Is it possible to get expression/formula of Neural Network Toolbox?

Hi all,

I have a dependency P(x,y,z), thus, this is 4D function. My goal is to find an analytic expression of P as a function of x,y,z. I used Neural Network Toolbox to analyse my data (train, validated and so on). It seems that it gives very good fit with MSE of 1e-7 and R-square of 0.997. I am wondering if it is possible to get an expression where I could manually plug in x,y,z and get P values.

Best Regards Rokas,

[omar alrumayh]

Hi Rokas Bondzinskas,

I am trying to do the same. However, I could not get the same answer from the function that represent the NN.

x=randi([0 1],10000,1).';   %INPUT
y= (x./2);                            %OUTPUT
input= {x};
target= {y};
%--------------------------------------
net= fitnet(1);
net= train(net,input,target);
test= net(x);
view(net);
%---------------------------------------Here I want to get the weight and bias from the trained neural network
obtainedIW= cell2mat(net.IW);  %input weight
obtainedLW= cell2mat(net.LW);  %Layer weight
obtainedb= cell2mat(net.b);    %Biases

n=(obtainedIW.*0.5) + obtainedb(1);                    %My input here is 0.5
yCal= ((tansig(n)*obtainedLW +obtainedb(2))) ;

Answer 1

[Greg Heath]

 The equation for fitnet is

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

 where

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

Hope this helps.

Thank you for formally accepting my answer

Greg

[Rokas Bondzinskas]

Thank you for your answer. Now I am experimenting with 2D data just to see how NN toolbox works. Can you tell me what are the variables b, IW, LW related to the code below?

 % This script assumes these variables are defined:
 %
 %   x - input data.
 %   y - target data.

 x = x;
 t = y;

 % Choose a Training Function
trainFcn = 'trainlm';  % Levenberg-Marquardt

 % Create a Fitting Network
hiddenLayerSize = 10;
net = fitnet(hiddenLayerSize,trainFcn);

 % Choose Input and Output Pre/Post-Processing Functions
% For a list of all processing functions type: help nnprocess
net.input.processFcns = {'removeconstantrows','mapminmax'};
net.output.processFcns = {'removeconstantrows','mapminmax'};

 % Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
net.divideFcn = 'dividerand';  % Divide data randomly
net.divideMode = 'sample';  % Divide up every sample
net.divideParam.trainRatio = 90/100;
net.divideParam.valRatio = 5/100;
net.divideParam.testRatio = 5/100;

 % Choose a Performance Function
% For a list of all performance functions type: help nnperformance
net.performFcn = 'mse';  % Mean squared error

 % Choose Plot Functions
% For a list of all plot functions type: help nnplot
net.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...
  'plotregression', 'plotfit'};

 % Train the Network
[net,tr] = train(net,x,t);

 % Test the Network
y = net(x);
e = gsubtract(t,y);
performance = perform(net,t,y)

 % Recalculate Training, Validation and Test Performance
trainTargets = t .* tr.trainMask{1};
valTargets = t  .* tr.valMask{1};
testTargets = t  .* tr.testMask{1};
trainPerformance = perform(net,trainTargets,y)
valPerformance = perform(net,valTargets,y)
testPerformance = perform(net,testTargets,y)

Answer 2

[Greg Heath]

Eliminating statements that assign default values yields

 x   = input;
 t   = target;           % Reserve the variable name y for the output
 MSE00 = mean(var(t',1)) % Reference MSE

 net = fitnet;           % Uses defaults

% Train the Network

 [ net, tr, y0, e ] = train(net, x, t); % e = t-y0

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

% Test the Network

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

 diffy = max(abs(y-y0))

 performance = mse(e)

 % Recalculate Training, Validation and Test Performance
  trainTargets     = t .* tr.trainMask{1};
  valTargets       = t .* tr.valMask{1};
  testTargets      = t .* tr.testMask{1};
 trainPerformance = perform(net,trainTargets,y)
 valPerformance   = perform(net,valTargets,y)
 testPerformance  = perform(net,testTargets,y)

[Rokas Bondzinskas]

Okay. First of all, this code is not working. The error says: Error using + Matrix dimensions must agree.

Error in model (line 59)

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

Where did you get this kind of information about these coefficients and so on? I could use some literature to figure out how it works.