Tony Fast presented on novel microstructure informatics approaches using statistical distributions and data mining techniques to establish structure-property and structure-processing relationships from large datasets in materials science. The μInformatics framework uses modular workflows involving microstructure representation, dimensionality reduction, classification, and regression to distill rich physical data into forms that facilitate comparisons and linkages between material structure and performance. Examples were given applying the framework to problems in metals, composites, and organic materials.

1. Novel and Enhanced Structure-Property-Processing
Relationships with Microstructure Informatics
Tony Fast
University of California Santa Barbara
Materials Department
PSED seminar at Northwestern, November 8, 2012
GA Tech: S.R. Kalidindi, D.M. Turner, LANL: S.R. Niezgoda, Drexel: A.
Cecan, C. Kumbur, Teledyne: B. Cox, LLNL: H. Bale, ISU: O.
Wodo, Basker G., Dartmouth: U. Wegst, OSU: H. Fraser, P. Collins

2. From Materials Selection to Microstructure (μS) Informatics…
Materials selection relies on effective material descriptors.
H. Fraser, OSU.
U. Wegst, Dartmouth
H. Bale, LLNL
Advances in characterization and computational materials
science are contributing to the materials data deluge.

3. μInformatics workflow is a system
A robust paradigm to address dimensionality challenges in materials science
Future Work
Each module is self-contained
μInformatics is material and hierarchy independent statistical framework aimed to distill rich
physical data into tractable forms that facilitate structural taxonomies and bi-direction
structure-property-processing homogenization and localization relationships.

4. Image Segmenting identifies important features of the μS
A necessary evil in data-driven materials science
Virtual Metallic
Image Segmentation uses DSP methods to
minimize the human interaction necessary
to analyze digital images. Most problems
problems are subjective and ill-posed.
Hough transform Methods
 Raw Segmented
(EM/MPM) @ bluequartz.net
Kalidindi, S.R., S.R. Niezgoda, and A.A. Salem, Microstructure informatics using Ceramic Matrix Composite
higher-order statistics and efficient data-mining protocols. JOM, 2011. 63(4): p. 34-41.

5. The primitive basis converts any μS to a digital signal
Informatics benefit from a generalized higher-order microstructure description
H H
Primitive Basis h h h h
m v
s s
ms 1, 0 ms 1
Function
h 1 h 1
First-Order Higher-Order n
m6
0 s
white / solid n
m1 ms
n n
m3
m
h Local conformation n
m2
s
Discrete
1 s
black / pore of pixels n
m5
~
Extensible to any number ~h
ms
h h
m s 0 m s 1 t1  m s N t N
h
of discrete phases
~
s s
,  s , s Gradients contain
local conformation
Continuous
 f s
h h2
ms 1 f s
ms
~
~h
ms
h
ms 0 ms 1 ms
h h2
Other Basis Functions: Legendre, Generalized Spherical Harmonics, Chebyshev

6. Statistical distributions are the crux of μInformatics
Distributions capture traditional effective statistical measures
The rich internal structure of the material is the
microstructure. However, the μS
provides statistical, not deterministic
material information.
B. C.
A.
A. 2-pt Correlation Function – Statistical correlation between random points in space/time and
reveals systematic patterns in the microstructure
B. Chord Length Distribution – length and orientation of chords in a heterogeneous medium
C. Interfacial Surface Distribution - The principal curvatures of surfaces in the μS.
Chen et al., Morphological and topological analysis of coarsened nanoporous gold by x-ray nanotomography, Advanced Physics Letters 2010.

7. The Microstructure as a stochastic process
Distributions provide a framework to effectively compare microstructures
Microstructure HT1.1 HT1.2 Difference
- =
The direct comparison of the μS is useless due to the lack of origin.
Autocorrelation
- =
(+) Provide a ground truth and metric space for comparison, or there is a natural origin
(+) Autocorrelation contains all of the information in its respective μS.
(+) Amenable to homogenization and localization relationships
(-) Very large dimensionality

8. Data-mining modules are the vehicle for linkages
Dimensionality reduction, classification, and regression
 Regression methods allow the salient microstructure features to be
connected with homogenized and localized materials static and evolving
properties. (Structure-Property and Structure-Processing)
 Dimension reduction converts large dimensional data (D) to a reduced
space (d) based upon specfic characteristics of the data
 Clustering and classification provide methods to automatically identify
microstructures with certain performance or structural criterion. Ideal for
searching the intrinsically large space of microstructures.
Maaten, et al., Dimension Reduction: A Comparative Review, Tilburg centre for Creative Computing, Tilburg University, 2009.

