Reservoir properties from well logs using neural networks 1

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

List of Acronyms:

CM: committee machine

MLP: multilayer perceptron network

MLR: multiple linear regression

MNLR: multiple nonlinear regression

OLC: optimal linear combination

MNN: modular neural network

CPI log: computer processed interpretation log

MWD: measurement while drilling

LMS: least mean square

MLFF: multilayer feed forward

Summary and Introduction

The basic unit of a CM is a MLP whose optimum architecture and size of training dataset has been discovered by using synthetic data for each application.

All the programming has been doing using MATLAB programming language and different functions from the neural network toolbox.

ANNs are most likely to be superior to other methods under the following conditions:

(1)  The data is ‘fuzzy’.

(2)  The pattern is hidden.

(3)  The data exhibits non-linearity.

(4)  The data is chaotic.

A single MLP, when repeatedly trained on the same patterns, will reach different minima of the objective function each time and hence give a different set of neuron weights. A common approach therefore is to train many networks, and then select the one that yields the best generalization performance.

CM, where a number of individually trained networks are combined, in one way or another, improves the accuracy and robustness.

CM was demonstrated to improve porosity and permeability predictions from well logs using ensemble combination of neural networks rather than selecting the single best by trial and error.

Chapter 2: Neural Networks

Mathematically the function of the neuron k can be expressed by

y_k=φ(u_k+b_k), where u_k=∑_(j=1)^m▒〖w_kj x_j 〗.

Hardlimit function

φ(ν)={█(1 if υ≥0@ 0 if υ<0 )┤

A symmetrical hard limit function is described as 

φ(ν)={█(+1 if υ≥0@ -1 if υ<0 )┤

It is most commonly used in pattern recognition problems.

Linear function

φ(ν)=ν

This activation function is used in pattern recognition and in function approximation problems.

Sigmoid function

φ(ν)=1/(1+exp⁡(-aν))

This is the most common form of activation function used in the construction of multilayer networks that are trained using BP algorithm.

Tomorrow, I will read more of the dissertation.