The document provides an overview of materials informatics and the Materials Genome Initiative. It discusses how materials informatics uses data-driven approaches and techniques from fields like signal processing, machine learning and statistics to generate structure-property-processing linkages from materials science data and improve understanding of materials behavior. This includes extracting features from materials microstructure, using statistical analysis and data mining to discover relationships and create predictive models, and evaluating how knowledge has improved.

1. +
Materials Informatics
Overview
Tony Fast
NIST Workshop – Monday, January 13, 2014

2. +
The Materials Genome Initiative
Experiment
Digital Data
Simulation
MGI places a new focus on how
materials generators and materials
data analysts create and ingest new
and legacy information.

3. +
Materials Science Knowledge
Structure
Process
Property
Information is generated with the goal
of improving the knowledge of
structure-property-processing
relationships.

4. +
An Applied Representation of
Materials Information
S
c
a
l
e
Homogenization
.
Localization
.
Time
Physics based models, via either simulation or experiment, are designed
and refined to generate structure-response information that will either
support or challenge the current knowledge of the material behavior.

5. +
An Applied Representation of
Materials Information
S
c
a
l
e
Homogenization
.
Localization
.
Models generate
relationships between the
structure and its effective
response (bottom-up), its
local response (topdown), or its change
during processing.
Time
The responses or changes are controlled by the mesoscale
arrangement of the material features. The materials structure
is the independent variable.

6. +
Some Spatial Material Features
Most information generated is spatial & really expensive.
Volume Variety Velocity

7. +
A lot of the spatial information is ignored
CT information
Top view
Cut out a square, its easier.

8. +
Microstructure Informatics
n
Microstructure informatics is an emerging data-driven
approach to generating structure-property-processing
linkages for materials science information.
n
Microstructure informatics appropriates ideas from signal
processing, machine learning, computer science, statistics,
algorithms, and visualization to address emerging and
legacy challenges in pushing the knowledge of materials
science further.

9. +
Microstructure Informatics
INTELLIGENT DESIGN OF
EXPERIMENTS
PHYSICS BASED MODELS
SIMULATION | EXPERIMENT
MICROSTRUCTURE (MATERIAL)
SIGNAL MODULES
ADVANCED & OBJECTIVE
STATISTICAL MODULES
DATA MINING MODULES
VALUE ASSESSMENT
Scrape the relevant data and
metadata about the structure,
responses, and structure changes
from any available simulated or
experimental models.

10. +
Microstructure Informatics
INTELLIGENT DESIGN OF
EXPERIMENTS
PHYSICS BASED MODELS
SIMULATION | EXPERIMENT
MICROSTRUCTURE (MATERIAL)
SIGNAL MODULES
ADVANCED & OBJECTIVE
STATISTICAL MODULES
DATA MINING MODULES
VALUE ASSESSMENT
Eke out the desired features
& encode them into signals
that can be analyzed.

11. +
,
Grains Grain Boundaries,
& Grain Orientations

12. +
Fiber Centroids in a Massive 3-D Image

13. +
Heterogeneous Signals in Polycrystals

14. +
Microstructure Informatics
INTELLIGENT DESIGN OF
EXPERIMENTS
PHYSICS BASED MODELS
SIMULATION | EXPERIMENT
MICROSTRUCTURE (MATERIAL)
SIGNAL MODULES
ADVANCED & OBJECTIVE
STATISTICAL MODULES
DATA MINING MODULES
VALUE ASSESSMENT
Use algorithms and image
processing to extract statistics
from the material structure to use
as the independent variable in
the informatics process.

15. + Grain size, Grain Faces, Number of Grains,
Mean Curvature, & Nearest Grain Analysis

16. +
Chord Length Distribution

17. +
Vector Resolved Spatial Statistics

18. +
Microstructure Informatics
INTELLIGENT DESIGN OF
EXPERIMENTS
PHYSICS BASED MODELS
SIMULATION | EXPERIMENT
MICROSTRUCTURE (MATERIAL)
SIGNAL MODULES
ADVANCED & OBJECTIVE
STATISTICAL MODULES
DATA MINING MODULES
VALUE ASSESSMENT
Numerical methods, machine
learning, and new models to
create structure-propertyprocessing linkages.

19. +
Data mining applications & the
goal of the workshop
n
Homogenization – Improved bottom-up linkages using
improved feature detection, richer datasets, & better
statistical descriptors.
n
Localization – “How can I execute a model on a new material
structure faster and sacrifice precision a tiny bit?”
n
Structure-Structure – Quantitative comparison between
materials with different structures, but similar ontologies.
We will solve localization problems today, homogenization and
structure quantification are tomorrow."