9. Linear dimension reduction with PCA
Dimension reduction to deal with the scale of data
 Principal Component Analysis: Reduced
embedding of linearly independent
variables that correspond to decreasing
levels of variance starting with the
highest (Dd)
 PCA (most DR methods) require a
natural origin for the data-points
 PCA is typical for linear systems and
exploratory data analysis.
 Many nonlinear techniques exist.
Principal Component Analysis, Wikipedia

10. k-Means clustering for automatic feature recognition
Quantitative data-mining techniques
k-Means Clustering: A data-mining approach that creates cluster partitions based
on the means of clusters to automatically classify datapoints.
Classification cases - compare
training classes to predicted classes
TP – Correct classification
TN – Correct nonclassification
FP – Incorrect classification
FN – Incorrect nonclassification
Sensitivity – metric for accurate classification
Specificity – metric for accurate nonclassification
Range between 0 and 1
K-means Clustering, Wikipedia

11. μS informatics is a versatile framework that relies on workflows
Plug-n-play operations with modules provide solutions for diverse problems
μInformatics is a growing suite of modular functions that when combined into a
workflow system provide solutions to traditional empirical relationships and
emerging big data in materials science. μInformatics can be seamlessly applied to
1-D, 2-D,3-D, and 4-D datasets generated empirically or computationally.
 Improved homogenization relationships for diffusivity in porous media (sProp)
Experiments First-Order Signal Autocorrelation PCA Regression
 Localization meta-model for the evolution of a binary alloy (sProc)
Simulation First-Order Signal N/A Regression
 Localization meta-model for medium contrast dual phase composites (sProp)
400 Simulation Higher-Order Signal N/A Regression
 μS Taxonomy of α-β Ti (s-s)
130 Experiments First-Order Signal Autocorrelation PCA Data-Mining
 μS Taxonomy of Organic Blends in Solar Cells (s-s)
First-Order Signal Autocorrelation
1100 Simulations PCA K-means
Higher-Order Signal N-pt Statistics

12. Data-driven structural diffusion coefficients in fuel cells
Experiments
Simulation First-Order Signal Autocorrelation
N/A PCA
Regression Regression
FIB-SEM XCT
RVE’s from the experimental data are input into a Fickian diffusion model to evaluate the diffusivity.
GDL
Each point is one RVE
~1e6 variables
MPL
Data-driven fitting outperforms traditional fitting methods and extends the
reach of the fit to both the GDL and MPL layers.

13. The Materials Knowledge System
Extracting compact knowledge from boat loads of information
Stress, strain, evolution
 Many Inputs and Many Outputs
 Repetitive simulation is demanding
 Simulation produces a lot of data, but what
is determined about the system?
How can information about new structures be extracted?
What knowledge is gained?

14. The Materials Knowledge System
Extracting compact knowledge from boat loads of information
 DSP representation of local structure-local response
 Localization relationship and its influence coefficients
 Influence coefficients capture the combined point
effects of the MS configuration on the local response
 Strong implications on multi-scale modeling

15. An evolutionary meta-model for phase separation
Simulation First-Order Signal N/A Regression
A Materials Knowledge System for structure-processing relationships
2 df c a 2

ca D ca K ca
dc a
 Phase separation guided by a negative energy gradient
 Cahn Hilliard Relationship evolved by way of Euler forward
 Double well potential free energy curve
 Simulated using Phase Field Model (PFM)
 Concentration is continuous between spinodal points [.15, .23]
- Bounds of microstructure
 Interested in structure evolution of spinodal structure
Cahn JW. On spinodal decomposition. Acta Metallurgica 1961;9:795.

