1. Bayesian Neural Networks and Irradiated Materials Properties Richard Kemp University of Cambridge

2. Neural networks (and why Bayes?) Modelling materials properties Genetic algorithms Materials Algorithm Project (MAP)

3. Problems Prediction of irradiation hardening Prediction of irradiation embrittlement Physical models?

4. A simple neural network

5. 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)

6. Why Bayes? Predict the next two numbers 2, 4, 6, 8 … ?

9. Bayesian neural networks

10. ANN design Data availability Dimensionality reduction? Over/under fitting

11. (Number of hidden units) Fitting error

12. materials modelling

13. 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

14. Inhomogeneous data

15. Testing of physics Saturation? Arrhenius (temperature-dependent) effects? Helium effects?

17. Model performance

18. Unirradiated Eurofer 97

19. Model performance Unirradiated and irradiated F82H

20. 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

24. Effects of chromium

25. Effects of phosphorus

26. Eurofer 97 yield stress Extrapolation to fusion?

27. Genetic algorithms

28. Circle of life Good Bad

29. 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

30. 0.13C-9Cr-2W-0.1Ta-0.15V-0.25Mn

31. Further issues Missing data –Confounding factors and correlations –Fusion-relevant irradiation? Genetic algorithm design –Satisfaction of multiple design criteria

33. Thanks to Geoff Cottrell and Harry Bhadeshia www.msm.cam.ac.uk/phase-trans