library.Advances in Neural Information Processing Systems, pages 8024–8035, 2019

  44. [44]

    D. Ruhe, J. Brandstetter, and P. Forr ´e. Clifford Group Equivariant Neural Networks. Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https: //openreview.net/forum?id=n84bzMrGUD

  45. [45]

    F. Tran, L. Kalantari, B. Traor ´e, X. Rocquefelte, and P. Blaha. Nonlocal van der Waals functionals for solids: Choosing an appropriate one.Phys. Rev. Materials, 3(6):063602, June

  46. [46]

    doi: 10.1103/PhysRevMaterials.3.063602

    ISSN 2475-9953. doi: 10.1103/PhysRevMaterials.3.063602. URL https://link.aps. org/doi/10.1103/PhysRevMaterials.3.063602. 12

  47. [47]

    R. Tran, J. Lan, M. Shuaibi, B. M. Wood, S. Goyal, A. Das, J. Heras-Domingo, A. Kolluru, A. Rizvi, N. Shoghi, A. Sriram, F. Therrien, J. Abed, O. V oznyy, E. H. Sargent, Z. Ulissi, and C. L. Zitnick. The open catalyst 2022 (oc22) dataset and challenges for oxide electrocatalysts. ACS Catal., 13(5):3066–3084, 2023. doi: 10.1021/acscatal.2c05426. URL https:...

  48. [48]

    Van Gool, T

    L. Van Gool, T. Moons, E. Pauwels, and A. Oosterlinck. Vision and lie’s approach to invariance. Image and vision computing, 13(4):259–277, 1995

  49. [49]

    G. Wang, C. Wang, X. Zhang, Z. Li, J. Zhou, and Z. Sun. Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations. Iscience, 27(5), 2024

  50. [50]

    Weiler, M

    M. Weiler, M. Geiger, M. Welling, W. Boomsma, and T. S. Cohen. 3D steerable CNNs: Learning rotationally equivariant features in volumetric data.Advances in Neural Information Processing Systems, pages 10381–10392, 2018

  51. [51]

    Weiler, P

    M. Weiler, P. Forr´e, E. Verlinde, and M. Welling. Equivariant and coordinate independent convolutional networks.A Gauge Field Theory of Neural Networks, page 110, 2023

  52. [52]

    H. Yang, C. Hu, Y . Zhou, X. Liu, Y . Shi, J. Li, G. Li, Z. Chen, S. Chen, C. Zeni, et al. MatterSim: A deep learning atomistic model across elements, temperatures and pressures.arXiv preprint arXiv:2405.04967, 2024

  53. [53]

    Y . Zhou, S. Hu, X. Zhang, H. Wang, G. Tan, and W. Jia. MatRIS: Toward reliable and efficient pretrained machine learning interatomic potentials. InThe F ourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum? id=5xBT5Ziute. 13 A Reference Energy in DFT Dilemma In principle, density functional theory (DFT) p...