1. Radu Calin Dimitriu http://www.msm.cam.ac.uk/phase-trans/ Modelling the Hot-Strength of Creep-Resistant Ferritic Steels and Relationship to Creep-Rupture Data

2. Outline: - 1 st Part The Technique - 2 nd Part The Model

3. The Technique Neural networks in a Bayesian framework was employed to model the residual stress A neural network is a non-linear method of regression In neural networks data are fitted to a function in order to capture the complex relations that exist between the inputs and the output

4. Structure of a three layer neural network

5. Input variables C, Mn, Si, Ni, Cr, Mo, V, Co, B, N, O, … Thermomechanical processing of steel Subsequent heat treatment Steel properties Operating conditions...

6. The general form of the neural network y – represents the output w – represents the weights h – represents the hidden units θ – represents the bias x – represents the inputs i, j – represent subscripts

7. Hyperbolic Tangents

8. Problem Powerful non-linear regression methods → overfitting

9. Training and testing data sets

10. Advantage of neural networks in a Bayesian framework - the uncertainties are quantified - ant then transformed in error bars

11. Outline: - 1 st Part The Technique - 2 nd Part The Model

15. Significance

16. Predictions

17. Calculations

18. Correlation

19. ACKNOWLEDGEMENTS Many thanks to professor H.K.D.H. Bhadeshia The Department of Material Science and Metallurgy The University of Cambridge The European Commission under the Marie Curie Early Stage Research Training Programme