Title: Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics

Journal Article · · Computer Methods in Applied Mechanics and Engineering

Machine learning has been effective at detecting patterns and predicting the response of systems that behave free of natural laws. Examples include learning crowd dynamics, recommender systems and autonomous mobility. There also have been applications to the search for new materials that draw upon big-data classification problems. Though, when it comes to physical systems governed by conservation laws, the role of machine learning has been more limited. Here, we present our recent work in exploring the role of machine learning methods in discovering, or aiding, the search for physics. Specifically, we focus on using machine learning algorithms to represent high-dimensional free energy surfaces with the goal of identifying precipitate morphologies in alloy systems. Traditionally, this problem has been approached by combining phase field models, which impose first-order dynamics, with elasticity, to traverse a free energy landscape in search of minima. Equilibrium precipitate morphologies occur at these minima. Here, we exploit the machine learning methods to represent high-dimensional data, combined with surrogate optimization, sensitivity analysis and multifidelity modeling as an alternate framework to explore phenomena controlled by energy extremization. This combination of data-driven methods offers an alternative to the imposition of first-order dynamics via phase field methods, and represents one aspect of applying machine learning to materials physics.

Research Organization:
University of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0008637
OSTI ID:
1611102
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 344; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (40)

Microstructural Evolution in Inhomogeneous Elastic Media journal February 1997
Constrained multifidelity optimization using model calibration journal January 2012
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening journal June 1979
On the distribution of points in a cube and the approximate evaluation of integrals journal January 1967
The dynamics of precipitate evolution in elastically stressed solids—I. Inverse coarsening journal May 1996
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates journal February 2001
A phase-field model for evolving microstructures with strong elastic inhomogeneity journal June 2001
A diffuse interface model for microstructural evolution in elastically stressed solids journal March 1998
Equilibrium particle morphologies in elastically stressed coherent solids journal February 1999
Linking phase-field model to CALPHAD: application to precipitate shape evolution in Ni-base alloys journal March 2002
Multiscale modeling of θ′ precipitation in Al–Cu binary alloys journal June 2004
Simulation study of precipitation in an Mg–Y–Nd alloy journal July 2012
A simulation study of the shape of β′ precipitates in Mg–Y and Mg–Gd alloys journal January 2013
Predicting β′ precipitate morphology and evolution in Mg–RE alloys using a combination of first-principles calculations and phase-field modeling journal September 2014
Analytics for microstructure datasets produced by phase-field simulations journal January 2016
On the early stages of precipitation in dilute Mg–Nd alloys journal April 2016
A unified description of ordering in HCP Mg-RE alloys journal February 2017
A thermodynamic description of the Gd–Mg–Y system journal March 2007
Data driven modeling of plastic deformation journal May 2017
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality journal June 2017
Multi-fidelity optimization of super-cavitating hydrofoils journal April 2018
A simulation study of the distribution of β′ precipitates in a crept Mg-Gd-Zr alloy journal April 2017
Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index journal February 2010
A hybrid multi-fidelity approach to the optimal design of warm forming processes using a knowledge-based artificial neural network journal February 2007
A data-driven approach to establishing microstructure–property relationships in porous transport layers of polymer electrolyte fuel cells journal January 2014
Finding Nature’s Missing Ternary Oxide Compounds Using Machine Learning and Density Functional Theory journal June 2010
Machine-learning-assisted materials discovery using failed experiments journal May 2016
Predicting crystal structure by merging data mining with quantum mechanics journal July 2006
Machine learning phases of matter journal February 2017
Learning phase transitions by confusion journal February 2017
Accelerating materials property predictions using machine learning journal September 2013
Free Energy of a Nonuniform System. I. Interfacial Free Energy journal February 1958
Combinatorial screening for new materials in unconstrained composition space with machine learning journal March 2014
Phase-field model for binary alloys journal December 1999
Multiscale Modeling of Precipitate Microstructure Evolution journal March 2002
XSEDE: Accelerating Scientific Discovery journal September 2014
Surrogate-based methods for black-box optimization: Surrogate-based methods for black-box optimization journal April 2016
ALGORITHM 659: implementing Sobol's quasirandom sequence generator journal March 1988
Prediction of alloy precipitate shapes from first principles journal July 2001
The deal.II Library, Version 8.4 journal January 2016

Cited By (6)

A graph theoretic framework for representation, exploration and analysis on computed states of physical systems journal July 2019
A Deep Learning Framework for Design and Analysis of Surgical Bioprosthetic Heart Valves journal December 2019
Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences text January 2019
A Deep Learning Framework for Design and Analysis of Surgical Bioprosthetic Heart Valves journal December 2019
Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences journal November 2019
Multiscale modeling meets machine learning: What can we learn? preprint January 2019