Multiscale Materials Design Using Informatics

S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan

AFOSR-FA9550-12-1-0458

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Hierarchical Material Structure

Kalidindi and DeGraef, ARMS, 2015

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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

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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

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�(����

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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

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Complete Set of �����for all possible �.

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Produces a very large number of microstructure descriptors!6

2-Point Statistics: Definition and Visualization

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• 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

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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

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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

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Cross-Disciplinary Collaboration