Machine learning properties of binary wurtzite superlattices

The burgeoning paradigm of high-throughput computations and materials informatics brings new opportunities in terms of targeted materials design and discovery. The discovery process can be significantly accelerated and streamlined if one can learn effectively from available knowledge and past data to predict materials properties efficiently. Indeed, a very active area in materials science research is to develop machine learning based methods that can deliver automated and cross-validated predictive models using either already available materials data or new data generated in a targeted manner. In the present contribution, we show that fast and accurate predictions of a wide range of properties of binary wurtzite superlattices, formed by a diverse set of chemistries, can be made by employing state-of-the-art statistical learning methods trained on quantum mechanical computations in combination with a judiciously chosen numerical representation to encode materials’ similarity. These surrogate learning models then allow for efficient screening of vast chemical spaces by providing instant predictions of the targeted properties. Moreover, the models can be systematically improved in an adaptive manner, incorporate properties computed at different levels of fidelities and are naturally amenable to inverse materials design strategies. While the learning approach to make predictions for a wide range of properties (including structural, elastic and electronic properties) is demonstrated here for a specific example set containing more than 1200 binary wurtzite superlattices, the adopted framework is equally applicable to other classes of materials as well.

[1]  Andrea Widener,et al.  Materials Genome Initiative , 2014 .

[2]  Lars Samuelson,et al.  Strain mapping in free-standing heterostructured wurtzite InAs/InP nanowires , 2007 .

[3]  J. Nørskov,et al.  Chemical bonding at surfaces and interfaces , 2008 .

[4]  J. Vybíral,et al.  Big data of materials science: critical role of the descriptor. , 2014, Physical review letters.

[5]  Felix A Faber,et al.  Machine Learning Energies of 2 Million Elpasolite (ABC_{2}D_{6}) Crystals. , 2015, Physical review letters.

[6]  J Behler,et al.  Representing potential energy surfaces by high-dimensional neural network potentials , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[7]  Chiho Kim,et al.  From Organized High-Throughput Data to Phenomenological Theory using Machine Learning: The Example of Dielectric Breakdown , 2016 .

[8]  S. M. Sze,et al.  Physics of semiconductor devices , 1969 .

[9]  Matthias Rupp,et al.  Machine learning for quantum mechanics in a nutshell , 2015 .

[10]  Weitao Yang,et al.  Fractional charge perspective on the band gap in density-functional theory , 2007, 0708.3175.

[11]  Marco Buongiorno Nardelli,et al.  The high-throughput highway to computational materials design. , 2013, Nature materials.

[12]  Rampi Ramprasad,et al.  Adaptive machine learning framework to accelerate ab initio molecular dynamics , 2015 .

[13]  Haoyan Huo,et al.  Unified Representation for Machine Learning of Molecules and Crystals , 2017 .

[14]  Wei Chen,et al.  Predicting defect behavior in B2 intermetallics by merging ab initio modeling and machine learning , 2016, npj Computational Materials.

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

[16]  Chiho Kim,et al.  Machine learning in materials informatics: recent applications and prospects , 2017, npj Computational Materials.

[17]  James Theiler,et al.  Accelerated search for materials with targeted properties by adaptive design , 2016, Nature Communications.

[18]  Zhongqiu Wang,et al.  Nanobelts, Nanocombs, and Nanowindmills of Wurtzite ZnS , 2003 .

[19]  Wei Chen,et al.  A Statistical Learning Framework for Materials Science: Application to Elastic Moduli of k-nary Inorganic Polycrystalline Compounds , 2016, Scientific Reports.

[20]  Christopher M Wolverton,et al.  High-Throughput Computational Screening of Perovskites for Thermochemical Water Splitting Applications , 2016 .

[21]  Edward O. Pyzer-Knapp,et al.  Space-Filling Curves as a Novel Crystal Structure Representation for Machine Learning Models , 2016 .

[22]  Marvin J. Weber,et al.  Handbook of Optical Materials , 2002 .

[23]  Rampi Ramprasad,et al.  Learning scheme to predict atomic forces and accelerate materials simulations , 2015, 1505.02701.

[24]  Chiho Kim,et al.  Finding New Perovskite Halides via Machine Learning , 2016, Front. Mater..

[25]  Alok Choudhary,et al.  Combinatorial screening for new materials in unconstrained composition space with machine learning , 2014 .

[26]  M. Schlüter,et al.  Density-Functional Theory of the Energy Gap , 1983 .

[27]  T. Karzig,et al.  Exponential lifetime improvement in topological quantum memories , 2015, 1512.04528.

[28]  Arun Mannodi-Kanakkithodi,et al.  Machine Learning Strategy for Accelerated Design of Polymer Dielectrics , 2016, Scientific Reports.

[29]  S. Broderick,et al.  Computational discovery of stable M 2 A X phases , 2016 .

[30]  Phillip B. Messersmith,et al.  Bioinspired antifouling polymers , 2005 .

[31]  Ryan O'Hayre,et al.  Predicting Density Functional Theory Total Energies and Enthalpies of Formation of Metal—Nonmetal Compounds by Linear Regression , 2016 .

[32]  S. Liou,et al.  The electrostatic coupling of longitudinal optical phonon and plasmon in wurtzite InN thin films , 2010 .

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

[34]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.

[35]  L. Weston,et al.  Machine learning the band gap properties of kesterite I2−II−IV−V4 quaternary compounds for photovoltaics applications , 2017, Physical Review Materials.

[36]  Richard M. Martin Electronic Structure: Frontmatter , 2004 .

