Artificial Neural Network - Equations?

Let say I want to predict the strength of a composite material using ANN. Is it possible to return a series of equations in the output layer in ANN model? The reason I asked is simply because I want to know how the ANN correlates the independent variables in the input layer and hidden layers, also whether or not that relationship makes any sense in practice.

My gut tells me that it is not possible. Please correct me if I am wrong.

Answer 1

[JESUS DAVID ARIZA ROYETH]

Neural networks are very complex models including a lot of parameters, so a neural network that gives an equation as an answer doesn't make much sense, unless you have a few number of them, but the way a neural network works is a black box from wich you can obtain an answer based of an input. If you want to know how strong the relationship between the input and the output is you can use the pearson coefficient if your data is quantitative

[wesleynotwise]

Yes. I think the black box in the neural network is my biggest fear for using it in my case (input and output are quantitative), as the relationship of variable to the output is not clear to the user. For example, if Variable A (one of the input) is directly proportional to the dependent variable (the output), how to know if this relationship still holds in the ANN?

Answer 2

[Greg Heath]

The equation for a single hidden layer is

 yn = B1 + LW * tanh( B2 + IW*) *xn

where xn and tn are normalized to [-1,1].

weights IW1 IW2 and biases B1 B2 are

obtained directly fron the trained net.

 IW = net.IW , etc.

Hope this helps,

Thank you for formally accepting my answer.

Greg

[wesleynotwise]

I think if I need the final equation in the output layer, it is likely to be very long, bulky and chunky, and perhaps not meaningful for the output which is quantitative.

[Greg Heath]

y is obtained from yn by using the inverse part of MAPMINMAX.

 y = [(tmax - tmin)/2]*yn + [(tmax + tmin)/2]

Hope this helps.

Greg

Answer 3

[venu T]

Hi

I have run the ANN network and got the answer which is not what is predicted in the ANN I am here with giving all the data please help me

These are the W1 =[-0.098638 -1.478 -0.79801;

1.1991 -0.55255 1.9752;

0.097697 -1.2753 0.79466;

1.8374 0.95918 -0.0096127;

-1.7067 1.3765 1.1093]

W2[-0.43348 0.46505 -0.63726 -0.35395 0.3389]

B1[-3.3287;

-1.1953;

-0.17204;

0.92245;

3.515]

B2 [-0.63614]

Input X (1)= 200

X(2)=1.5

X(3)=5

Answer got for the values is 64.71233 in ANN run by the program

Tansig method

The equation I used from the weight and bais is this

Y=((-0.63614 + (-0.43348*(tansig(-0.098638*x(1)-1.478*x(2)-0.79801*x(3)-3.3287))) +(0.46505*(tansig(1.1991*x(1)-0.55255*x(2)+1.9752*x(3)-1.1953)))+(-0.63726*(tansig(0.097697*x(1)-1.27530*x(2)+0.79466*x(3)-0.17204) ))+(-0.35395* (tansig(1.8374*x(1)+0.95918*x(2)+0.0096127*x(3)+0.92245)))+(0.3389*(tansig(-1.7067*x(1)+1.3765*x(2)-1.1093*x(3)+3.515)))))

Ans is

Y =

-1.0677

which is not correct please hep

[Greg Heath]

It doesn't look like you took the automatic normalizations and denormalizations into account.

Greg

[Harshvardhan Solanki]

Hey can you help me with you example you have done...

[Jayferd John]

Hello, how about logsig function?

Answer 4

[Ali Zakeri]

hi my friends

i have some concetration kinetic data and calculated reaction rate and must curve fitting by neural network.

i trained my network but by ignored of great error , i should fit on a langmuir hinshelwood model and define K parameters. i need this equation for kinetic reaction to use in process software and CFD calculations.

thanks

clc

clear all

close all

Bz=xlsread('exdata.xlsx','O3:O62');

CHX=xlsread('exdata.xlsx','P3:P62');

H2=xlsread('exdata.xlsx','Q3:Q62');

r=xlsread('exdata.xlsx','R3:R62');

input=[Bz CHX H2 ];

% Solve an Input-Output Fitting problem with a Neural Network

% Script generated by Neural Fitting app

% Created 24-Apr-2021 19:15:59

%

% This script assumes these variables are defined:

%

% input - input data.

% r - target data.

x = input';

t = r';

% Choose a Training Function

% For a list of all training functions type: help nntrain

% 'trainlm' is usually fastest.

% 'trainbr' takes longer but may be better for challenging problems.

% 'trainscg' uses less memory. Suitable in low memory situations.

trainFcn = 'trainbr'; % Bayesian Regularization backpropagation.

% Create a Fitting Network

hiddenLayerSize = 20;

net = fitnet(hiddenLayerSize,trainFcn);

% Setup Division of Data for Training, Validation, Testing

net.divideParam.trainRatio = 70/100;

net.divideParam.valRatio = 15/100;

net.divideParam.testRatio = 15/100;

% Train the Network

[net,tr] = train(net,x,t);

% Test the Network

y = net(x);

e = gsubtract(t,y);

performance = perform(net,t,y)

% View the Network

view(net)

% Plots

% Uncomment these lines to enable various plots.

%figure, plotperform(tr)

%figure, plottrainstate(tr)

%figure, ploterrhist(e)

%figure, plotregression(t,y)

%figure, plotfit(net,x,t)

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Langmuir model %%%%%%%%%%%%%%%%%%%%%%%

function y=rate2(x)

global Pbz Ph2 Pchx r

k1=x(1);

k2=x(2);

Kbz=x(3);

Kh2=x(4);

y=((k1.*Pbz.*Ph2-k2.*Pchx)./(1+Kbz.*Pbz+Kh2.*Ph2))+r;

@JESUS DAVID ARIZA ROYETH

@Greg Heath