Materials Informatics Overview

+

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

+The Materials Genome Initiative

Experiment

Simulation

Digital Data

MGI places a new focus on how materials generators and materials data analysts create and ingest new and legacy information.

+Materials Science Knowledge

Structure

Property

Process

Information is generated with the goal of improving the knowledge of structure-property-processing relationships.

+An Applied Representation of Materials Information

Localization .

Homogenization .

Time

Scale

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.

+An Applied Representation of Materials Information

Localization .

Homogenization .

Time

Scale

Models generate relationships between the structure and its effective response (bottom-up), its local response (top-down), or its change during processing.

The responses or changes are controlled by the mesoscale arrangement of the material features. The materials structure

is the independent variable.

+Some Spatial Material Features

Most information generated is spatial & really expensive.

Volume Variety Velocity

+

A lot of the spatial information is ignored

Top view

Cut out a square, its easier.

CT information

+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.

+

PHYSICS BASED MODELS SIMULATION | EXPERIMENT

MICROSTRUCTURE (MATERIAL) SIGNAL MODULES

ADVANCED & OBJECTIVE STATISTICAL MODULES

DATA MINING MODULES

VALUE ASSESSMENT

INTE

LLIG

EN

T D

ESI

GN

OF

EX

PER

IME

NTS

Microstructure Informatics

Scrape the relevant data and metadata about the structure, responses, and structure changes from any available simulated or experimental models.

+

PHYSICS BASED MODELS SIMULATION | EXPERIMENT

MICROSTRUCTURE (MATERIAL) SIGNAL MODULES

ADVANCED & OBJECTIVE STATISTICAL MODULES

DATA MINING MODULES

VALUE ASSESSMENT

INTE

LLIG

EN

T D

ESI

GN

OF

EX

PER

IME

NTS

Microstructure Informatics

Eke out the desired features & encode them into signals that can be analyzed.

+

Grains, Grain Boundaries, & Grain Orientations

+

Fiber Centroids in a Massive 3-D Image

+

Heterogeneous Signals in Polycrystals

+

PHYSICS BASED MODELS SIMULATION | EXPERIMENT

MICROSTRUCTURE (MATERIAL) SIGNAL MODULES

ADVANCED & OBJECTIVE STATISTICAL MODULES

DATA MINING MODULES

VALUE ASSESSMENT

INTE

LLIG

EN

T D

ESI

GN

OF

EX

PER

IME

NTS

Microstructure Informatics

Use algorithms and image processing to extract statistics from the material structure to use as the independent variable in the informatics process.

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

+Chord Length Distribution

+Vector Resolved Spatial Statistics

+

PHYSICS BASED MODELS SIMULATION | EXPERIMENT

MICROSTRUCTURE (MATERIAL) SIGNAL MODULES

ADVANCED & OBJECTIVE STATISTICAL MODULES

DATA MINING MODULES

VALUE ASSESSMENT

INTE

LLIG

EN

T D

ESI

GN

OF

EX

PER

IME

NTS

Microstructure Informatics

Numerical methods, machine learning, and new models to create structure-property-processing linkages.

+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."

+

PHYSICS BASED MODELS SIMULATION | EXPERIMENT

MICROSTRUCTURE (MATERIAL) SIGNAL MODULES

ADVANCED & OBJECTIVE STATISTICAL MODULES

DATA MINING MODULES

VALUE ASSESSMENT

INTE

LLIG

EN

T D

ESI

GN

OF

EX

PER

IME

NTS

Microstructure Informatics

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?

+Success Stories in Microstructure Informatics

n  Homogenization n  Improved regression models for the diffusivity in fuel cells

n  Localization n  Meta-models for spinodal decomposition n  Meta-models for highly nonlinear elastic, plastic, and

thermomechanical responses

n  Structure-Structure n  Quantitative comparison between heat treated a-b experimental

Titanium datasets. n  Degree of crystallization in Polymer Molecular Dynamics

simulation. n  Model verification in Molecular Dynamics simulations.

+

ps = athms+t

h

h∑

t∑

Materials Knowledge System Overview

n  Localization is provides a spatially resolved response for a particular material structure

FEM"ε=5e-4"

+

INPUT OUTPUT Control"

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.

Any

Mod

el

ps = athms+t

h

h∑

t∑

Materials Knowledge System Overview Generalized

+Applications of Localization

n Model scale is intractable

n Fast, scalable, computationally efficient top-down linkages are necessary

+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

+Information & Knowledge

Microstructure Signal Response Signal

Regression transforms information to knowledge

in the form of influence coefficients

+

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  Symmetric-first derivative of the Green’s function

n  Relates to perturbation theory

n  Have fading memory

n  Can be scaled.

ps = athms+t

h

h∑

t∑

Convolution Relationship

+

( )yxf , ( )yxg ,

Image Filtering

1=h

fhg ∗=

( )vuh ,

+

( )yxf , ( )yxg ,

( )vuh ,

Image Filtering - Blurring

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

0001110100

100

110

111

110

100

( )=vuh ,

fhg ∗=

+

( )yxf , ( )yxg ,

( )vuh ,

Image Filtering - Embossing

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−

−−

110101011

( )=vuh ,

fhg ∗=Filtering modifies a pixel at (x,y) by

some function of the local neighorhood defined by h

+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.  Choose an encoding

2.  Choose a calibration set

3.  Fourier transform of microstructure and response signal

4.  Calibrate in the Fourier space

5.  Convert influence coefficients to the real space

4.  Validate the Influence Coefficients

+Core elements of the Materials Knowledge System

n  What we need to know n  Methods to determine independent and dependent variables

n  Linear regression

n  Prior knowledge about your information

n  What we need to use n  Fast Fourier Transforms

n  Linear Regression

n  Numerical Methods to generate data

+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.

+Topology of the Influence Coefficients

63ta

Fading Memory

Influence scaling easy because of the fading memory and scale better than most models.

+

•  From an initial starting structure, ONE set of influence coefficients can be used to evolve the material structure"

Time Derivative"

MSE Error"

Application: Spinodal Decomposition (1)

+Time Derivative"

MSE Error"

Application: Spinodal Decomposition (2)

+

OTHER APPLICATIONS"Spinodal Decomposition, Grain Coarsening, "

Thermo-mechanical, Polycrystalline

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.

Application: High contrast elasticity

+On to the next one.

Have Fun!