Knowledge-transfer-based cost-effective search for interface structures: A case study on fcc-Al [110] tilt grain boundary

Determining the atomic configuration of an interface is one of the most important issues in materials science research. Although theoretical simulations are effective tools, an exhaustive search is computationally prohibitive due to the high degrees of freedom of the interface structure. In the interface structure search, multiple energy surfaces created by a variety of orientation angles need to be explored, and the necessary computational costs for different angles vary substantially owing to significant variations in the supercell sizes. In this paper, we introduce two machine-learning concepts, called transfer learning and cost-sensitive search, to the interface-structure search. As a case study, we demonstrate the effectiveness of our method, called cost-sensitive multi-task Bayesian optimization (CMB), using the fcc-Al [110] tilt grain boundary. Four microscopic parameters, the three-dimensional rigid body translation, and the number of atomic columns, are optimized by transferring knowledge of energy surfaces among different orientation angles. We show that transferring knowledge of different energy surfaces can accelerate the structure search, and that considering the cost variations further improves the total efficiency.

[1]  Shin Kiyohara,et al.  Bayesian optimization for efficient determination of metal oxide grain boundary structures , 2017 .

[2]  Atsuto Seko,et al.  Prediction of Low-Thermal-Conductivity Compounds with First-Principles Anharmonic Lattice-Dynamics Calculations and Bayesian Optimization. , 2015, Physical review letters.

[3]  Bernd Kabius,et al.  Electron microscopy image enhanced , 1998, Nature.

[4]  D. Warner,et al.  A continuously growing web-based interface structure databank , 2012 .

[5]  V. Vítek,et al.  On the structure of tilt grain boundaries in cubic metals II. Asymmetrical tilt boundaries , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6]  Arash Dehghan Banadaki,et al.  A simple faceting model for the interfacial and cleavage energies of Σ3 grain boundaries in the complete boundary plane orientation space , 2016 .

[7]  Qiang Yang,et al.  A Survey on Transfer Learning , 2010, IEEE Transactions on Knowledge and Data Engineering.

[8]  V. Vítek,et al.  On the structure of tilt grain boundaries in cubic metals I. Symmetrical tilt boundaries , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[9]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[10]  Koji Tsuda,et al.  Acceleration of stable interface structure searching using a kriging approach , 2016 .

[11]  F. Flores,et al.  Interfaces in crystalline materials , 1994, Thin Film Physics and Applications.

[12]  Masayuki Karasuyama,et al.  Machine-learning-based selective sampling procedure for identifying the low-energy region in a potential energy surface: A case study on proton conduction in oxides , 2015, 1512.00623.

[13]  V. Vítek,et al.  On the structure of tilt grain boundaries in cubic metals. III. Generalizations of the structural study and implications for the properties of grain boundaries , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[14]  Masayuki Karasuyama,et al.  Fast and scalable prediction of local energy at grain boundaries: machine-learning based modeling of first-principles calculations , 2017 .

[15]  Y. Ikuhara Grain boundary atomic structures and light-element visualization in ceramics: combination of Cs-corrected scanning transmission electron microscopy and first-principles calculations. , 2011, Journal of electron microscopy.

[16]  Benjamin W. Wah,et al.  Editorial: Two Named to Editorial Board of IEEE Transactions on Knowledge and Data Engineering , 1996 .

[17]  Koji Tsuda,et al.  COMBO: An efficient Bayesian optimization library for materials science , 2016 .

[18]  Christopher K. I. Williams,et al.  Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) , 2005 .

[19]  Gábor Csányi,et al.  Comparing molecules and solids across structural and alchemical space. , 2015, Physical chemistry chemical physics : PCCP.

[20]  Eric R. Homer,et al.  Discovering the building blocks of atomic systems using machine learning: application to grain boundaries , 2017, npj Computational Materials.

[21]  高橋 秀俊,et al.  Japanese Journal of Applied Physics , 1962, Nature.

[22]  M. Finnis,et al.  The Structure of Grain Boundaries in Strontium Titanate: Theory, Simulation, and Electron Microscopy , 2010 .

[23]  David L. Olmsted,et al.  Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy , 2009 .

[24]  A. Sutton,et al.  Rules for combining structural units of grain boundaries , 1990 .

[25]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[26]  Alexander Tropsha,et al.  Materials Informatics , 2019, J. Chem. Inf. Model..

[27]  Michael J. Mehl,et al.  Interatomic potentials for monoatomic metals from experimental data and ab initio calculations , 1999 .

[28]  D. Muller,et al.  Electron microscopy: probing the atomic structure and chemistry of grain boundaries, interfaces and defects , 1999 .

[29]  D. Wolf Correlation between energy and volume expansion for grain boundaries in FCC metals , 1989 .