DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Robust data-driven approach for predicting the configurational energy of high entropy alloys

Abstract

High entropy alloys (HEAs) are promising next-generation materials due to their various excellent properties. To understand these properties, it's necessary to characterize the chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed for the accurate and efficient prediction of configurational energy of high entropy alloys. The recently proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary truncation of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence when data is sparse.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1570041
Alternate Identifier(s):
OSTI ID: 1619044
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Published Article
Journal Name:
Materials & Design
Additional Journal Information:
Journal Name: Materials & Design Journal Volume: 185 Journal Issue: C; Journal ID: ISSN 0264-1275
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English
Subject:
36 MATERIALS SCIENCE; High entropy alloys; Uncertainty quantification; Bayesian regression; Bayesian information criterion; First-principles calculations; Machine learning

Citation Formats

Zhang, Jiaxin, Liu, Xianglin, Bi, Sirui, Yin, Junqi, Zhang, Guannan, and Eisenbach, Markus. Robust data-driven approach for predicting the configurational energy of high entropy alloys. United Kingdom: N. p., 2020. Web. doi:10.1016/j.matdes.2019.108247.
Zhang, Jiaxin, Liu, Xianglin, Bi, Sirui, Yin, Junqi, Zhang, Guannan, & Eisenbach, Markus. Robust data-driven approach for predicting the configurational energy of high entropy alloys. United Kingdom. https://doi.org/10.1016/j.matdes.2019.108247
Zhang, Jiaxin, Liu, Xianglin, Bi, Sirui, Yin, Junqi, Zhang, Guannan, and Eisenbach, Markus. Wed . "Robust data-driven approach for predicting the configurational energy of high entropy alloys". United Kingdom. https://doi.org/10.1016/j.matdes.2019.108247.
@article{osti_1570041,
title = {Robust data-driven approach for predicting the configurational energy of high entropy alloys},
author = {Zhang, Jiaxin and Liu, Xianglin and Bi, Sirui and Yin, Junqi and Zhang, Guannan and Eisenbach, Markus},
abstractNote = {High entropy alloys (HEAs) are promising next-generation materials due to their various excellent properties. To understand these properties, it's necessary to characterize the chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed for the accurate and efficient prediction of configurational energy of high entropy alloys. The recently proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary truncation of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence when data is sparse.},
doi = {10.1016/j.matdes.2019.108247},
journal = {Materials & Design},
number = C,
volume = 185,
place = {United Kingdom},
year = {2020},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.matdes.2019.108247

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Square lattice with effective pair interaction highlighted. (a) The nearest-neighbor pair is marked in blue, while the next nearest-neighbor pair is marked in yellow; (b) the pair marked in green, pink and red correspond to the 3rd, 4th and 5th neighbor respectively. Equivalent interacted pairs (same distance) aremore » marked in the same color.« less

Save / Share:

Works referenced in this record:

From Organized High-Throughput Data to Phenomenological Theory using Machine Learning: The Example of Dielectric Breakdown
journal, February 2016


Investigating phase formations in cast AlFeCoNiCu high entropy alloys by combination of computational modeling and experiments
journal, August 2017


Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures
journal, September 2018


Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy
journal, May 2017


Bayesian uncertainty quantification in the evaluation of alloy properties with the cluster expansion method
journal, November 2014

  • Kristensen, Jesper; Zabaras, Nicholas J.
  • Computer Physics Communications, Vol. 185, Issue 11
  • DOI: 10.1016/j.cpc.2014.07.013

Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys
journal, May 2011


Efficient Monte Carlo resampling for probability measure changes from Bayesian updating
journal, January 2019


Estimating mechanical properties from spherical indentation using Bayesian approaches
journal, June 2018


Machine-learning the configurational energy of multicomponent crystalline solids
journal, November 2018


Microstructures and properties of high-entropy alloys
journal, April 2014


Microstructural origins of the high mechanical damage tolerance of NbTaMoW refractory high-entropy alloy thin films
journal, May 2019


Generalized cluster description of multicomponent systems
journal, November 1984

  • Sanchez, J. M.; Ducastelle, F.; Gratias, D.
  • Physica A: Statistical Mechanics and its Applications, Vol. 128, Issue 1-2
  • DOI: 10.1016/0378-4371(84)90096-7

Automating first-principles phase diagram calculations
journal, August 2002


High-Entropy Alloys: A Critical Review
journal, April 2014


Hybrid Monte Carlo/Molecular Dynamics Simulation of a Refractory Metal High Entropy Alloy
journal, October 2013

  • Widom, Michael; Huhn, W. P.; Maiti, S.
  • Metallurgical and Materials Transactions A, Vol. 45, Issue 1
  • DOI: 10.1007/s11661-013-2000-8

Short-Range Order in High Entropy Alloys: Theoretical Formulation and Application to Mo-Nb-Ta-V-W System
journal, July 2017

  • Fernández-Caballero, A.; Wróbel, J. S.; Mummery, P. M.
  • Journal of Phase Equilibria and Diffusion, Vol. 38, Issue 4
  • DOI: 10.1007/s11669-017-0582-3

