A Framework and Infrastructure for Uncertainty Quantification and Management in Materials Design

Changning Niu, Abhinav Saboo, Jiadong Gong, Greg Olson
Work funded by
August 1, 2019
Artificial Intelligence for Materials Science (AIMS) Workshop
Gaithersburg, MD
Hosted by
A Framework and Infrastructure for Uncertainty
Quantification and Management in Materials Design

QuesTek Innovations LLC
• A global leader in Integrated Computational Materials
Engineering (ICME)
• Many proprietary models to predict Process-Structure-
Property-Performance relationships
• Designing/deploying novel materials for government and
industrial applications, including Energy, Aerospace,
Automotive, Defense, etc.
• Example: four commercially available Ferrium® steels
licensed to Carpenter Technology
• QuesTek is a partner of CHiMaD
• Center for Hierarchical Materials Design, a NIST-
sponsored center of excellence in Chicagoland
Ferrium S53 flying
on rockets
Ferrium C61 rotor shaft for helicopters
Ferrium M54 hook shank for T-45 aircraft
Aug 1, 2019
Artificial Intelligence for Materials Science (AIMS)
Workshop 2019
2

Outline
Aug 1, 2019
Workshop 2019
3
 Overview
 MaGICMaT
 Uncertainty Management
 Cloud-Based Platform

Enhanced ICME with MGI and AI
Aug 1, 2019
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ICME
MGI AI
1. MaGICMaT 2. Uncertainty Management
Materials Genome and
Integrated Computational
Materials Toolkit
Uncertainty Quantification
(UQ) & Propagation (UP)
3. Cloud-Based Platform
QuesTek is exploring ways to incorporate MGI and AI into its ICME practice.

Motivation: MaGICMaT
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Hierarchy of Present and Future Materials Genome Methods, Tools and Databases.
Figure from: Olson, G. B., & Kuehmann, C. J. (2014). Materials genomics: From
CALPHAD to flight. Scripta Materialia, 70, 25–30
MaGICMaT
Build bridges between Materials Genome and
ICME
• Data retrieval from complex sources
• Data & PSP linkages management
• Interfaces with ICME & AI models
ICME
MGI AI
1. MaGICMaT

Motivation: Uncertainty Management
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Uncertainty Management
Build up uncertainty from fundamental
thermodynamic data
• Assess uncertainty within thermodynamic
databases (TDBs)
• Manage and apply the uncertainty in
CALPHAD and ICME
ICME
MGI AI
2. Uncertainty
Management

Motivation: Cloud-Based Platform
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Cloud-Based Platform
Unified platform with an HPC backend
• Rapid development and deployment
• User friendly on multiple levels
ICME
MGI AI
3. Cloud-Based Platform

Outline
Aug 1, 2019
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 Overview
 MaGICMaT

Current Data & PSP Linkage Management
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StructureProcessing Properties
Alloy
Composition
Rapid Hot
Pressing
Anneal
Matrix Phase
Charge Carrier Doping
Band Engineering
2nd-Phase Nanostructures
Interface Engineering
Grain Refinement
Grain Boundary Engineering
Thermal
Cond.
k
Electronic
Th. Con.
ke
Electrical
Conductivity
s
Seebeck
Coefficient
S
Carrier Con.
n
Effective Mass
m*
Degeneracy
Nv
Interface Res.
ri
Scattering
t
zT
Lattice
Thermal
Cond.
kL
Int. Th. Res.
1/ki
Grain Lat. TC
kL,g
Mobility
m
Getting data from
public databases
A storage tool for
collected data
Management of
PSP linkages
• Matminer
• Web APIs
• etc.
• MDCS
• etc.
• iCMD
• Pymatgen
• Jupyter Notebook?
MaGICMaT to fill these gaps

Ability to Manage & Generate Design Charts
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Experimental approach using literature High-throughput approach using DFT data
 Fast exploration of ICME design methods
 Calibration of high-throughput approach using experimental data
data
data
Proprietary Information Proprietary Information

