1. Modelleerimine ja Juhtimine Tehisnärvivõrgudega ---------------------------------------------- Identification and Control with artificial neural networks Eduard Petlenkov, Eduard Petlenkov, 2015

2. Artificial neuron Eduard Petlenkov, 2015 Weighted sum Nonlinear element Input vector: Vector of weight coeffitients: Weighted sum :

3. 3 Biological neuron and biological neural networks Eduard Petlenkov, 2015

4. Activation functions (1) Eduard Petlenkov, 2015 OUT=f(NET) Sigmoid functions are having an "S" shape (sigmoid curve) 1 Logistic function 2 Hyperbolic tangent

5. Types of artificial neural networks Structure: Feedforward Feedback internal feedback external feedback Training/ learning: Supervised learning Selflearning (unsupervised) inputs etalon Training criteria Eduard Petlenkov, 2015

6. How to use artificial neural networks Network Inputs Outputs Eduard Petlenkov, 2015 Data preprocessing Interpritation of results

7. Feedforward neural networks and multilayer perceptron Eduard Petlenkov, 2015 Feedforward networks are networks in which an output of a neuron can be connected only with an input of a next layer neuron. “from each to each” - Input layer - Output layer - Hidden layer - Weighting coefficients, where is the number of the neuron’s input - neuron’s number in the layer - number of the layer

8. Mathematical function of a two-layer perceptron Eduard Petlenkov, 2015 - Activation function of the hiddent layer neurons; - Activation function of the output layer neurons.