Molecular Dynamics with On-the-Fly Machine Learning of Quantum-Mechanical Forces
journal, March 2015


Metastable high-entropy dual-phase alloys overcome the strength–ductility trade-off
journal, May 2016

  • Li, Zhiming; Pradeep, Konda Gokuldoss; Deng, Yun
  • Nature, Vol. 534, Issue 7606
  • DOI: 10.1038/nature17981

The generalization of Latin hypercube sampling
journal, April 2016


Computational modeling of high-entropy alloys: Structures, thermodynamics and elasticity
journal, October 2017

  • Gao, Michael C.; Gao, Pan; Hawk, Jeffrey A.
  • Journal of Materials Research, Vol. 32, Issue 19
  • DOI: 10.1557/jmr.2017.366

Machine learning phases of matter
journal, February 2017

  • Carrasquilla, Juan; Melko, Roger G.
  • Nature Physics, Vol. 13, Issue 5
  • DOI: 10.1038/nphys4035

Machine-learning phase prediction of high-entropy alloys
journal, May 2019


Bayesian approach to cluster expansions
journal, July 2009


Evolutionary approach for determining first-principles hamiltonians
journal, April 2005

  • Hart, Gus L. W.; Blum, Volker; Walorski, Michael J.
  • Nature Materials, Vol. 4, Issue 5
  • DOI: 10.1038/nmat1374

Compressive sensing as a paradigm for building physics models
journal, January 2013


Accelerating materials property predictions using machine learning
journal, September 2013

  • Pilania, Ghanshyam; Wang, Chenchen; Jiang, Xun
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep02810

A Theory of Cooperative Phenomena
journal, March 1951


Inverse molecular design using machine learning: Generative models for matter engineering
journal, July 2018


CLEASE: a versatile and user-friendly implementation of cluster expansion method
journal, May 2019

  • Chang, Jin Hyun; Kleiven, David; Melander, Marko
  • Journal of Physics: Condensed Matter, Vol. 31, Issue 32
  • DOI: 10.1088/1361-648X/ab1bbc

Using deep neural network with small dataset to predict material defects
journal, January 2019


Quantifying uncertainties in first-principles alloy thermodynamics using cluster expansions
journal, October 2016

  • Aldegunde, Manuel; Zabaras, Nicholas; Kristensen, Jesper
  • Journal of Computational Physics, Vol. 323
  • DOI: 10.1016/j.jcp.2016.07.016

Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes
journal, May 2004

  • Yeh, J.-W.; Chen, S.-K.; Lin, S.-J.
  • Advanced Engineering Materials, Vol. 6, Issue 5, p. 299-303
  • DOI: 10.1002/adem.200300567

Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials
journal, May 2019

  • Kostiuchenko, Tatiana; Körmann, Fritz; Neugebauer, Jörg
  • npj Computational Materials, Vol. 5, Issue 1
  • DOI: 10.1038/s41524-019-0195-y

Density-functional Monte-Carlo simulation of CuZn order-disorder transition
journal, January 2016


Effective design space exploration of gradient nanostructured materials using active learning based surrogate models
journal, December 2019


A critical review of high entropy alloys and related concepts
journal, January 2017


Using genetic algorithms to map first-principles results to model Hamiltonians: Application to the generalized Ising model for alloys
journal, October 2005


Modeling the structure and thermodynamics of high-entropy alloys
journal, July 2018


High-entropy alloy: challenges and prospects
journal, July 2016


The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets
journal, June 2018

  • Zhang, Jiaxin; Shields, Michael D.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 334
  • DOI: 10.1016/j.cma.2018.01.045

A high-bias, low-variance introduction to Machine Learning for physicists
journal, May 2019


Outstanding radiation resistance of tungsten-based high-entropy alloys
journal, March 2019


First-principles study of order-disorder transitions in multicomponent solid-solution alloys
journal, April 2019

  • Eisenbach, Markus; Pei, Zongrui; Liu, Xianglin
  • Journal of Physics: Condensed Matter, Vol. 31, Issue 27
  • DOI: 10.1088/1361-648X/ab13d8

Construction of ground-state preserving sparse lattice models for predictive materials simulations
journal, August 2017


Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations
journal, October 2009


Order- N Multiple Scattering Approach to Electronic Structure Calculations
journal, October 1995


Machine-learning-assisted materials discovery using failed experiments
journal, May 2016

  • Raccuglia, Paul; Elbert, Katherine C.; Adler, Philip D. F.
  • Nature, Vol. 533, Issue 7601
  • DOI: 10.1038/nature17439

Machine learning of accurate energy-conserving molecular force fields
journal, May 2017

  • Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.
  • Science Advances, Vol. 3, Issue 5
  • DOI: 10.1126/sciadv.1603015

Machine learning: Trends, perspectives, and prospects
journal, July 2015


A general-purpose machine learning framework for predicting properties of inorganic materials
journal, August 2016


On the quantification and efficient propagation of imprecise probabilities resulting from small datasets
journal, January 2018


Machine learning based interatomic potential for amorphous carbon
journal, March 2017


Machine learning for molecular and materials science
journal, July 2018


Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one
journal, November 2015


Efficient Ab initio Modeling of Random Multicomponent Alloys
journal, March 2016