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A Euclidean transformer for fast and stable machine learned force fields

Author

Listed:
  • J. Thorben Frank

    (TU Berlin
    Berlin Institute for the Foundations of Learning and Data)

  • Oliver T. Unke

    (Google DeepMind)

  • Klaus-Robert Müller

    (TU Berlin
    Berlin Institute for the Foundations of Learning and Data
    Google DeepMind
    Korea University)

  • Stefan Chmiela

    (TU Berlin
    Berlin Institute for the Foundations of Learning and Data)

Abstract

Recent years have seen vast progress in the development of machine learned force fields (MLFFs) based on ab-initio reference calculations. Despite achieving low test errors, the reliability of MLFFs in molecular dynamics (MD) simulations is facing growing scrutiny due to concerns about instability over extended simulation timescales. Our findings suggest a potential connection between robustness to cumulative inaccuracies and the use of equivariant representations in MLFFs, but the computational cost associated with these representations can limit this advantage in practice. To address this, we propose a transformer architecture called SO3krates that combines sparse equivariant representations (Euclidean variables) with a self-attention mechanism that separates invariant and equivariant information, eliminating the need for expensive tensor products. SO3krates achieves a unique combination of accuracy, stability, and speed that enables insightful analysis of quantum properties of matter on extended time and system size scales. To showcase this capability, we generate stable MD trajectories for flexible peptides and supra-molecular structures with hundreds of atoms. Furthermore, we investigate the PES topology for medium-sized chainlike molecules (e.g., small peptides) by exploring thousands of minima. Remarkably, SO3krates demonstrates the ability to strike a balance between the conflicting demands of stability and the emergence of new minimum-energy conformations beyond the training data, which is crucial for realistic exploration tasks in the field of biochemistry.

Suggested Citation

  • J. Thorben Frank & Oliver T. Unke & Klaus-Robert Müller & Stefan Chmiela, 2024. "A Euclidean transformer for fast and stable machine learned force fields," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-50620-6
    DOI: 10.1038/s41467-024-50620-6
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    References listed on IDEAS

    as
    1. Kristof T. Schütt & Farhad Arbabzadah & Stefan Chmiela & Klaus R. Müller & Alexandre Tkatchenko, 2017. "Quantum-chemical insights from deep tensor neural networks," Nature Communications, Nature, vol. 8(1), pages 1-8, April.
    2. Albert Musaelian & Simon Batzner & Anders Johansson & Lixin Sun & Cameron J. Owen & Mordechai Kornbluth & Boris Kozinsky, 2023. "Learning local equivariant representations for large-scale atomistic dynamics," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    3. Huziel E. Sauceda & Luis E. Gálvez-González & Stefan Chmiela & Lauro Oliver Paz-Borbón & Klaus-Robert Müller & Alexandre Tkatchenko, 2022. "BIGDML—Towards accurate quantum machine learning force fields for materials," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    4. Simon Batzner & Albert Musaelian & Lixin Sun & Mario Geiger & Jonathan P. Mailoa & Mordechai Kornbluth & Nicola Molinari & Tess E. Smidt & Boris Kozinsky, 2022. "E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    5. Yusong Wang & Tong Wang & Shaoning Li & Xinheng He & Mingyu Li & Zun Wang & Nanning Zheng & Bin Shao & Tie-Yan Liu, 2024. "Enhancing geometric representations for molecules with equivariant vector-scalar interactive message passing," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    6. Oliver T. Unke & Stefan Chmiela & Michael Gastegger & Kristof T. Schütt & Huziel E. Sauceda & Klaus-Robert Müller, 2021. "SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects," Nature Communications, Nature, vol. 12(1), pages 1-14, December.
    7. Tsz Wai Ko & Jonas A. Finkler & Stefan Goedecker & Jörg Behler, 2021. "A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    8. Stefan Chmiela & Huziel E. Sauceda & Klaus-Robert Müller & Alexandre Tkatchenko, 2018. "Towards exact molecular dynamics simulations with machine-learned force fields," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
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