MATLAB: How to get the correct output from a fitnet artificial neural network

Question

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!

Answer 1

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