How do I get the correct output from a fitnet artificial neural network?

I'm getting started with building an artificial neural network and testing it with a simple example (see code below).

I'm trying to get the artificial neural network (using fitnet) to predict that the function is y=a*5+b.*c+7*c. The neural network is successfully trained. However, when I try using the function:

y = b2 + LW*tanh(b1+IW*x)

followed by a reverse mapminmax, I do not obtain the correct value.

In the code below, I have tried defining

X = [0.5, 0.5, 0.5]

The output is (y2 is obtained by using the reverse mapminmax, y1 is using sim(net,x), and y1compare is the actual output target):

y2 = 9.5759

y1 = 6.2795

y1compare = 6.2500

My entire code is below:

clc
clear all

a=rand(1,1000);
b=rand(1,1000);
c=rand(1,1000);
n=rand(1,1000)*0.05;

y=a*5+b.*c+7*c+n;

I=[a; b; c];
O=y;

% Create network for curve fitting
hiddenLayerSize = 10; % Number of intermediate network neurons
net = fitnet(hiddenLayerSize);

% Setting the pre and post process data
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
net.outputs{2}.processFcns = {'removeconstantrows','mapminmax'};

% Setting the sample size
net.divideFcn = 'dividerand';  % Split random data
net.divideMode = 'sample';
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;

net=train(net,I,O);

% syms p q r real
% X = [p,q,r]';
X = [0.5 0.5 0.5]';

b1 = net.b{1}
b2 = net.b{2}
IW = net.IW{1,1};
LW = net.LW{2,1};

[tn, tsettings] = mapminmax(O);

tsettings

yn = b2 + LW * tanh(b2 + (IW * X))
y2 = mapminmax.reverse(yn,tsettings)

y1 = sim(net,X)
y1compare = X(1)*5+X(2).*X(3)+7*X(3)

Thanks in advance!

[Jeffrey Hung]

Found a code that works!

clc
clear all

% Create network for curve fitting
hiddenLayerSize = 4;      % Number of intermediate network neurons
net = fitnet(hiddenLayerSize);
WB  = getwb(net);          %  Only net.b{1} = zeros(10,1)is defined
rng(4151945);              % Initialize the RNG so that results can be duplicated

M = [1:1:10];
M = [M,M,M,M,M].*rand();
M = [M,M].*rand();
M = [M,M,M,M,M].*10;
M = [M,M].*10;

a=M.*rand().*2^rand()+5*rand()-5*rand();
b=M.*rand().*2^rand()+5*rand()-5*rand();
c=M.*rand().*2^rand()+5*rand()-5*rand();
n=rand(1,1000)*0.05;

y = 5*a + b.*c + 7*c + n;

x=[a; b; c];
t=y;

% Setting the sample size
net.divideFcn = 'dividerand';  % Split random data
net.divideMode = 'sample';
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;

net = train(net,x,t);

[xn, xsettings] = mapminmax(x);
[tn, tsettings] = mapminmax(t);

% syms p q r real
% X = [p,q,r]';
X = [22,25,21]'

x000 = mapminmax('apply',X,xsettings);

b1 = net.b{1};
b2 = net.b{2};
IW = net.IW{1,1};
LW = net.LW{2,1};

yn = b2 + LW * tanh(b1 + (IW * x000))
y2 = mapminmax.reverse(yn,tsettings)

y1 = sim(net,X)
y1compare = 5*X(1) + X(2)*X(3) + 7*X(3)

Answer 1

[Greg Heath]

1. Very often you have to use several choices of the random initial weights in order to get a good answer.

2. You forgot to take into account the input normalization.

Hope this helps.

Thank you for formally accepting my answer

Greg