16. IC provide accurate simulation results
Simulation First-Order Signal N/A Regression
 Iterations of PFM used to calibrate coefficients
 Discretization contains 125 discrete points on a 20x20
spatial domain
Time derivative of concentration is captured
extremely accurately by MKS method

17. IC are amenable to numerical integration
Simulation First-Order Signal N/A Regression
• From an initial starting structure, ONE set of influence
coefficients can be used to evolve the material structure
Time Derivative
Attenuated Error
MSE Error

18. Influence coefficients can be used to scale the simulation
Simulation First-Order Signal N/A Regression
Original Scaled
63 63
at at
Ø Padding

19. Scaled linkages are provide accurate predictions
Simulation First-Order Signal N/A Regression
20x20:
100x100:

20. Scaled IC allow for scaled evolution simulations
Simulation First-Order Signal N/A Regression
Time Derivative
MSE Error

21. Meta-modeling of moderate contrast strain fields in composites
400 Simulation Higher-Order Signal N/A Regression
A Materials Knowledge System for Structure-Property relationships
FEM
ε=5e-4
E1
E2
 Contrast (nonlinearity) – Young’s modulus ratio
 First-order microstructure descriptors are ineffective for high
contrast
 Results are presented for uniaxial 1-1 strain
 Calibrating coefficients for other modes is trivial
 Random distribution of phases in 21x21x21 microstructure

22. Influence coefficients accurately capture the response fields
400 Simulation Higher-Order Signal N/A Regression
E1 E1
5 10
E2 E2
 HOIC of increasing order captures local information better
 Drastic improvement of linkages of FOIC
 Accuracy has a strong dependence on nonlinearity
Case 1: First Order  Case 2 – 7: Second Order  Case 8-9: Seventh Order

23. Accurate agreement between calibration and validation
400 Simulation Higher-Order Signal N/A Regression
E1 E1
5 10
E2 E2
 Different HOICs calibrated from 400 FEM simulations
 Training (calibration) set vs. Validation set describes how well
knowledge is captured
Case 1: First Order  Case 2 – 7: Second Order  Case 8-9: Seventh Order

24. Scalability of the influence coefficients
400 Simulation Higher-Order Signal N/A Regression
 153 influences coefficients have finite memory
and decay to zero at larger distances
 FEM required 45 min on supercomputer
 MKS required 15 seconds on a desktop computer
 MKS – NlogN(N)
Case 9: Seventh-Order to First Neighborhood and Second-Order to Sixth Neighborhoods

25. Microstructure taxonomy of α-βTitanium
130 Experiments First-Order Signal Autocorrelation PCA Data-Mining
H., Fraser, OSU PCA Embedding
Each point in the PCA indicate ONE μS, or ~6e6 variables.
Microstructures generated by similar heat treatments naturally
cluster together in the reduced embedding.
Kalidindi, S.R., S.R. Niezgoda, and A.A. Salem, Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM, 2011. 63(4): p. 34-41.

26. μS Taxonomy of Continuous Material States
An Application to Organic Blends in Solar Cells
Many Topologies 11 Distinct Topologies
10% FAST PHASE SEPARATION 90% SLOW GRAIN COARSENING
FINAL STRUCTURES
Use data driven techniques to classify the final topology before the
Isosurfaces of atomic fraction
End Goal
simulation is complete. i.e. Reduce Redundancy, Time Savings
1100 Datasets
Develop Microstructure Taxonomies of the Final Structures
First Goal
i.e. Build Utilities for Continuous Materials Features
First-Order Signal Autocorrelation
1100 Simulations PCA K-means
Higher-Order Signal N-pt Statistics
Olga Wodo and Baskar Ganapathysubramanian at ISU.

27. Microstructure taxonomy of binary organic blends
1100 Simulations
First-Order Signal Autocorrelation PCA K-means
 Each point describes 21^3 variables and each color is a different topology
 Binning and microstructure features effect the clustering quality
 Hard clustering in the PCA space allows the final topologies to be classified qualitatively

28. Microstructure taxonomy of binary organic blends
1100 Simulations
Higher-Order Signal N-pt Statistics PCA K-means
 Different choices of local
state descriptions lead to
different levels of clustering

29. Class A
Quantitative Measures of Clustering Class B
1100 Simulations Higher-Order Signal N-pt Statistics PCA K-means
Sensitivity and specificity analysis of PCA embedding Class C
AF – Atomic Fraction FG FG
FG – First Gradient AF
SG – Second Gradient AF SG
SG
Clockwise
FG,SG
AF,SG
AF,FG
AF,FG,SG

30. PCA embedding can be used to visualize 3-D processing history
μInformatics collectively can visualize SPP linkages
Each path is defined by the spinodal decomposition and grain
coarsening simulation. The paths are created by a reduced
embedding of the N-pt statistics of 21x21x21 periodic microstructures.

31. PCA embedding can be used to visualize 3-D processing history
μInformatics can collectively visualize bidirectional SPP linkages
Structure-Property
Homogenization
Structure-Processing MKS
Processing History
Structure-Property
Localization