[37]  Kristian Sommer Thygesen,et al.  Computational 2D Materials Database: Electronic Structure of Transition-Metal Dichalcogenides and Oxides , 2015, 1506.02841.

[38]  M. Koguchi,et al.  Crystal Structure Change of GaAs and InAs Whiskers from Zinc-Blende to Wurtzite Type , 1992 .

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

[40]  Ekin D. Cubuk,et al.  Representations in neural network based empirical potentials. , 2017, The Journal of chemical physics.

[41]  Chiho Kim,et al.  Machine Learning and Materials Informatics: Recent Applications and Prospects , 2017 .

[42]  Stefano Curtarolo,et al.  How the Chemical Composition Alone Can Predict Vibrational Free Energies and Entropies of Solids , 2017, 1703.02309.

[43]  Somnath Datta,et al.  Informatics-aided bandgap engineering for solar materials , 2014 .

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

[45]  S. Sze,et al.  Physics of Semiconductor Devices: Sze/Physics , 2006 .

[46]  R. Martin,et al.  Electronic Structure: Basic Theory and Practical Methods , 2004 .

[47]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[48]  O. Madelung Semiconductors: Data Handbook , 2003 .

[49]  Sanguthevar Rajasekaran,et al.  Accelerating materials property predictions using machine learning , 2013, Scientific Reports.

[50]  James E. Gubernatis,et al.  Multi-fidelity machine learning models for accurate bandgap predictions of solids , 2017 .

[51]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[52]  McGill,et al.  Commutativity of the GaAs/AlAs(100) band offset. , 1988, Physical review. B, Condensed matter.

[53]  Rampi Ramprasad,et al.  Machine Learning Force Fields: Construction, Validation, and Outlook , 2016, 1610.02098.

[54]  LeSarRichard Materials informatics: An emerging technology for materials development , 2009 .

[55]  Atsuto Seko,et al.  Machine learning with systematic density-functional theory calculations: Application to melting temperatures of single- and binary-component solids , 2013, 1310.1546.

[56]  Xiaoning Qian,et al.  Accelerated search for BaTiO3-based piezoelectrics with vertical morphotropic phase boundary using Bayesian learning , 2016, Proceedings of the National Academy of Sciences.

[57]  Weitao Yang,et al.  Localization and delocalization errors in density functional theory and implications for band-gap prediction. , 2007, Physical review letters.

[58]  Richard LeSar,et al.  Materials informatics: An emerging technology for materials development , 2009, Stat. Anal. Data Min..

[59]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[60]  Roy E. Welsch,et al.  Descriptors of Oxygen-Evolution Activity for Oxides: A Statistical Evaluation , 2016 .

[61]  Kristian Sommer Thygesen,et al.  Stability and bandgaps of layered perovskites for one- and two-photon water splitting , 2013 .

[62]  James E. Gubernatis,et al.  Structure classification and melting temperature prediction in octet AB solids via machine learning , 2015 .

[63]  Gerbrand Ceder,et al.  Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species , 2017, 1706.06293.

[64]  Walter Kohn,et al.  Nobel Lecture: Electronic structure of matter-wave functions and density functionals , 1999 .

[65]  G. Pilania,et al.  Machine learning bandgaps of double perovskites , 2016, Scientific Reports.

[66]  Krishna Rajan,et al.  Application-Driven Data Analysis , 2009 .

[67]  M. Rupp,et al.  Machine learning of molecular electronic properties in chemical compound space , 2013, 1305.7074.

[68]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[69]  Alán Aspuru-Guzik,et al.  Accelerated computational discovery of high-performance materials for organic photovoltaics by means of cheminformatics , 2011 .

[70]  Gustavo E. Scuseria,et al.  Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)] , 2006 .

[71]  Zheng Li,et al.  Feature engineering of machine-learning chemisorption models for catalyst design , 2017 .

[72]  R. Kondor,et al.  On representing chemical environments , 2012, 1209.3140.

[73]  Arun Mannodi-Kanakkithodi,et al.  Accelerated materials property predictions and design using motif-based fingerprints , 2015, 1503.07503.

[74]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[75]  Li Li,et al.  Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals , 2015, ArXiv.

[76]  Tom K Woo,et al.  Rapid and Accurate Machine Learning Recognition of High Performing Metal Organic Frameworks for CO2 Capture. , 2014, The journal of physical chemistry letters.

[77]  S. Ong,et al.  New opportunities for materials informatics: Resources and data mining techniques for uncovering hidden relationships , 2016 .

[78]  Anubhav Jain,et al.  Computational predictions of energy materials using density functional theory , 2016 .

[79]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[80]  G. Pilania,et al.  First-principles identification of novel double perovskites for water-splitting applications , 2017, Journal of Materials Science.

[81]  Tim Mueller,et al.  Machine Learning in Materials Science , 2016 .

[82]  Engineering,et al.  Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques , 2016 .

[83]  B. Uberuaga,et al.  Using Machine Learning To Identify Factors That Govern Amorphization of Irradiated Pyrochlores , 2016, 1607.06789.

[84]  Chiho Kim,et al.  Machine Learning Assisted Predictions of Intrinsic Dielectric Breakdown Strength of ABX3 Perovskites , 2016 .

[85]  O. A. von Lilienfeld,et al.  Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity. , 2016, The Journal of chemical physics.

[86]  Ridwan Sakidja,et al.  A genomic approach to the stability, elastic, and electronic properties of the MAX phases , 2014 .

[87]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[88]  Atsuto Seko,et al.  Descriptors for Machine Learning of Materials Data , 2017, 1709.01666.