Reservoir properties from well logs using neural networks 2

Today, I read the dissertation ‘Reservoir Properties from Well Logs Using Neural Networks’. The reading parts are Chapter 2.

Summary

There are many types of learning algorithms that can be arranged into three main classes.

(i)             Supervised learning

The learning role is provided with proper inputs and outputs.

(ii)           Reinforcement learning

The algorithm is only given inputs and a grade.

(iii)         Unsupervised learning

The weights and biases are adjusted in response to network inputs only.

Perceptron Architecture: hardlimit transfer function

, one decision boundary .

The error e for k^th iteration is given by

and the adjustments to weights and bias is given by

, .

ADALINE Architecture：

, one decision boundary .

The algorithm will adjust the weights and biases of the ADALINE architecture by minimizing the mean square error between the targeted output and the computed output, defined by .

The adjustments for k^th iteration is given by

,

where  is a constant known as learning factor.

Both the ADALINE and perceptron have the same limitation that they could classify only linearly separable problems.

The LMS algorithm is optimal for a single neuron because the mean squared error surface for a single neuron has only one minimum point and constant curvature, providing a unique solution.

However, the LMS algorithm fails to produce a unique solution in multilayer networks.

The credit assignment problem was solved using the error back-propagation (BP) method which is generalization of the LMS algorithm.

Multilayer perceptron

Steepest descent algorithm: -∇F(a)。

LMBP algorithm:

The main drawback of the algorithm is the need for large memory and storage space of the free parameters in the computers.

Overfitting is the result of more hidden neurons than is actually necessary. However, if the number of hidden neurons is less than the optimum number then the network is unable to learn the correct input output mapping. Hence it is important to determine the optimum number of hidden neurons for a given problem.

Generalization is influenced by three factors:

The size of the training set

The architecture of the neural network

The complexity of the problem at hand

This problem can be solved in terms of the Vapnik-Chervonenkis (VC) dimension, which is a measure of the capacity or expressive power of the family of classification functions realized by a network. It can be defined as the maximum number of training examples for which a function can correctly classify all the patterns in a test dataset.

An accuracy of (1-e) needs the number of training samples to be w/e.

Tomorrow, I will read more of the dissertation.