# Artificial Neural Networks in Materials Science (Part I)

Schematic draw of a neural network consisted a input layer (red), hidden layer (blue) and output layer (yellow). (Image from:  fdecomite via Flickr Creative Commons )

I wrote this post based on a project that a friend of mine (Iman Ghane Ghanad) and I performed together.

As material scientists time to time we are dealing with processes which require to model a complex system. Unfortunately most of the time finding and developing a suitable model is a very time consuming process that involves variety of parameters. On the other hand in order to mathematically model a system one needs to simplify a complex system by eliminating some parameters which in turn reduces the accuracy of the model. To overcome these issues, artificial intelligence based computational methods are introduced since many years ago.

Today, I aim to describe one of the most popular artificial intelligence method known as Artificial Neural Networks (ANNs). Lets consider human learning process. If we show three or four different cats to a child who never see any type of cat in his life, in the fifth attempt he can most probably distinguish a cat that is not shown to him before from a dog. The chance that the child makes a correct guess can be increased if he saw more and more cats in advance. This is exactly how a neural network model works, i.e. by feeding input and output data to the network it will learn the relationship that exist between different parameters of the system. Since the neural network modeling is a “black box” linking the input to output data, little prior knowledge of the physical and chemical mechanisms of the process under simulation is required, so this method can benefit the industry, as materials science or chemical industries are often have to solve their problems without full comprehension of the scientific background.

ANNs are consisted of highly interconnected structure similar to brain cells of human neural networks including large number of simple processing elements called neurons, which are arranged in different layers in the network. The NN, based on a statistical approach, has the potentiality to handle problems such as pattern classification, clustering, function approximation (modeling), forecasting, optimization, association and control in complex non-linear systems.

Neural network models usually assume that computation is distributed over several simple units called neurons, which are interconnected and operate in parallel. Through these interconnections, neurons send signals to each other and communicate. Each connection between two neurons has an associate value called weight which specifies the strength of the connection between the one neuron in a layer and another neuron in the next layer. Among different types of NNs, the multi-layer perceptron network is the most popular one in engineering applications. This type of network includes an input layer, one or more hidden layers and an output layer, all of them consisting of neurons and connections between them.

The training process involves with determining the weights that produce the optimum non-linear relationship of the predicted outputs over the entire training data set. An input vector is introduced into the input layer which propagates in the network toward the output layer. The difference between the computed output vector and the target vector is used to determine the weights in order to minimize the suitable error function.

In the future posts I am going to highlight some interesting materials science research projects which are used ANNs.

References:

[1] A. Fathi, A.A. Aghakouchak, Prediction of fatigue crack growth rate in welded tubular joints using neural network, International Journal of Fatigue 29 (2007) 261– 275.

[2] I.A. Basheer, M. Hajmeer, Artificial neural networks: fundamentals, computing, design, and application, Journal of Microbiological Methods 43 (2000) 3–31.

[3] Z. Guo, W. Sha, Modeling the correlation between processing parameters and properties of maraging steels using artificial neural network, Computational Materials Science 29 (2004) 12-28.

[4] Y. G. Du et. al, Effect of pH on metal solubilization from sewage sludge: a neural- net-based approach, Canadian journal of civil engineering 21 (1994) 728-735.

[5] Du, Tyagi, Sreekrishnan, Operational strategy for metal bioleaching based on pH measurements, Journal of Environmental Engineering 121 (1995) 527-535.

[6] D.T. Pham, P.T.N. Pham, Artificial intelligence in engineering, International Journal of Machine Tools & Manufacture 39 (1999) 937-949.