Time-reversal equivariant neural network potential and Hamiltonian for magnetic materials

: This work presents Time-reversal Equivariant Neural Network (TENN) framework. With TENN, the time-reversal symmetry is considered in the equivariant neural network (ENN), which generalizes the ENN to consider physical quantities related to time-reversal symmetry such as spin and velocity of atoms. TENN-e3, as the time-reversal-extension of E(3) equivariant neural network, is developed to keep the Time-reversal E(3) equivariant with consideration of whether to include the spin-orbit effect for both collinear and non-collinear magnetic moments situations for magnetic material. TENN-e3 can construct spin neural network potential and the Hamiltonian of magnetic material from ab-initio calculations. Time-reversal-E(3)-equivariant convolutions for interactions of spinor and geometric tensors are employed in TENN-e3. Compared to the popular ENN, TENN-e3 can describe the complex spin-lattice coupling with high accuracy and keep time-reversal symmetry which is not preserved in the existing E(3)-equivariant model. Also, the Hamiltonian of magnetic material with time-reversal symmetry can be built with TENN-e3. TENN paves a new way to spin-lattice dynamics simulations over long-time scales and electronic structure calculations of large-scale magnetic materials.

[1]  Simon L. Batzner,et al.  Learning local equivariant representations for large-scale atomistic dynamics , 2022, Nature Communications.

[2]  M. Geiger,et al.  e3nn: Euclidean Neural Networks , 2022, ArXiv.

[3]  X. Gong,et al.  Graph Neural Network Potential for Magnetic Materials , 2022, ArXiv.

[4]  S. Sanvito,et al.  Spectral neighbor representation for vector fields: Machine learning potentials including spin , 2022, Physical Review B.

[5]  Jingli Luo,et al.  Toward Excellence of Electrocatalyst Design by Emerging Descriptor‐Oriented Machine Learning , 2022, Advanced Functional Materials.

[6]  Weile Jia,et al.  Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms , 2022, PPoPP.

[7]  J. Kermode,et al.  Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models , 2021, npj Computational Materials.

[8]  T. Jaakkola,et al.  Crystal Diffusion Variational Autoencoder for Periodic Material Generation , 2021, ICLR.

[9]  Michele Ceriotti,et al.  Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties. , 2021, The Journal of chemical physics.

[10]  Steven J. Plimpton,et al.  LAMMPS - A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales , 2021, Computer Physics Communications.

[11]  Yong Xu,et al.  Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation , 2021, Nature Computational Science.

[12]  Jonathan P. Mailoa,et al.  E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials , 2021, Nature Communications.

[13]  A. Shapeev,et al.  Magnetic Moment Tensor Potentials for collinear spin-polarized materials reproduce different magnetic states of bcc Fe , 2020, npj Computational Materials.

[14]  Matthias Rupp,et al.  Unified representation of molecules and crystals for machine learning , 2017, Mach. Learn. Sci. Technol..

[15]  S. Botti,et al.  Crystal graph attention networks for the prediction of stable materials , 2021, Science advances.

[16]  Tobias Pfaff,et al.  Learning ground states of quantum Hamiltonians with graph networks , 2021, ArXiv.

[17]  Jiucheng Cheng,et al.  A geometric-information-enhanced crystal graph network for predicting properties of materials , 2021, Communications Materials.

[18]  Mario Barbatti,et al.  Choosing the right molecular machine learning potential , 2021, Chemical science.

[19]  H. Xiang,et al.  Nature of spin-lattice coupling in two-dimensional CrI3 and CrGeTe3 , 2021, Science China Physics, Mechanics & Astronomy.

[20]  Michael Gastegger,et al.  SE(3)-equivariant prediction of molecular wavefunctions and electronic densities , 2021, NeurIPS.

[21]  Brian L. DeCost,et al.  Atomistic Line Graph Neural Network for improved materials property predictions , 2021, npj Computational Materials.

[22]  Florian Becker,et al.  GemNet: Universal Directional Graph Neural Networks for Molecules , 2021, NeurIPS.

[23]  A. Nakano,et al.  Dielectric Constant of Liquid Water Determined with Neural Network Quantum Molecular Dynamics. , 2021, Physical review letters.

[24]  J. Behler,et al.  High-dimensional neural network potentials for magnetic systems using spin-dependent atom-centered symmetry functions , 2021, npj Computational Materials.

[25]  Longfei Zhang,et al.  Inverse design of glass structure with deep graph neural networks , 2021, Nature Communications.

[26]  Edirisuriya M. D. Siriwardane,et al.  AlphaCrystal: Contact map based crystal structure prediction using deep learning , 2021, 2102.01620.

[27]  F. Liu,et al.  Atomistic Mechanism Underlying the Si(111)-(7×7) Surface Reconstruction Revealed by Artificial Neural-Network Potential. , 2020, Physical review letters.

[28]  E Weinan,et al.  86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy , 2020, Comput. Phys. Commun..

[29]  Johannes T. Margraf,et al.  Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules , 2020, ArXiv.

[30]  Qianxiao Li,et al.  Inverse design of crystals using generalized invertible crystallographic representation , 2020, ArXiv.

[31]  Stephan Günnemann,et al.  Directional Message Passing for Molecular Graphs , 2020, ICLR.

[32]  Filippo Federici Canova,et al.  DScribe: Library of Descriptors for Machine Learning in Materials Science , 2019, Comput. Phys. Commun..

[33]  G. R. Schleder,et al.  From DFT to machine learning: recent approaches to materials science–a review , 2019, Journal of Physics: Materials.

[34]  Georg Kresse,et al.  On-the-fly machine learning force field generation: Application to melting points , 2019, Physical Review B.

[35]  Naftali Tishby,et al.  Machine learning and the physical sciences , 2019, Reviews of Modern Physics.

[36]  Chi Chen,et al.  Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals , 2018, Chemistry of Materials.

[37]  Justin S. Smith,et al.  Machine learning for molecular dynamics with strongly correlated electrons , 2018, Physical Review B.

[38]  Zhen Lin,et al.  Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network , 2018, NeurIPS.

[39]  E Weinan,et al.  End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems , 2018, NeurIPS.

[40]  Li Li,et al.  Tensor Field Networks: Rotation- and Translation-Equivariant Neural Networks for 3D Point Clouds , 2018, ArXiv.

[41]  Aidan P. Thompson,et al.  Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics , 2018, J. Comput. Phys..

[42]  K-R Müller,et al.  SchNet - A deep learning architecture for molecules and materials. , 2017, The Journal of chemical physics.

[43]  Jeffrey C Grossman,et al.  Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. , 2017, Physical review letters.

[44]  Cormac Toher,et al.  Universal fragment descriptors for predicting properties of inorganic crystals , 2016, Nature Communications.

[45]  A. Choudhary,et al.  Perspective: Materials informatics and big data: Realization of the “fourth paradigm” of science in materials science , 2016 .

[46]  Zhenwei Li,et al.  Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. , 2015, Physical review letters.

[47]  J. Behler.  Atom-centered symmetry functions for constructing high-dimensional neural network potentials. , 2011, The Journal of chemical physics.

[48]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[49]  O. Isayev,et al.  ANI-1: an extensible neural network potential with DFT accuracy at force fi eld computational cost † , 2017 .