Bayesian Neural Networks and Irradiated Materials Properties

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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
z 0.8tanh(nx-2) tanh(x2-n) tanh(ny2)
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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Bayesian neural networks
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ANN design

• Data availability
• Dimensionality reduction?
• Over/under fitting

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Fitting error
(Number of hidden units)
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materials modelling
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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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Extrapolation to fusion?
Eurofer 97 yield stress
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Genetic algorithms
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Circle of life
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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