mlsanityData to 14 Oct 2026

A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures

arXiv 2503.05771 ↗First posted 25 Feb 2025cs.LG cond-mat.mtrl-sci physics.comp-phcited by 4

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Abstract (arXiv)

Machine learning interatomic potentials (MLIPs) can predict energy, force, and stress of materials and enable a wide range of downstream discovery tasks. A key design choice in MLIPs involves the trade-off between invariant and equivariant architectures. Invariant models offer computational efficiency but may not perform as well, especially when predicting high-order outputs. In contrast, equivariant models can capture high-order symmetries, but are computationally expensive. In this work, we propose HIENet, a hybrid invariant-equivariant materials interatomic potential model that integrates both invariant and equivariant message passing layers, while provably satisfying key physical constraints. HIENet achieves state-of-the-art performance with considerable computational speedups over prior models. Experimental results on both common benchmarks and downstream materials discovery tasks demonstrate the efficiency and effectiveness of HIENet.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 19 of its 64 references that are in the map. First posted on arXiv 25 Feb 2025.

Builds on

19 of 64 references.

References · 19

  1. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  2. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  3. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  4. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  5. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  6. 2020Directional Message Passing for Molecular Graphscited by 561
  7. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  8. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  9. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  10. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
  11. 2021Spherical Message Passing for 3D Graph Networkscited by 168
  12. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
7 more
  1. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  2. 2024Open Materials 2024 (OMat24) Inorganic Materials Dataset and Modelscited by 52
  3. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  4. 2023Efficient Approximations of Complete Interatomic Potentials for Crystal Property Predictioncited by 37
  5. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  6. 2024Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Predictioncited by 6
  7. 2024Accelerating CALPHAD-based Phase Diagram Predictions in Complex Alloys Using Universal Machine Learning Potentials: Opportunities and Challengescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Training a Foundation Model for Materials on a Budgetcited by 6
  2. 2026PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentialscited by 6
  3. 2026From Evaluation to Design: Using Potential Energy Surface Smoothness Metrics to Guide Machine Learning Interatomic Potential Architecturescited by 1
  4. 2026A strategic roadmap for an atomistic machine-learning ecosystemcited by 0