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Multiscale Materials Design Using Informatics
S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan
AFOSR-FA9550-12-1-0458
1
Hierarchical Material Structure
Kalidindi and DeGraef, ARMS, 2015
3
Main Challenges in Multiscale Materials Design
• Statistical Quantification of Hierarchical Structure (including chemistry)
• Templated Workflows for Mining Core Knowledge (PSP Linkages)
• Multiscale Design and Optimization
• Cross-Disciplinary Collaboration
Conventional microstructure descriptors are devised
based on observation, intuition or expertise:
• Connectivity/Percolation/Tortuosity
• Average Grain/Particle Coordination Number
4
Structure Quantification: Conventional Approaches
• Phase Volume Fraction or Porosity
• Average Grain/Pore/Particle/Fiber Size
� The “important” features or
their relative importance
change from expert to
expert.
� Takes years of experience and
knowhow to obtain a linkage.
Main Challenges:
n-point Correlation Functions as a Microstructure Descriptors
• Appears naturally in the best known composite theories
• Accounts/quantifies anisotropy in the structure
• Utilizes a statistical framework that inherently captures variance and uncertainty
• Provides a natural origin in registering structure
• Generates a vast pool of microstructure features
�∗ = �̅ − ��Γ�� + ��Γ��Γ�� −⋯�′Γ�′ = �′Γ�′ = � � � � ℎ, ℎ� � �� ℎ Γ −� �� ℎ� �ℎ�ℎ′��
�(����
5
Comprehensive & Systematic Structure Quantification
Probability of finding h and h’ at the head and tail of a vector r
2-point Statistics
nth term needs n-point statistics of structure
Broadly applicable to many properties
����� = #����� !"##$ �"�#����� %&&$'(&$�
%50
%0
Complete Set of �����for all possible �.
Not Allowed
Produces a very large number of microstructure descriptors!6
2-Point Statistics: Definition and Visualization
7
%50
%10
• Provides a natural origin for registering structure
Main Benefit of 2-Point Statistics
x
yp1
p2
p1
p2
p1
Original Axes Principal Axes Reduced Axis
Obtain the first handful dimensions (out of possibly thousands
or millions) that show the highest variation within the dataset
Why PCA?
• Objective and hierarchical identification of most characteristic features.
• Features are independent and uninformed of process and property.
Feature Extraction Using PCA
Initial Microstructure
Final Microstructure
Principal Component Analysis (PCA)
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Tracking Microstructure Evolution
2-Point Statistics
• Diverse boundary assumptions
• Irregular regions
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Project Product: Extensible Framework for Spatial Correlations
• Diverse length/structure scales (atomistic to mesoscales
• Diverse local state descriptors
• Examples will be presented in follow-up talks
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Efficient Resource Utilization in Computing Spatial Correlations
Full Sweep Minimal for Laptop for Desktop
Memory (GBs)Time (minutes)
New Computational Algorithms for Large Datasets
• Need a framework to capture uncertain (or incomplete) knowledge into computationally efficient and easily accessible databases
• Express the core knowledge in invertible metamodels (i.e., surrogate models)• Harmoniously blend known physics with data science tools in formulating and
expressing high value, low computational cost, PSP linkages
Process-Structure-Property (PSP) Linkages
Conventional Approaches
1. Experimentation
• Time-consuming and expensive• Hard to generalize the result
2. Physics-based simulations (e.g., FE)
• High computational cost• Scale-bridging is a major challenge• Large uncertainty in model forms and
parameters
3. First principle methods
• Numerous gaps in known physics, especially for mechanical properties• High computational cost
Templated Workflows for Mining PSP Linkages
Meta-Model Learning
• Multivariate Polynomial Regression
• Decision Table• Instance Based KNN• KStar (Entropy KNN)• Support Vector Machines• Linear Regression (Line)• Robust Regression (Line)• Pace Regression (Clustering)• Artificial Neural Networks• M5 Model Tree
Leave One Out Cross Validation
Choose a model the has low
average error, while minimizing
the effect of individual data
points on the final model.• Allow automation, efficient large scale exploration• Allow sharing and facilitate productive e-collaborations
Conventional Approaches
1. Mathematical methods• Linear, nonlinear and dynamic programming• These methods represent a limited approach, and no single method is
completely efficient and robust for all types of optimization problems.
