# Bayesian Neural Network

The software implemented for the neural networks with Bayesian framework is developed by Dr.Mackey. Bayesian formalism utilizes learning from data and uncertainty about the relationship being learned is represented by probability. We have prior belief about the data and this is expressed as probability distribution over the networks of weights. After seeing data our revised belief is expressed in terms of posterior distribution over network weights.

Database used to implement the neural network on titanium alloys developed by CAMM standard stereological procedures. The database used to model the network is normalized and divided into training data set and test data set. The training data set is used to train the network and test data set is used to test the network trained by training data set. Database is trained with different seeds and hidden nodes. The network which has minimum test error generalizes data better. This model which has the minimum test set error is used to predict the outputs. Mackay developed Bayesian frame work in which uncertainty in predictions are represented with error bars. These error bars are large when the data is sparse or locally noisy.

Advantages of Bayesian approach [2]:

- Complexity of the non linear models is automatically controlled.
- Reliability of the model prediction is represented with the error bars.
- Automatic relevance determination of the various input variables

**Applications of BNN in CAMM**

- Prediction of tensile properties of titanium alloys (alternate chemistry and base line composition, b-processed and a-b processed)
- Prediction of fracture toughness of b processed and a-b processed titanium alloys
- Prediction of fatigue life cycles of titanium alloys

Input variables:

- Volume fraction of total alpha
- Volume fraction of equiaxed alpha
- Size of the equiaxed alpha,
- Thickness of the alpha laths
- Grain boundary alpha
- Colony scale factor
- Composition (Aluminum, Vanadium, Oxygen , and Iron)