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