2. Exhaustive searches (e.g., gradient search)• Subject to local optima• Sensitive to initial values; solutions usually end up in the
neighborhood of the starting point.
• Complexity of calculating derivatives• Large amount of enumeration memory required• Mostly intractable in high dimensional searches
Material selection is currently approached with repetitive and
inefficient trials that rely largely on serendipity
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Multiscale Design and Optimization
Motivation is to explore
microstructure–property
relationship in the design of
magnetoelastic Fe-Ga alloy.
Objective is to obtain accurate,
complete ODF microstructures
with desired optimized property in
an effective manner.
Techniques developed
include data mining
enhanced combinatory
search within a large space.
Sampling • Elastic Modulus
• Yield Strength
• MagnetostrictiveStrain
Homogenization
Microstructure Statistical descriptor (ODF) Properties
reconstruction Optimization
The orientation distribution
function (ODF) is applied for
the quantification of
crystallographic texture.
Theoretically computing
properties given microstructure
are known but inversion of
relationships is challenging.
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Nonlinear and Multi-Objective Optimization
Five Design Problems (ms, E, Y, F1 and F2) are presented, each attempting to attain an extremal property by tailoring the distribution of various crystal orientations.
Optimal properties are achieved through searching among ODF candidate guided by data mining heuristics.
(d) A composite function
(e) A composite function
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Nonlinear and Multi-Objective Optimization
Fingerprint of entire unexplored ternary composition space!
B. Meredig*, A. Agrawal*, S. Kirklin, J. E. Saal, J. W. Doak, A. Thompson, K. Zhang, A. Choudhary, and C. Wolverton, “Combinatorial screening for
new materials in unconstrained composition space with machine learning”, Phys. Rev. B, 89, 094104, March 2014.
Interesting insights:• Highest ranked ternary: SiYb3F5
• Si acts as an anion• Validated with structure and DFT calculations
• pnictides, chalcogenides, halides• Pt-X-Y• Pm12S19Se– a missing binary Pm2S3?
Construc on of FE predic on database
• Consists of compounds with known forma on energy (FE)
• Empiric periodic table informa on added (e.g. electro nega vity, mass,
atomic radii, # valence s, p, d, f electrons)
Predic ve Modeling
• Construct data mining models to predict forma on energy using chemical formula and derivable
empirical informa on
Model Evalua on
• Test model on unseen data • 10-fold cross valida on (data divided into 10 segments, model built on 9 segments and tested on remaining 1
segment; process repeated 10 mes with different test segment)
Large scale FE predic on
• Run combinatorial list of compounds through the FE model
Screening
• Thermodynamic stability and heuris cs
Valida on
• Structure predic on • Quantum mechanical
modeling
Combinatorial
list of ternary
compounds
List of
predic ons
Shortlisted
high-
poten al
candidates
FE
model
Stable
discovered
structures
(a)
(b)
Screening for New Materials in Composition Space
A. Agrawal, P. D. Deshpande, A. Cecen, G. P. Basavarsu, A. N. Choudhary, and S. R. Kalidindi, “Exploration of data science techniques to predict fatigue
strength of steel from composition and processing parameters,” Integrating Materials and Manufacturing Innovation, 3 (8): 1–19, 2014.
R2 > 0.98
Process-Fatigue Linkages
18
New Machine learning approach for multiscale materials design
• Meta-heuristics developed to expedite the search in large dimensional spaces
• Allows for incorporation of legacy domain knowledge
• Able to find better solution than traditional searches
• Able to find multiple design candidates that fit the stipulated criterion; these choices can then be downselected based on real-world constraints
Sampling • Elastic Modulus
• Yield Strength
• MagnetostrictiveStrain
Homogenization
Microstructure Statistical descriptor (ODF) Properties
reconstruction Optimization
19
Project Outcomes
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Cross-Disciplinary Collaboration
Engage and exploit cross-disciplinary expertise to create
high value information for multiscale materials design
Cross-disciplinary Integration demands e-Collaboration
Simulations
Experiments
Data Science
Reliable PSP
Linkages
Domain Expertise
Uncertainty Quantification
Multiscale
Materials Design
Current Users
• Nucleation of a core community
• Development and curation of tools that facilitate intermediate publishing and sharing of information
• Materials Informatics Course: 9 teams used this for diverse research projects
21
Cross-Disciplinary Collaboration