20. +
Microstructure Informatics
INTELLIGENT DESIGN OF
EXPERIMENTS
PHYSICS BASED MODELS
SIMULATION | EXPERIMENT
MICROSTRUCTURE (MATERIAL)
SIGNAL MODULES
ADVANCED & OBJECTIVE
STATISTICAL MODULES
DATA MINING MODULES
VALUE ASSESSMENT
How much did the knowledge
improve? Is new data needed?
Is a better mining technique
available? Can better statistics
be extracted? Can another
feature be included?

21. +
Success Stories in Microstructure
Informatics
n
Homogenization
n
n
Localization
n
n
n
Improved regression models for the diffusivity in fuel cells
Meta-models for spinodal decomposition
Meta-models for highly nonlinear elastic, plastic, and
thermomechanical responses
Structure-Structure
n
n
n
Quantitative comparison between heat treated a-b experimental
Titanium datasets.
Degree of crystallization in Polymer Molecular Dynamics
simulation.
Model verification in Molecular Dynamics simulations.

22. +
Materials Knowledge System
Overview
n
Localization is provides a spatially resolved response for a
particular material structure
FEM"
ε=5e-4"
h
ps = ∑∑ ath ms+t
t
h

23. Any Model
+ Materials Knowledge System Overview Generalized
INPUT
Control"
OUTPUT
h
ps = ∑∑ ath ms+t
t
h
The MKS design filters that capture the effect of the local arrangement of
the microstructure on the response. The filters are learned from physics
based models and can only be as accurate as the model never better.

24. +
Applications of Localization
n Model
scale is intractable
n Fast, scalable, computationally
linkages are necessary
efficient top-down

25. +
Information & Knowledge
Microstructure Signal
Response Signal
Same Size
Under a set of control parameters and boundary conditions, the arrangement of
the features described by the microstructure signal can be connected to the final
response the arrangement

26. +
Information & Knowledge
Microstructure Signal
Response Signal
Regression transforms
information to knowledge
in the form of influence coefficients

27. +
The Influence Coefficients
n
Contain knowledge of the physics expressed by the material
information
n
Any assumptions, or uncertainty, is propagated in the influence
coefficients.
n
Originally devised from Kroner’s on heterogeneous medium
n
The are filters that contain the physics of the spatial interaction
with the spatial arrangement of features
n
n
Symmetric-first derivative of the Green’s function
Relates to perturbation theory
n
Have fading memory
n
Can be scaled.
h
ps = ∑∑ ath ms+t
t
h
Convolution Relationship

28. +
Image Filtering
h(u, v )
f (x, y )
h =1
g = h∗ f
g (x, y )

29. +
Image Filtering - Blurring
h(u, v )
f (x, y )
h(u, v) =
⎡0 01 0 0⎤
⎢0 1 1 1 0⎥
⎢
⎥
⎢1 1 1 1 1 ⎥
⎢
⎥
0 1 1 1 0⎥
⎢
⎢0 01 0 0⎥
⎣
⎦
g = h∗ f
g (x, y )

30. +
Image Filtering - Embossing
h(u, v )
f (x, y )
h(u, v) =
⎡− 1 − 1 0⎤
⎢− 1 0 1⎥
⎢
⎥
⎢ 0 1 1⎥
⎣
⎦
g (x, y )
Filtering modifies a pixel at (x,y) by
some function of the local
g = h ∗ f by h
neighorhood defined

31. +
Generating Knowledge – A workflow
1.
Gather or generate microstructure and spatial response
information
2.
Extract and encode the feature of the microstructure
3.
Calibrate the Influence Coefficients
1.
2.
Choose an encoding
Choose a calibration set
4.
Fourier transform of microstructure and response signal
Calibrate in the Fourier space
5.
Convert influence coefficients to the real space
3.
4.
Validate the Influence Coefficients

32. +
Core elements of the Materials
Knowledge System
n
What we need to know
n
Methods to determine independent and dependent variables
Linear regression
n
Prior knowledge about your information
n
n
What we need to use
n
Fast Fourier Transforms
n
Linear Regression
n
Numerical Methods to generate data

33. +
Fourier Transforms of a
Convolution
n
The Fourier space decouples the spatial dependencies
n
The influence coefficients are calibrated in the Fourier space
because the initially it appears to simplify the problem.

34. +
Topology of the Influence Coefficients
Fading Memory
a
63
t
Influence scaling easy because of the fading
memory and scale better than most models.

35. + Application: Spinodal Decomposition (1)
• From an initial starting structure, ONE set of influence
coefficients can be used to evolve the material structure"
Time Derivative"
MSE Error"

36. + Application: Spinodal Decomposition (2)
Time Derivative"
MSE Error"

37. + Application: High contrast elasticity
The MKS is a scalable, parallel meta-model that learns from physics based
models to enable rapid simulation at a cost in accuracy.
N2 vs. Nlog(N) complexity
It learns top-down localization relationships to extra extreme value events
and enables multiscale integration.
OTHER APPLICATIONS"
Spinodal Decomposition, Grain Coarsening, "
Thermo-mechanical, Polycrystalline

38. +
On to the next one.
Have Fun!