bayesian neural networks and irradiated materials properties richard kemp university of cambridge
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Bayesian Neural Networks and Irradiated Materials Properties
Richard Kemp
University of Cambridge
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Neural networks
(and why Bayes?)
Modelling materials properties
Genetic algorithms
Materials Algorithm Project (MAP)
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Problems
• Prediction of irradiation hardening
• Prediction of irradiation embrittlement
• Physical models?
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A simple neural network
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A simple neural network
QuickTime™ and aAnimation decompressor
are needed to see this picture.
z = 0.8[tanh(nx-2) + tanh(x2-n) + tanh(ny+2) + tanh(y2-n) + 1]
(i.e. two inputs and four hidden units)
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Why Bayes?
Predict the next two numbers
2, 4, 6, 8 … ?
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0
2
4
6
8
10
12
14
0 2 4 6 8
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Bayesian neural networks
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ANN design
• Data availability
• Dimensionality reduction?
• Over/under fitting
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(Number of hidden units)
Fit
ting
err
or
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mate
rials
modelli
ng
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Modelling irradiation hardening
• No current strongly predictive model
• Data collected by Yamamoto et al and from European RAFM database
• ~1800 data up to 90 dpa– 36 input variables– No heat treatment information included
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Inhomogeneous data
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Testing of physics
• Saturation?
• Arrhenius (temperature-dependent) effects?
• Helium effects?
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Model performance
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Model performance
Unirradiated Eurofer 97
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Model performance
Unirradiated and irradiated F82H
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Modelling irradiation embrittlement
• Modelling Charpy ∆DBTT
• Miniaturised specimens for fusion materials research
• 461 data available– 26 input variables– Heat treatment data included– Reduced compositional information
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Effects of chromium
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Effects of phosphorus
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Eurofer 97 yield stress
Extrapolation to fusion?
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Genetic algorithms
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Circle of life
Good
Bad
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Genetic algorithms
• Cope with non-linear functions
• Cope with large numbers of variables efficiently
• Cope with modelling uncertainties
• Do not require knowledge of the function
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0.13C-9Cr-2W-0.1Ta-0.15V-0.25Mn
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Further issues
• Missing data– Confounding factors and correlations– Fusion-relevant irradiation?
• Genetic algorithm design– Satisfaction of multiple design criteria
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Thanks to Geoff Cottrell and Harry Bhadeshia
www.msm.cam.ac.uk/phase-trans