Outline
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 Overview
 MaGICMaT

Uncertainty from Bayesian Inference
𝑃 𝜃 𝐷 =
𝐷 𝜃 ( )
( )
, 𝜃 is vector in parameter space e.g. (a,b)
• 𝑃(𝜃) prior probability, probability before considering data D
• 𝑃 𝐷 𝜃 likelihood
• How likely this data is to be measured if the (true) model has parameters 𝜃
• 𝑃 𝜃 𝐷 posterior probability, probability after considering data D
• 𝑃(𝐷), normalizing factor (complex integral)
Classical (least-squre)
Model
𝑦 = 𝑎𝑥 + 𝑏
Result
𝑎 = 2, 𝑏 = 1
Bayesian
𝑎 =
𝑏 =
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CALPHAD Theory
• Unary:
• 𝐺 = 𝑎 + 𝑏𝑇 + 𝑐𝑇ln 𝑇 + Σ 𝑑 𝑇
• Binary/higher order:
• 𝐺 𝑥 = ∑ 𝑥 𝐺 , + ∑ 𝑅𝑇𝑥 ln 𝑥 + ∑ 𝑥 𝑥 𝐿 , (𝑥 − 𝑥 ) , 𝐿 , = 𝑎 , 𝑇 + 𝑏 ,
• Measurable quantities can be derived from the Gibbs energy, e.g.:
• Enthalpy: 𝐻 = 𝐺 − 𝑇
• Heat capacity: 𝐶 (𝑇, 𝜃) = −𝑇 𝐺
• Activity: 𝑎 = 𝑒
∅
, 𝜇 =
• Phase boundaries: 𝐺 𝑥 , 𝑇 = 𝐺 𝑥 , 𝑇
Unary energy Ideal mixing energy Excess mixing energy
It is possible to assess these quantities analytically.
In this study, we use the ThermoCalc engine, which
is regarded as a black box.
 Generalized for common TDB files
 Good performance from ThermoCalc
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CALPHAD UQ Steps
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TDB file
Synthetic Data
UQ Calc
TDB + UQ
Same?
+ noiseThermo-Calc
Thermo-Calc
1. Algorithm Validation 2. UQ Assessment
Real Data
UQ Calc
TDB + UQ
Thermo-Calc
3. UQ Calculation
TDB + UQ
HT Calc
UQ Results
Thermo-Calc

System to Start with: Ni-Cr
𝐺 𝑥 = 𝑥 𝐺 , + 𝑅𝑇𝑙𝑛 𝑥
+𝑥 𝑥 𝑳 𝑨,𝟎(𝑥 − 𝑥 ) + 𝑥 𝑥 𝑳 𝑨,𝟏(𝑥 − 𝑥 )
𝐿0(𝐵𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐵𝐶𝐶 ∗ 𝑇 + 𝑏0, 𝐵𝐶𝐶
𝐿1(𝐵𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐵𝐶𝐶 ∗ 𝑇 + 𝑏1, 𝐵𝐶𝐶
𝐿0(𝐹𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐹𝐶𝐶 ∗ 𝑇 + 𝑏0, 𝐹𝐶𝐶
𝐿1(𝐹𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐹𝐶𝐶 ∗ 𝑇 + 𝑏1, 𝐹𝐶𝐶
𝐿0(𝐿𝐼𝑄𝑈𝐼𝐷, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐿𝐼𝑄 ∗ 𝑇 + 𝑏0, 𝐿𝐼𝑄
𝐿1(𝐿𝐼𝑄𝑈𝐼𝐷, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐿𝐼𝑄 ∗ 𝑇 + 𝑏1, 𝐿𝐼𝑄
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First study was on Ni-Cr system because of:
• Availability of raw data for CALPHAD assessment
• Simplicity of phase diagram
• 12 parameters were assessed

Synthetic Data: Ground Truth vs. Prediction
No. of steps
Parametervalue
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Algorithm is validated by the synthetic data results.

