uncertainty of thermodynamic data: humans and …
TRANSCRIPT
UNCERTAINTY OF THERMODYNAMIC DATA: HUMANS AND MACHINES
drhgfdjhngngfmhgmghmghjmghfmf
MARIUS STANSenior Scientist and Group LeaderComplex Physical SystemsSystems Security CenterANL
ATPESC 2017St, Charles, ILAug. 5, 2017
THE PROBLEM
Temperature-composition phase diagrams
3
Humans can draw simple diagrams
4
Ternary diagram
Binary diagram
HUMANS ONLY
The Gibbs rule
J. W. Gibbs, On the Equilibrium of Heterogeneous Substances, in Transactions of the Connecticut Academy of Arts and Sciences (1875-1878).
6
Josiah Willard Gibbs (1839-1903)
),,(),,(
),,(),,(
xPTxPT
xPTxPT
BB
AA
At thermodynamic equilibrium, the chemical potential of
each component A, B, C … must be the same in all
phases α, β, γ …
Calculating equilibrium binary phase diagrams
M. I. Baskes, K. Muralidharan, M. Stan, S. M. Valone, and F. J. Cherne, JOM, 55 (2003) 41-50. 7
0 1
T = T1
,
A
,
B
)(xG
)(xG
A B
x
PT
Ax
xPTGxxPTGxPT
,
),,(),,(),,(
Phase diagram
Free energy of components A, B, C …
in phases α, β, γ …
Chemical potentials
PT
Bx
xPTGxxPTGxPT
,
),,()1(),,(),,(
Thermodynamic equilibrium
(Gibbs’ rule)
),,(),,(
),,(),,(
xPTxPT
xPTxPT
BB
AA
),,(...,,
...,, xPTG CBA
The Hf-O Phase Diagram
8
HUMANS AND MACHINES
Solid (A11)
M.I. Baskes et al., Phys. Rev. B, 66 (2002) 104
Liquid Liquid
Melting via Molecular Dynamics
10
),,(
),,(
xPTfH
xPTfH
S
L
Enthalpy
Predicting the equilibrium phase diagrams from atomistic simulations
1M. I. Baskes, K. Muralidharan, M. Stan, S. M. Valone, and F. J. Cherne, JOM, 55 (2003) 41-50.2M. I. Baskes and M. Stan, Metall. Mater. Trans. 34A (2003) 435-39
11
PT
Ax
xPTGxxPTGxPT
,
),,(),,(),,(
Phase diagram
Free energy of components A, B, C …
in phases α, β, γ …by thermal integration1,2
Chemical potentials by
composition derivation
PT
Bx
xPTGxxPTGxPT
,
),,()1(),,(),,(
Thermodynamic equilibrium
(Gibbs’ rule)
),,(),,(
),,(),,(
xPTxPT
xPTxPT
BB
AA
''
),,'(),,(),,(2
T
T
ref
refref
ref
dTT
xPTH
T
xPTG
T
xPTG
LEARNING MACHINES
The Bayesian Method1
1Philosophical Transactions of London, 53 (1763) 370 (free on Google Books).13
Take a guess Acquire info Improve model
N
i
ii
jj
j
MPMDP
MPMDPDM
1
|
||
Prior
Posterior
Reverend Thomas Bayes (1702-1761)That is how Humans and Machines learn
Bayesian Polynomial Regression
14
Bayes Rule:
𝑝 𝐰 𝐗, 𝐭 ∝ 𝑝 𝐭 𝐗,𝐰 𝑝 𝐰
predictive distribution:
𝑝 t 𝐱, 𝐗, 𝐭 = න𝑝 t 𝐱,𝐰 𝑝 𝐰 𝐗, 𝐭 𝑑𝐰
posterior likelihood prior
likelihood posterior
deg: 1
deg: 2
N. Paulson et al.
𝐰 𝑙 samples using MCMC (Metropolis-Hastings algorithm)
Uncertainty Quantification of Phase Diagrams
REFERENCES
3200
3100
3000
2900
2800
2700
Liquidus [2]
Liquidus [1]
Solidus [1]
Solidus [2]
3200
UO2 PuO2
3100
3000
2900
2800
2700
Te
mp
era
ture
(K
)
Mol % PuO2
20 40 60 80
UO2 + PuO2
Liquid
* M. Stan and B. J. Reardon, CALPHAD, 27 (2003) 319-323.
[1] M. G. Adamson, E. A. Aitken, and R. W. Caputi, J. Nucl. Mater., 130 (1985) 349-365.
[2] T. D. Chikalla, J. Am. Ceram. Soc., 47 (1964) 309-309.
• Uncertainty in fuel thermo-mechanical properties is often >10%
• Uncertainty of chemical properties (free energy) can be 10-15 %
Example:
• Uncertainty quantification the UO2-PuO2phase diagram*. ΔT = ±50K, δc = 5%
• Bayesian analysis of 15 data sets (melting temperatures , transformation enthalpies, …).
• Optimization via a genetic algorithm.
15
Bayesian Analysis
M. Stan and B. Reardon, CALPHAD 27 (2003) 319
TM
B
M
A
M
B
M
A TTHHM ,,,
TNDDDD ,...,, 21
Model parameter vector
Data vector
Diagram line model m
B
m
A
S
B
S
A
S
m
B
m
A
L
B
L
A
L
TTHHTfx
TTHHTfx
,,,,
,,,,
N
i
ii
jj
j
MPMDP
MPMDPDM
1
|
||Bayes’ Theorem
The mean model j
jj
i
i DMMM |
Standard deviation l
llCSTD
Correlation matrix mmll
lmlm
CC
CR
Posterior covariance matrix T
i
T
i
i
i MMDMMMC ||
16
Evolutionary (Genetic) Algorithms
17
TM
B
M
A
M
B
M
A TTHHM ,,,
TNDDDD ,...,, 21
TM
B
M
A
M
B
M
A TTHHM ,,,
m
B
m
A
L
B
L
A
S
m
B
m
A
L
B
L
A
L
TTHHTfx
TTHHTfx
,,,,
,,,,
18
Uncertainty of Hf-O Lattice Parameters
19
Thermodynamics of Hf-O1
1D. Shin, R. Arroyave, Z.K. Liu, CALPHAD, 30 (2006) 375-386
Uncertainty of the Hf-O Phase Diagram
20
THERMODYNAMIC DATA
NIST ThermoData Engine (TDE)
• Requires
– Knowledge Base: A trusted data archive with full, machine-interpretable metadata
– Inference Engine: software developed via systematic, test-driven analysis of real data systems with a team of subject experts
• Delivers
– A virtual data expert backed by a well-curated library for engineers
CMOS Gate Stack: it is very smallNIST/TRC SOURCE
Data Archival System
as of 2017-01-05
System Type
Chemical Systems
Data Points
Pure 24,000 1,600,000
Binary 52,000 3,300,000
Ternary 15,000 1,100,000
Reactions 7,200 17,000
TDE - NIST SRD 103a/b
Uncertainty Evaluation
Simulation software
Direct data dissemination
Property Prediction
Critically Evaluated Data
22
OUTLOOK
The role of computation is changing
24
19901950 1970 2010
com
ple
xity
calculations
document
processing
intelligent
assistance
simulations
Impact on Science and Technology
25
MATERIAL GENOME INITIATIVECreate a multi-dimensional Periodic Table of
multi-component, multi-phase materials
Personal assistance
Immersive visualization
26
Augmented reality
Impact on You