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
z = 0.8[tanh(nx-2) + tanh(x 2 -n) + tanh(ny+2) + tanh(y 2 -n) + 1] (i.e. two inputs and four hidden units)
Why Bayes? Predict the next two numbers 2, 4, 6, 8 … ?
Bayesian neural networks
ANN design Data availability Dimensionality reduction? Over/under fitting
(Number of hidden units) Fitting error
materials modelling
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
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