Real Data: Prediction vs. Original TDB
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Parametervalue
No. of steps • Good results from UQ calculations
• Deviation of parameters from original TDB due to weights on datasets

Phase Diagram with Uncertainty from Real Data
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TDB File UQ Trace TDB * 1000
QT Cloud Thermo-Calc
• We have developed a package to combine TDB with UQ traces for automatic
CALPHAD calculations using Thermo-Calc on HPC.
• Unlike regular CALPHAD assessment, CALPHAD UQ can continuously “grow”
as we collect new data without using old data.

Outlier Sensitivity: Theory
𝑓 𝑥 𝜇, 𝑏 =
1
2𝑏
exp −
𝑥 − 𝜇
𝑏
𝑓 𝑥 𝜇, 𝜎 =
1
2𝜋𝜎
exp −
𝑥 − 𝜇
2𝜎
Gaussian Distribution Laplace Distribution
Images from Wikipedia
The Laplace distribution has heavier tails (than the Gaussian distribution). The
Laplace distribution often leads to median regression, which is more robust to
outliers than mean regression.”
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Outlier Sensitivity: Performance
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With outliers, Gaussian
With outliers, Laplace
No outliers, Gaussian
No outliers, Laplace
When outliers exist, Laplace distribution performs much better than Gaussian distribution.
• This doesn’t mean Laplace is always better than Gaussian.
• Choosing correct distribution requires domain knowledge.
Parameter value
Probability
(Synthetic data)

Outlier Sensitivity: Performance
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Weighting Datasets
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Weighted, Gaussian
Not weighted, Laplace
Weighted, Gaussian
Not weighted, Laplace
When we add proper weights to datasets, we get good results regardless of the distribution.
• The proper weights on each dataset requires domain knowledge.
(Synthetic data)

Weighting Datasets
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Outline
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 Overview
 MaGICMaT

Architecture of Cloud-Based Platform
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(demo available upon request)
• Middleware between frontend and calculations
• Central storage of relevant data
Middleware
• QuesTek’s Proprietary Packages
• CALPHAD results from Thermo-Calc & TC-Python
• Uncertainty data
Calculations
• Web apps to run basic CALPHAD calculations
• Extra features for CALPHAD UQ
Frontend
Regular Users
Experts
APIs
APIs

Acknowledgements
MaGICMaT
QuesTek (Intern)
• Ramya Gurunathan
Northwestern University
• Prof. Jeff Snyder
Argonne National Lab
• Logan Ward, Ph.D.
U Chicago & Argonne Nat. Lab
• Ben Blaiszik, Ph.D.
Funded by Department of Energy
• SBIR Phase I (DE-SC0019679)
CALPHAD in the Cloud
QuesTek (Intern)
• Ramon Frey
Rice University
• Prof. Meng Li
Thermo-Calc Software
• Johan Jeppsson, Ph.D.
• Adam Hope, Ph.D.
Funded by Department of Energy
• SBIR Phase II (DE-SC0017234)
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Summary & Future Work
Summary
MaGICMaT
• Materials Genome and ICME Toolkit
• Data & PSP linkage management
Uncertainty Management
• A framework for CALPHAD UQ
• Outlier tolerance
• Weight on data sets
• A toolkit for application of CALPHAD UQ
• User friendly frontend
Cloud-Based Platform
• Web apps with an HPC backend
Future Work
Contribute to CHiMaD Phase II
• Thermoelectrics
• Uncertainty Quantification of Phase Equilibria and
Thermodynamics (UQPET)
More opportunities of MGI & AI for enhanced ICME
• Current cloud platform can be an enabler for many
more technologies embedded for ICME
Aug 1, 2019
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ICME
MGI AI
More
Opportunities
More
Opportunities
Contact:
Changning Niu
cniu@questek.com

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