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Bayesian Neural Networks and Irradiated Materials Properties
Richard Kemp
University of Cambridge
Neural networks
(and why Bayes?)
Modelling materials properties
Genetic algorithms
Materials Algorithm Project (MAP)
Problems
• Prediction of irradiation hardening
• Prediction of irradiation embrittlement
• Physical models?
A simple neural network
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)
Why Bayes?
Predict the next two numbers
2, 4, 6, 8 … ?
0
2
4
6
8
10
12
14
0 2 4 6 8
Bayesian neural networks
ANN design
• Data availability
• Dimensionality reduction?
• Over/under fitting
(Number of hidden units)
Fit
ting
err
or
mate
rials
modelli
ng
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
Inhomogeneous data
Testing of physics
• Saturation?
• Arrhenius (temperature-dependent) effects?
• Helium effects?
Model performance
Model performance
Unirradiated Eurofer 97
Model performance
Unirradiated and irradiated F82H
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
Effects of chromium
Effects of phosphorus
Eurofer 97 yield stress
Extrapolation to fusion?
Genetic algorithms
Circle of life
Good
Bad
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
0.13C-9Cr-2W-0.1Ta-0.15V-0.25Mn
Further issues
• Missing data– Confounding factors and correlations– Fusion-relevant irradiation?
• Genetic algorithm design– Satisfaction of multiple design criteria
Thanks to Geoff Cottrell and Harry Bhadeshia
www.msm.cam.ac.uk/phase-trans