why I obtained different result from NN sim and manual calculation using the weights

I use newff generate a very simple neural network with one input layer, one hidden layer (just one neuron for easy manual calculation), and one output layer like this:

>>x1=[-15:1:15];

>>y1=0.05*x1.^3-0.2*x1.^2-3*x1+20;

% the hidden layer and output layer both use "purelin" as transfer function. 

>>net=newff(x1,y1, 1, {'purelin'});

%training the network

>>net=train(net,x1,y1);

% I use 15 as test, the output from sim is 49.8170

>> output=sim(net, 15)

output =  49.8170

%%%%%%and I also manually calculate the output using 15 as input, 
%my calculation is like this ,  first, I obtained the input and layer weights, and the bias are as following:

>>IW=net.IW

IW =  
    [0.6972]
    []

>>LW=net.LW

LW = 
    []   []

      [0.5009]    []

>> b=net.b

b = 
    [-0.5228]
    [ 0.5173]

% the my calculation like this

>> (15*0.6972-0.5228)*0.5009+0.5173

ans =    5.4938

Why the "sim" and my manual calculation is different? Where is wrong? ??

Answer 1

[Bing]

Thanks for the answer.

But the "a" of purelin function in matlab is 1. This is what I got from matlab

>> purelin((purelin(15*0.6972-0.5228))*0.5009+0.5173)

ans =

    5.4938

[Thijs]

yeah just figured i was full of it sorry

Answer 2

[Thijs]

doing some matlab hackery i think i found the answer. both the inputs and the outputs of the neural network are mapped onto a minmax range, the inputs are mapped from -15 to 15 onto 0 to 1 (so 15 becomes 1). these mapped inputs are then passed through the neural network. purelin((purelin(1*0.6972-0.5228))*0.5009+0.5173)=0.8196. This output is then mapped from -1 to 1 onto ymin to ymax.

You can find ymin and ymax by entering: >>net.outputs{2}.range

conclusion: to manually duplicate the network performance:

    input=15;
    %find the input and output mapping
    input_range=net.inputs{1}.range;
    output_range=net.outputs{2}.range;
    %perform the mapping
    in=(input-input_range(1))/(input_range(2)-input_range(1));
    %pass the input through the net
    temp=(IW{1}*1+b{1})*LW{2,1}+b{2}
    %map the output
    y1=(temp--1)/2*(output_range(2)-output_range(1))+output_range(2)

Answer 3

[Bing]

your anweer to input=15 is right. I also test input=-15. maunally, I got 6.604 but sim generate -36.6091

>> temp=(IW{1}*0+b{1})*LW{2,1}+b{2}

temp =

    0.2554

 y1=(temp+1)/2*(output_range(2)-output_range(1))-148.75

y1 =

    6.6040

output=sim(net, -15)

output =

-36.6091

Answer 4

[hassan khatir]

use this function:

function y2=sim2(net,x)

xoffset=net.inputs{1}.processSettings{1}.xoffset;

gain=net.inputs{1}.processSettings{1}.gain;

ymin=net.inputs{1}.processSettings{1}.ymin;

w1 = net.IW{1}; % (10x6)

w2 = net.LW{2}; % (2x10)

b1 = net.b{1}; % (10x1)

b2 = net.b{2};

% Input 1

y1 = (x-xoffset).*gain+ymin;

% Layer 1

a1 = 2 ./ (1 + exp(-2*(repmat(b1,1,size(x,2)) + w1*y1))) - 1;

% output

outputs=repmat(b2,1,size(x,2)) + w2*a1;

gain = net.outputs{2}.processSettings{:}.gain;

ymin = net.outputs{2}.processSettings{:}.ymin;

xoffset = net.outputs{2}.processSettings{:}.xoffset;

y2 = (outputs-ymin)./gain + xoffset;

end